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1
López, Segovia Lucas. "Survival data analysis with heavy-censoring and long-term survivors." Doctoral thesis, Universitat Politècnica de Catalunya, 2014. http://hdl.handle.net/10803/276170.
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The research developed in this thesis has been motivated by two datasets, which are introduced in Chapter 2, one concerning the mortality of calves from birth to weaning while the other refers to survival of patients diagnosed with melanoma. In both cases the percentage of censoring is high, it is very likely to have immune individuals and proper analysis accounting for the possibility of a not negligible proportion of cured individuals has to be performed. Cure models are introduced in Chapter 3 together with the available software to perform the analysis, such as SAS, R and STATA, among others. We investigate the effect that heavy censoring could have on the estimation of the regression coefficients in the Cox model via a simulation study which considers several scenarios given by different sample sizes and censoring levels, results presented in Chapter 4. An application of a mixture cure model, which includes a Cox model for the survival part and a logistic model for the cure part of patients with melanoma, is described in Chapter 5. In addition, discussions about test for sufficient follow-up and censoring levels are also presented for this data. The data analysis is carried out using the macro in SAS: PSPMCM. The results show that patients with Sentinel Lymph Node (SLN): negative status to biopsy, Clark's level of invasion I-III, Histopathological of Malignant Melanoma subtype: Superficial Spreading Melanoma (SSM), younger than 46 years, and female, are more likely to be cured, whereas patients with melanoma in head and neck, Breslow's micrometric depth = 4mm and ulceration presents, are patients with increased risk of relapse. In particular, patients with Breslow's micrometric depth = 4mm are at higher risk for death. Furthermore, since mixture cure models do not have the property of proportional hazards for the entire population, they can be extended to non-mixture cure models by means of nonlinear transformation models as defined in Tsodikov (2003). An application of the extended hazard models is presented for the mortality of calves in Chapter 6. The methodology allows to get estimates for the cure rate as well as for genetic and environmental effects for each herd. A relevant feature of the non-mixture cure models is that they model, separately, factors which could affect survival from those affecting the cure model, making the interpretation of these models relatively easy. Results are shown in section 6.3.1, and were obtained using the library NLTM of the statistical package R. The short (mortality) and long term (survivors) effects are determined for each factors, as well as its statistical significance in each herd. For example in the herd 1, we find that calving month and difficulty at birth is the set of statistically significant factors for the nonsusceptible (long-term survivors) proportion. Calves born in the period march-august have lower probability of survive than those born in September-February; and the probability of survive is much lower for those that have difficulties at calving for herd 1. For herd 7 the effect of difficulty at calving is different as for herd 1, here only is significative the category strongly assisted. Calves that born from strongly assisted calving have lower probability of survive that calves from without assistance calving. Regarding short-term (mortality) effects, we only find statistically significant predictors in herd 7 where the risk of death of calves born from older mothers, hence with a longer reproductive life, is twice the risk of death of calves born from younger mothers. The obtained results have been compared with those coming from standard survival models. It is also included, a discussion about the likely erroneous conclusions that may yield from standard models, without taking into account the cure.La investigación desarrollada en esta tesis ha sido motivada por dos conjuntos de datos, introducidos en el capítulo 2, uno relacionado con la mortalidad de terneros desde el nacimiento hasta el destete, el otro con la supervivencia de los pacientes diagnosticados con melanoma. En ambos el porcentaje de censura es alto, la presencia de individuos inmunes es probable y un modelo que tome en cuenta esta proporción no despreciable de individuos inmunes será el más apropiado para su análisis. Los modelos de cura combinados se introducen en el capítulo 3 junto con el software disponible para realizar el análisis, tales como SAS, R y STATA, entre otros. Investigamos el efecto que una alta censura podría tener en la estimación de los coeficientes de regresión en el modelo de Cox, vía estudios de simulación para varios escenarios dado por diferentes tamaños de muestra y niveles de censura. Los resultados son presentados en el capítulo 4. La aplicación de un modelo de cura combinado, que incluye un modelo de Cox para la parte de supervivencia y un modelo logístico para la parte de cura de los pacientes con melanoma, se describe en el capítulo 5. Se presentan discusiones acerca de la prueba para el seguimiento suficiente y niveles de censura. El análisis se realiza mediante la macro de SAS: PSPMCM. Los resultados muestran que los pacientes con ganglios linfáticos Centinela (SLN): con biopsia negativa, nivel de Clark de invasión I-III, subtipo histopatológica de Melanoma maligno: con extensión superficial (SSM), menores de 46 años y mujer, tienen más probabilidades de ser curados, mientras que pacientes con melanoma en cabeza o cuello, Breslow micrométrico mayor o igual a 4mm de profundidad y ulceración presente, son pacientes con mayor riesgo de recaída. En particular, pacientes con Breslow micrométrico mayor o igual 4mm de profundidad están en riesgo de muerte. Por otra parte, como los modelos de cura combinados no tienen la propiedad de riesgos proporcionales para la población, estos pueden ser extendidos a modelos de cura no combinados via modelos de transformación no lineal definidos en Tsodikov (2003). Se presenta aplicación de los modelos de riesgo extendido para los datos de mortalidad de terneros en el capítulo 6. La metodología permite obtener estimaciones de la proporción de cura, así como los efectos de los factores genéticos y ambientales para cada rebaño. Una característica relevante de los modelos de cura no combinados es que modelan por separado, los factores que podrían afectar la supervivencia de aquellos que afectan el modelo de cura, y la interpretación es relativamente fácil. Los resultados se muestran en la sección 6.3.1 y se obtuvieron utilizando la librería NLTM del paquete estadístico R. Los efectos a corto plazo (mortalidad) y a largo plazo (sobrevivientes) son determinados para cada factor, así como su significación estadística en cada rebaño. Por ejemplo en el rebaño 1, encontramos que el mes del parto y la dificultad al nacer son estadísticamente significativos para la proporción no susceptible (sobrevivientes a largo plazo). Terneros nacidos en el periodo Marzo-Agosto tienen baja probabilidad de sobrevivir que aquellos nacidos en septiembre y febrero; y la probabilidad de sobrevivir es mucho menor para aquellos que tienen dificultades en el parto. Para el rebaño 7 el efecto de la dificultad al parto es diferente al rebaño 1, sólo es significativa la categoría fuertemente asistida. Los terneros de partos fuertemente asistidos tienen menor probabilidad de sobrevivir que aquellos sin asistencia. Respecto a los efectos a corto plazo (mortalidad), sólo encontramos predictores estadísticamente significativos en el rebaño 7 donde el riesgo de muerte de los nacidos de madres con una larga vida reproductiva, están al doble del riesgo de muerte que los nacidos de madres más jóvenes. Se incluye una discusión sobre las conclusiones erróneas que pueden obtenerse de los modelos estándar sino se toma en cuenta la cura.
2
Xiao, Tao. "Bayesian Threshold Regression for Current Status Data with Informative Censoring." The Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1438272888.
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Chiung-Yu, Huang. "Modeling and estimation for recurrent event data with dependent censoring." Available to US Hopkins community, 2002. http://wwwlib.umi.com/dissertations/dlnow/3048475.
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Raikou, Maria. "Estimating medical care costs : an examination under conditions of censoring." Thesis, City University London, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.269356.
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Younger, Jaime. "Goodness-of-Fit for Length-Biased Survival Data with Right-Censoring." Thesis, Université d'Ottawa / University of Ottawa, 2012. http://hdl.handle.net/10393/20670.
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Cross-sectional surveys are often used in epidemiological studies to identify subjects with a disease. When estimating the survival function from onset of disease, this sampling mechanism introduces bias, which must be accounted for. If the onset times of the disease are assumed to be coming from a stationary Poisson process, this bias, which is caused by the sampling of prevalent rather than incident cases, is termed length-bias. A one-sample Kolomogorov-Smirnov type of goodness-of-fit test for right-censored length-biased data is proposed and investigated with Weibull, log-normal and
log-logistic models. Algorithms detailing how to efficiently generate right-censored length-biased survival data of these parametric forms are given. Simulation is employed to assess the effects of sample size and censoring on the power of the test. Finally, the test is used to evaluate the goodness-of-fit using length-biased survival data of patients with dementia from the Canadian Study of Health and Aging.
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Chatora, Tinashe. "Joint models for nonlinear longitudinal profiles in the presence of informative censoring." Doctoral thesis, University of Cape Town, 2018. http://hdl.handle.net/11427/29564.
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Malaria is the parasitic disease which affects the most humans, with Plasmodium falciparum malaria being responsible for the majority of severe malaria and malaria related deaths. The asexual form of the parasite causes the signs and symptoms associated with malaria infection. The sexual form of the parasite, also known as a gametocyte, is the stage responsible for infectivity of the human host (patient) to the mosquito vector, and thus ongoing transmission of malaria and the spread of antimalarial drug resistance. Historically malaria therapeutic efficacy studies have focused mainly on the clearance of asexual parasites. However, malaria in a community can only be truly combated if a treatment program is implemented which is able to clear both asexual and sexual parasites effectively. In this thesis focus will be on the modeling of the key features of gametocytemia. Particular emphasis will be on the modeling of the time to gametocyte emergence, the density of gametocytes and the duration of gametocytemia. It is also of interest to investigate the impact of the administered treatment on the aforementioned features. Gametocyte data has several interesting features. Firstly, the distribution of gametocyte data is zero-inflated with a long tail to the right. The observed longitudinal gametocyte profile also has a nonlinear relationship with time. In addition, since most malaria intervention studies are not designed to optimally measure the evolution of the longitudinal gametocyte profile, there are very few observation points in the time period where the gametocyte profile is expected to peak. Gametocyte data collected from malaria intervention studies are also affected by informative censoring, which leads to incomplete gametocyte profiles. An example of informative censoring is when a patient who experiences treatment failure is “rescued", and withdrawn, from the study in order to receive alternative treatment. This patient can be considered to be in worse health as compared to the patients who remain in this study. There are also competing risks of exit from the study, as a patient can either experience treatment failure or be lost to follow-up. The above mentioned features of gametocyte data make it a statistically appealing dataset to analyze. In literature there are several modeling techniques which can be used to analyze individual features of the data. These techniques include standard survival models for modeling the time to gametocyte emergence and the duration of gametocytemia. The longitudinal nonlinear gametocyte profile would typically be modeled using nonlinear mixed effect models. These nonlinear models could then subsequently be extended to accommodate the zero-inflation in the data, by changing the underlying assumption around the distribution of the response variable. However, it is important to note that these standard techniques do not account for informative censoring. Failure to account for informative censoring leads to bias in parameter estimates. Joint modeling techniques can be used to account for informative censoring. The joint models applied in this thesis combined the longitudinal nonlinear gametocyte densities and the time to censoring due to either lost to follow up or treatment failure. The data analyzed in this thesis were collected from a series of clinical trials conducted be- tween 2002 and 2004 in Mozambique and the Mpumulanga province of South Africa. These trials were a part of the South East African Combination Antimalarial Therapy (SEACAT) evaluation of the phased introduction of combination anti-malarial therapy, nested in the Lubombo Spatial Development Initiative. The aim of these studies was primarily to measure the efficacy of sulfadoxine-pyrimethamine (SP) and a combination of artesunate and sulfadoxine-pyrimethamine (ACT), in eliminating asexual parasites in patients. The patients enrolled in the study had uncomplicated malaria, at a time of increasing resistance to sulfadoxine-pyrimethamine (SP) treatment. Blood samples were taken from patients during the course of 6 weeks on days 0, 1, 2, 3, 7, 14, 21, 28 and 42. Analysis of these blood samples provided longitudinal measurements for asexual 1 parasite densities, gametocyte densities, sulfadoxine drug concentrations and pyrimethamine drug concentrations. The gametocyte data collected in this study was initially analyzed using standard survival modeling techniques. Non-parametric Cox regression models and parametric survival models were applied to the data as part of this initial investigation. These models were used to investigate the factors which affected the time to gametocyte emergence. Subsequently, using the subset of the population which experienced gametocytemia, accelerated failure time models were applied to investigate the factors which affected the duration of gametocytemia. It is evident that the findings from the aforementioned duration investigation would only be able to provide valid duration estimates for patients who were detected to have gametocytemia. This work was extended to allow for population level duration estimates by incorporating the prevalence of gametocytemia into the estimation of duration, for generic patients with specific covariate patterns. The prevalence of gametocytemia was modeled using an underlying binomial distribution. The delta method was subsequently used to derive confidence intervals for the population level duration estimates which were associated with specific covariate patterns. An investigation into the factors affecting the early withdrawal of patients from the study was also conducted. Early exit from the study arose either through loss to follow-up (LTFU) or through treatment failure. The longitudinal gametocyte profile was modeled using joint modeling techniques. The resulting joint model used shared random effects to combine a Weibull survival model, describing the cause- specific hazards of patient exit from the study, with a nonlinear zero-adjusted gamma mixed effect model for the longitudinal gametocyte profile. This model was used to impute the incomplete gametocyte profiles, after adjusting for informative censoring. These imputed profiles were then used to estimate the duration of gametocytemia. It was found, in this thesis, that treatment had a very strong effect on the hazard of gametocyte emergence, density of gametocytes and the duration of gametocytemia. Patients who received a combination of sulfadoxine-pyrimethamine and artesunate were found to have significantly lower hazards of gametocyte emergence, lower predicted durations of gametocytemia and lower predicted longitudinal gametocyte densities as compared to patients who received sulfadoxine-pyrimethamine treatment only.
7
Zhang, Yue. "Bayesian Cox Models for Interval-Censored Survival Data." University of Cincinnati / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1479476510362603.
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Zhao, Yonggang. "The general linear model for censored data." The Ohio State University, 2003. http://rave.ohiolink.edu/etdc/view?acc_num=osu1054781042.
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Cheng, Peiyao. "Efficiency of an Unbalanced Design in Collecting Time to Event Data with Interval Censoring." Scholar Commons, 2016. http://scholarcommons.usf.edu/etd/6479.
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In longitudinal studies, the exact timing of an event often cannot be observed, and is usually detected at a subsequent visit, which is called interval censoring. Spacing of the visits is important when designing study with interval censored data. In a typical longitudinal study, the spacing of visits is usually the same across all subjects (balanced design). In this dissertation, I propose an unbalanced design: subjects at baseline are divided into a high risk group and a low risk group based on a risk factor, and the subjects in the high risk group are followed more frequently than those in the low risk group. Using a simple setting of a single binary exposure of interest (covariate) and exponentially distributed survival times, I derive the explicit formula for the asymptotic sampling variance of the estimate for the covariate effect. It shows that the asymptotic sampling variance can be simply reduced by increasing the number of examinations in the high risk group. The relative reduction tends to be greater when the baseline hazard rate in the high risk group is much higher than that in the low risk group and tends to be larger when the frequency of assessments in the low risk group is relatively sparse. Numeric simulations are also used to verify the asymptotic results in small samples and evaluate the efficiency of the unbalanced design in more complicated settings. Beyond comparing the asymptotic sampling variances, I further evaluate the power and empirical Type I error from unbalanced design and compare against the traditional balanced design. Data from a randomized clinical trial for type 1 diabetes are further used to test the performance of the proposed unbalanced design, and the parametric analyses of these data confirmed the findings from the theoretical and numerical studies.
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Chen, Li. "A comparison of methods in the presence of censored cost data under different censoring mechanisms." Thesis, University of Ottawa (Canada), 2005. http://hdl.handle.net/10393/26868.
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Several approaches have recently been proposed in order to derive an accurate estimate of mean costs given censoring. The aim of this study was to compare methods for estimating mean costs given censoring across different censoring mechanisms and censoring levels. 736 "complete" cases from the CHART study were used to form a "complete" set where the mean cost was known. This "complete" cohort was used to generate simulated data sets. The accuracy of methods was measured by comparing the difference between estimates and the "true" cost. The Uncensored cases method, Cox's PH model and the Weighted method CHU consistently gave better estimates of mean costs across different censoring mechanisms and censoring levels. Estimates of mean costs from all methods deteriorated as the censoring level increased. The Uncensored cases method, Cox's PH model and the Weighted method CHU may be appropriate methods for estimating mean costs given censoring in short-term studies.
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Yau, Crystal Cho Ying. "Empirical Likelihood Confidence Intervals for the Difference of Two Quantiles with Right Censoring." Digital Archive @ GSU, 2008. http://digitalarchive.gsu.edu/math_theses/64.
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In this thesis, we study two independent samples under right censoring. Using a smoothed empirical likelihood method, we investigate the difference of quantiles in the two samples and construct the pointwise confidence intervals from it as well. The empirical log-likelihood ratio is proposed and its asymptotic limit is shown as a chi-squared distribution. In the simulation studies, in terms of coverage accuracy and average length of confidence intervals, we compare the empirical likelihood and the normal approximation method. It is concluded that the empirical likelihood method has a better performance. At last, a real clinical trial data is used for the purpose of illustration. Numerical examples to illustrate the efficacy of the method are presented.
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Sakaguchi, Shosei. "Essays on Econometric Methods for Panel and Duration Data Analysis." Kyoto University, 2018. http://hdl.handle.net/2433/232205.
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Tawiah, Richard. "Frailty Models for the Analysis of Recurrent Event Data in Studies of Chronic Diseases." Thesis, Griffith University, 2019. http://hdl.handle.net/10072/389146.
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Biomedical studies of chronic diseases often involve the observations of multiple
failure times related to recurrent clinical events. Examples include, sequence of
epileptic seizures in neurology studies, repeated attacks of myocardial infarctions
in cardiovascular studies and multiple regional or metastatic recurrences in oncology
studies. It is usually plausible to assume that the multiple failure times on the
same individual are correlated (termed as intra-subject correlation). However, sometimes
data from such event history studies are further characterised by multilevel
structure (due to subjects nested within clusters by, for example, multi-institutional
study design), cure fraction and a dependent censoring mechanism such as death.
To model the intra-subject correlation explicitly, frailty (random e_ect) models are
often considered. Nevertheless, in the presence of multilevel structure, cure fraction
and dependent censoring, inferences considered in frailty models can be invalid, as
they do not allow for the existence of these features. This thesis aims to consider
multilevel structure, cure fraction and dependent censoring within frailty models
and develop more general frailty-type models and inferential methodologies for estimation
of model parameters and prediction of random effects.
In the first study of the thesis, a multilevel frailty model is proposed to provide regression
analysis of multilevel clustered recurrent event data from multi-institutional
(multi-centre) clinical trials. With the use of random effects with unobservable and
observable covariate design matrices, the proposed model extends the standard proportional
hazards Cox model to incorporate subject effect and institutional effects, the later which is separately specified as institutional baseline risk heterogeneity
and treatment-by-institution interaction. The attractive feature of the model is that
the inherent intra-subject correlation is modelled by a multivariate random effect
with a covariance structure driven by a first order autoregressive (AR(1)) process,
thus providing a more general multilevel survival model that allows the frailties at
subject-level to be time-varying. The model is formulated through the generalised
linear mixed model methodology, with estimation facilitated by maximum likelihood
and residual maximum likelihood techniques. Simulation studies are carried out to
evaluate the performance of the maximum likelihood and the residual maximum
likelihood estimators and to assess the impact of misspecifying random effects distribution
on the proposed inference. Data sets from multi-institutionalised studies
of rhDNase and recurrent urinary tract infections (UTI) are analysed for illustration
of the model.
With the second study, the concept of cure fraction is considered in the presence
of uncured subjects who can experience the event of interest repeatedly over time.
Two new models are developed within the framework of mixture cure models, by
assuming a multivariate time-varying frailty with an AR(1) correlation structure for
each uncured patient and addressing multilevel recurrent event data accrued from
multi-institutional clinical trials, using extra random effect terms to adjust for main
institution effect and treatment-by-institution interaction. To solve the difficulties in
parameter estimation due to these highly complex correlation structures, an efficient
estimation procedure is developed via the expectation-maximisation (EM) algorithm
based on residual maximum likelihood through the generalised linear mixed model
methodology. Simulation studies are presented to validate the performances of the
models. Data sets from a colorectal cancer study and rhDNase multi-institutional
clinical trials are analysed to exemplify the proposed models. The results demonstrate
a large positive AR(1) correlation among frailties across successive gap times,
indicating a constant frailty may not be realistic in some situations. Comparisons of findings with existing frailty models are discussed.
Thirdly, recognising the possibility of cure fraction and death induced dependent
censoring mechanism in some data sets, a bivariate joint frailty mixture cure model
is proposed for recurrent event data. The latency part of the model consists of
two intensity functions for the hazard rates of recurrent events and death, wherein
a bivariate frailty is introduced by means of the generalised linear mixed model
methodology to adjust for dependent censoring. The model allows covariates and
frailties in both the incidence and the latency parts and it further accounts for
the possibility of cure after each recurrence. It includes the joint frailty model and
other related models as special cases. An EM-type algorithm is developed to provide
residual maximum likelihood estimation of model parameters. Through simulation
studies, the performance of the model is investigated under different magnitudes of
dependent censoring. The model is applied to data sets from two colorectal cancer
studies to illustrate its practical value.
In general, the simulation studies indicate that the proposed models provide
appropriate estimates with only small biases. Aspects of the real data applications
demonstrate that the models provide results which are of practical importance
and easy to interpret and articulate in the clinical setting. Extension of the proposed
models to the context of interval-censored recurrent event data is discussed
extensively. Of specific interest is the consideration of cure fraction and multilevel
structure in the presence of interval-censored recurrent event data. An investigation
of the generalised linear mixed model methodology for estimation of semiparametric
accelerated failure time frailty model is emphasised. The development of multistate
frailty models for survival data from multimorbidity studies are also discussed.Thesis (PhD Doctorate)
School of Medicine
Griffith Health
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Barrett, James Edward. "Gaussian process regression models for the analysis of survival data with competing risks, interval censoring and high dimensionality." Thesis, King's College London (University of London), 2015. http://kclpure.kcl.ac.uk/portal/en/theses/gaussian-process-regression-models-for-the-analysis-of-survival-data-with-competing-risks-interval-censoring-and-high-dimensionality(fe3440e1-9766-4fc3-9d23-fe4af89483b5).html.
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We develop novel statistical methods for analysing biomedical survival data based on Gaussian process (GP) regression. GP regression provides a powerful non-parametric probabilistic method of relating inputs to outputs. We apply this to survival data which consist of time-to-event and covariate measurements. In the context of GP regression the covariates are regarded as `inputs' and the event times are the `outputs'. This allows for highly exible inference of non-linear relationships between covariates and event times. Many existing methods for analysing survival data, such as the ubiquitous Cox proportional hazards model, focus primarily on the hazard rate which is typically assumed to take some parametric or semi-parametric form. Our proposed model belongs to the class of accelerated failure time models and as such our focus is on directly characterising the relationship between the covariates and event times without any explicit assumptions on what form the hazard rates take. This provides a more direct route to connecting the covariates to survival outcomes with minimal assumptions. An application of our model to experimental data illustrates its usefulness. We then apply multiple output GP regression, which can handle multiple potentially correlated outputs for each input, to competing risks survival data where multiple event types can occur. In this case the multiple outputs correspond to the time-to-event for each risk. By tuning one of the model parameters we can control the extent to which the multiple outputs are dependent thus allowing the specication of correlated risks. However, the identiability problem, which states that it is not possible to infer whether risks are truly independent or otherwise on the basis of observed data, still holds. In spite of this fundamental limitation simulation studies suggest that in some cases assuming dependence can lead to more accurate predictions. The second part of this thesis is concerned with high dimensional survival data where there are a large number of covariates compared to relatively few individuals. This leads to the problem of overtting, where spurious relationships are inferred from the data. One strategy to tackle this problem is dimensionality reduction. The Gaussian process latent variable model (GPLVM) is a powerful method of extracting a low dimensional representation of high dimensional data. We extend the GPLVM to incorporate survival outcomes by combining the model with a Weibull proportional hazards model (WPHM). By reducing the ratio of covariates to samples we hope to diminish the eects of overtting. The combined GPLVM-WPHM model can also be used to combine several datasets by simultaneously expressing them in terms of the same low dimensional latent variables. We construct the Laplace approximation of the marginal likelihood and use this to determine the optimal number of latent variables, thereby allowing detection of intrinsic low dimensional structure. Results from both simulated and real data show a reduction in overtting and an increase in predictive accuracy after dimensionality reduction.
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Liu, Kang Ernest. "Food demand in urban China an empirical analysis using micro household data /." Columbus, OH : Ohio State University, 2003. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1044408843.
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Thesis (Ph. D.)--Ohio State University, 2003.Title from first page of PDF file. Document formatted into pages; contains xiii, 150 p.: ill. Includes abstract and vita. Advisor: Wern S. Chem, Dept. of Agricultural, Environmental, and Development Economics. Includes bibliographical references (p. 143-150).
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Wan, Lijie. "CONTINUOUS TIME MULTI-STATE MODELS FOR INTERVAL CENSORED DATA." UKnowledge, 2016. http://uknowledge.uky.edu/statistics_etds/19.
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Continuous-time multi-state models are widely used in modeling longitudinal data of disease processes with multiple transient states, yet the analysis is complex when subjects are observed periodically, resulting in interval censored data. Recently, most studies focused on modeling the true disease progression as a discrete time stationary Markov chain, and only a few studies have been carried out regarding non-homogenous multi-state models in the presence of interval-censored data. In this dissertation, several likelihood-based methodologies were proposed to deal with interval censored data in multi-state models.
Firstly, a continuous time version of a homogenous Markov multi-state model with backward transitions was proposed to handle uneven follow-up assessments or skipped visits, resulting in the interval censored data. Simulations were used to compare the performance of the proposed model with the traditional discrete time stationary Markov chain under different types of observation schemes. We applied these two methods to the well-known Nun study, a longitudinal study of 672 participants aged ≥ 75 years at baseline and followed longitudinally with up to ten cognitive assessments per participant.
Secondly, we constructed a non-homogenous Markov model for this type of panel data. The baseline intensity was assumed to be Weibull distributed to accommodate the non-homogenous property. The proportional hazards method was used to incorporate risk factors into the transition intensities. Simulation studies showed that the Weibull assumption does not affect the accuracy of the parameter estimates for the risk factors. We applied our model to data from the BRAiNS study, a longitudinal cohort of 531 subjects each cognitively intact at baseline.
Last, we presented a parametric method of fitting semi-Markov models based on Weibull transition intensities with interval censored cognitive data with death as a competing risk. We relaxed the Markov assumption and took interval censoring into account by integrating out all possible unobserved transitions. The proposed model also allowed for incorporating time-dependent covariates. We provided a goodness-of-fit assessment for the proposed model by the means of prevalence counts. To illustrate the methods, we applied our model to the BRAiNS study.
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El, Ghouch Anouar. "Nonparametric statistical inference for dependent censored data." Université catholique de Louvain, 2007. http://edoc.bib.ucl.ac.be:81/ETD-db/collection/available/BelnUcetd-09262007-123927/.
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A frequent problem that appears in practical survival data analysis is censoring. A censored observation occurs when the observation of the event time (duration or survival time) may be prevented by the occurrence of an earlier competing event (censoring time). Censoring may be due to different causes. For example, the loss of some subjects under study, the end of the follow-up period, drop out or the termination of the study and the limitation in the sensitivity of a measurement instrument. The literature about censored data focuses on the i.i.d. case. However in many real applications the data are collected sequentially in time or space and so the assumption of independence in such case does not hold. Here we only give some typical examples from the literature involving correlated data which are subject to censoring. In the clinical trials domain it frequently happens that the patients from the same hospital have correlated survival times due to unmeasured variables like the quality of the hospital equipment. Censored correlated data are also a common problem in the domain of environmental and spatial (geographical or ecological) statistics. In fact, due to the process being used in the data sampling procedure, e.g. the analytical equipment, only the measurements which exceed some thresholds, for example the method detection limits or the instrumental detection limits, can be included in the data analysis. Many other examples can also be found in other fields like econometrics and financial statistics. Observations on duration of unemployment e.g., may be right censored and are typically correlated. When the data are not independent and are subject to censoring, estimation and inference become more challenging mathematical problems with a wide area of applications. In this context, we propose here some new and flexible tools based on a nonparametric approach. More precisely, allowing dependence between individuals, our main contribution to this domain concerns the following aspects. First, we are interested in developing more suitable confidence intervals for a general class of functionals of a survival distribution via the empirical likelihood method. Secondly, we study the problem of conditional mean estimation using the local linear technique. Thirdly, we develop and study a new estimator of the conditional quantile function also based on the local linear method. In this dissertation, for each proposed method, asymptotic results like consistency and asymptotic normality are derived and the finite sample performance is evaluated in a simulation study.
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Can, Mutan Oya. "Statistical Inference From Complete And Incomplete Data." Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/3/12611531/index.pdf.
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Let X and Y be two random variables such that Y depends on X=x. This is a very common situation in many real life applications. The problem is to estimate the location and scale parameters in the marginal distributions of X and Y and the conditional distribution of Y given X=x. We are also interested in estimating the regression coefficient and the correlation coefficient. We have a cost constraint for observing X=x, the larger x is the more expensive it becomes. The allowable sample size n is governed by a pre-determined total cost. This can lead to a situation where some of the largest X=x observations cannot be observed (Type II censoring). Two general methods of estimation are available, the method of least squares and the method of maximum likelihood. For most non-normal distributions, however, the latter is analytically and computationally problematic. Instead, we use the method of modified maximum likelihood estimation which is known to be essentially as efficient as the maximum likelihood estimation. The method has a distinct advantage: It yields estimators which are explicit functions of sample observations and are, therefore, analytically and computationally straightforward. In this thesis specifically, the problem is to evaluate the effect of the largest order statistics x(i) (i>n-r) in a random sample of size n (i) on the mean E(X) and variance V(X) of X, (ii) on the cost of observing the x-observations, (iii) on the conditional mean E(Y|X=x) and variance V(Y|X=x) and (iv) on the regression coefficient. It is shown that unduly large x-observations have a detrimental effect on the allowable sample size and the estimators, both least squares and modified maximum likelihood. The advantage of not observing a few largest observations are evaluated. The distributions considered are Weibull, Generalized Logistic and the scaled Student&rsquo
s t.
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Svensson, Ingrid. "Estimation of wood fibre length distributions from censored mixture data." Doctoral thesis, Umeå : Department of Mathematics and Mathematical Statistics, Umeå Univ, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-1094.
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Zhao, Yanxing. "Parametric inference from window censored renewal process data." Columbus, Ohio : Ohio State University, 2006. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1164678679.
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Bouadoumou, Maxime K. "Jackknife Empirical Likelihood for the Accelerated Failure Time Model with Censored Data." Digital Archive @ GSU, 2011. http://digitalarchive.gsu.edu/math_theses/112.
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Kendall and Gehan estimating functions are used to estimate the regression parameter in accelerated failure time (AFT) model with censored observations. The accelerated failure time model is the preferred survival analysis method because it maintains a consistent association between the covariate and the survival time. The jackknife empirical likelihood method is used because it overcomes computation difficulty by circumventing the construction of the nonlinear constraint. Jackknife empirical likelihood turns the statistic of interest into a sample mean based on jackknife pseudo-values. U-statistic approach is used to construct the confidence intervals for the regression parameter. We conduct a simulation study to compare the Wald-type procedure, the empirical likelihood, and the jackknife empirical likelihood in terms of coverage probability and average length of confidence intervals. Jackknife empirical likelihood method has a better performance and overcomes the under-coverage problem of the Wald-type method. A real data is also used to illustrate the proposed methods.
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Prasad, Jonathan P. "Zero-Inflated Censored Regression Models: An Application with Episode of Care Data." BYU ScholarsArchive, 2009. https://scholarsarchive.byu.edu/etd/2226.
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The objective of this project is to fit a sequence of increasingly complex zero-inflated censored regression models to a known data set. It is quite common to find censored count data in statistical analyses of health-related data. Modeling such data while ignoring the censoring, zero-inflation, and overdispersion often results in biased parameter estimates. This project develops various regression models that can be used to predict a count response variable that is affected by various predictor variables. The regression parameters are estimated with Bayesian analysis using a Markov chain Monte Carlo (MCMC) algorithm. The tests for model adequacy are discussed and the models are applied to an observed data set.
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Wang, Guoshen. "Analysis of Additive Risk Model with High Dimensional Covariates Using Correlation Principal Component Regression." Digital Archive @ GSU, 2008. http://digitalarchive.gsu.edu/math_theses/51.
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One problem of interest is to relate genes to survival outcomes of patients for the purpose of building regression models to predict future patients¡¯ survival based on their gene expression data. Applying semeparametric additive risk model of survival analysis, this thesis proposes a new approach to conduct the analysis of gene expression data with the focus on model¡¯s predictive ability. The method modifies the correlation principal component regression to handle the censoring problem of survival data. Also, we employ the time dependent AUC and RMSEP to assess how well the model predicts the survival time. Furthermore, the proposed method is able to identify significant genes which are related to the disease. Finally, this proposed approach is illustrated by simulation data set, the diffuse large B-cell lymphoma (DLBCL) data set, and breast cancer data set. The results show that the model fits both of the data sets very well.
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Bagdonavičius, Vilijandas B., Ruta Levuliene, Mikhail S. Nikulin, and Olga Zdorova-Cheminade. "Tests for homogeneity of survival distributions against non-location alternatives and analysis of the gastric cancer data." Universität Potsdam, 2004. http://opus.kobv.de/ubp/volltexte/2011/5152/.
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The two and k-sample tests of equality of the survival distributions against
the alternatives including cross-effects of survival functions, proportional and monotone hazard ratios, are given for the right censored data. The asymptotic power against approaching alternatives is investigated. The tests are applied to the well known chemio and radio therapy data of the Gastrointestinal Tumor Study Group. The P-values for both proposed tests are much smaller then in the case of other known tests. Differently from the test of Stablein and Koutrouvelis the new tests can be applied not only for singly but also to randomly censored data.
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TASSISTRO, ELENA. "Adverse events in survival data: from clinical questions to methods for statistical analysis." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2022. http://hdl.handle.net/10281/365520.
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Nello studio di un nuovo trattamento con un tempo di sopravvivenza come outcome, l’insuccesso può essere definito in modo da includere un evento avverso serio (AE) tra gli endpoint tipicamente considerati, come ad esempio ricaduta o progressione. Questi eventi si comportano come rischi competitivi, dove l’occorrenza di una ricaduta come primo evento e il conseguente cambio di trattamento escludono la possibilità di osservare AE legati al trattamento stesso.
L’analisi degli AE può essere affrontata mediante due diversi approcci:
1. descrizione dell’occorrenza osservata di AE come primo evento: la capacità del trattamento di proteggere dalla ricaduta ha un impatto sulla possibilità di osservare AE dovuti all’azione dei rischi competitivi.
2. Valutazione dell’impatto del trattamento sullo sviluppo di AE in pazienti che sono liberi da ricaduta nel tempo: si dovrebbe considerare l’occorrenza di AE come se la ricaduta non escludesse la possibilità di osservare AE legati al trattamento stesso.
Nella prima parte della tesi abbiamo rivisto la strategia di analisi per i due approcci partendo dal tipo di domanda clinica di interesse. Quindi abbiamo identificato le quantità più adatte e i possibili stimatori (proporzione grezza, tasso di AE, incidenza grezza, stimatori smoothed di Kaplan-Meier e di Aalen-Nelson per l’hazard causa-specifico) e li abbiamo valutati relativamente a due aspetti, solitamente necessari in un contesto di sopravvivenza:
(i) Lo stimatore dovrebbe tenere in considerazione la presenza di censura a destra
(ii) La quantità teorica e lo stimatore dovrebbero essere funzioni del tempo.
Nella seconda parte della tesi abbiamo proposto metodi alternativi, come modelli di regressione, curve di Kaplan-Meier stratificate e inverse probability of censoring weighting, per rilassare l’assunto di indipendenza tra i tempi potenziali di AE e di ricaduta. Abbiamo mostrato attraverso simulazioni che questi metodi superano i problemi legati all’uso dei classici stimatori per i rischi competitivi nel secondo approccio. In particolare, abbiamo simulato differenti scenari fissando l’hazard di ricaduta indipendente da due covariate binarie, dipendente da X1, dipendente da entrambe le covariate X1 e X2 anche attraverso la loro interazione. Abbiamo mostrato che si può gestire la selezione dei pazienti, e quindi ottenere indipendenza condizionata tra i tempi potenziali, aggiustando per tutte le covariate osservate. Si noti che anche aggiustando solo per poche covariate osservate come nella realtà a causa di covariate non misurate, si ottengono stime meno distorte rispetto a quelle che si ottengono dal Kaplan-Meier naive censurando per la ricaduta. Infatti, abbiamo dimostrato che la stima ottenuta con il Kaplan-Meier naive è sempre distorta a meno che l’hazard di ricaduta sia indipendente dalle covariate. In un ipotetico scenario dove tutte le covariate sono osservate, la stima della sopravvivenza media pesata ottenuta sia non parametricamente sia dal modello di Cox e la stima della sopravvivenza dall’inverse probability of censoring weighting dovrebbero essere non distorte (metodi applicati aggiustando per entrambe le covariate). Inoltre, segnaliamo che con l’inverse probability of censoring weighting si possono ottenere stime distorte quando tutte le possibili interazioni tra le covariate osservate non sono incluse nel modello per stimare i pesi. Tuttavia, l’inserimento dell’interazione non è necessario quando si usa il modello di Cox pesato, poiché condizionatamente alle covariate osservate, questo modello è robusto nella stima della sopravvivenza media. Ciò nonostante, una limitazione nell’uso del metodo della sopravvivenza media pesata è dato dal fatto che può essere utilizzato solo in presenza di covariate binarie (o categoriche), poiché se la covariata è continua non è possibile identificare i sottogruppi entro cui la funzione di sopravvivenza è stimata.When studying a novel treatment with a survival time outcome, failure can be defined to include a serious adverse event (AE) among the endpoints typically considered, for instance relapse or progression. These events act as competing risks, where the occurrence of relapse as first event and the subsequent treatment change exclude the possibility of observing AE related to the treatment itself. In principle, the analysis of AE could be tackled by two different approaches: 1. the description of the observed occurrence of AE as first event: treatment ability to protect from relapse has an impact on the chance of observing AE due to the competing risks action. 2. the assessment of the treatment impact on the development of AE in patients who are relapse free in time: one should consider the occurrence of AE as if relapse would not exclude the possibility of observing AE related to the treatment itself. In the first part of the thesis we reviewed the strategy of analysis for the two approaches starting from the type of clinical question of interest. Then we identified the suitable quantities and possible estimators (crude proportion, AE rate, crude incidence, Kaplan-Meier and Aalen-Nelson smoothed estimators of the cause-specific hazard) and judge them according to two features, usually needed in a survival context: (i) the estimator should address for the presence of right censoring (ii) the theoretical quantity and estimator should be functions of time. In the second part of the thesis we proposed alternative methods, such as regression models, stratified Kaplan-Meier curves and inverse probability of censoring weighting, to relax the assumption of independence between the potential time to AE and the potential time to relapse. We showed through simulations that these methods overcome the problems related to the use of standard competing risks estimators in the second approach. In particular, we simulated different scenarios setting the hazard of relapse independent from two binary covariates, dependent from X1 only, dependent from both covariates X1 and X2, also through their interaction. We showed that one can handle patients’ selection, and thus obtain conditional independence between the two potential times, adjusting for all the observed covariates. Of note, even adjusting only for few observed covariates as in the reality due to unmeasured covariates, gives less biased estimates with respect to the estimate obtained from the naive Kaplan-Meier censoring by relapse. In fact, we proved that the estimate obtained from the naive Kaplan-Meier is always biased unless the hazard of relapse is independent from the covariates values. In an hypothetical scenario where all the covariates are observed, the weighted average survival estimate obtained either non parametrically or by the Cox model and the survival estimate from the inverse probability of censoring weighting would be unbiased (methods applied adjusting for both covariates). In addition, we point out that with the inverse probability of censoring weighting method one could obtained biased estimates when all the possible interactions between the observed covariates are not included in the model to estimate the weights. However, the inclusion of the interaction is not needed when the weighted Cox model is used, since conditional on the observed covariates, this model is robust in estimating the average survival. Nevertheless, a limitation in the use of the weighted average survival method is given by the fact that it may be applied only in the presence of binary (or categorical) covariates, since if the covariate is continuous it is impossible to identify the subgroups in which the survival function is estimated.
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Jin, Yan. "Bayesian Solution to the Analysis of Data with Values below the Limit of Detection (LOD)." University of Cincinnati / OhioLINK, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1227293204.
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Arnqvist, Per. "Functional clustering methods and marital fertility modelling." Doctoral thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-130734.
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This thesis consists of two parts.The first part considers further development of a model used for marital fertility, the Coale-Trussell's fertility model, which is based on age-specific fertility rates. A new model is suggested using individual fertility data and a waiting time after pregnancies. The model is named the waiting model and can be understood as an alternating renewal process with age-specific intensities. Due to the complicated form of the waiting model and the way data is presented, as given in the United Nation Demographic Year Book 1965, a normal approximation is suggested together with a normal approximation of the mean and variance of the number of births per summarized interval. A further refinement of the model was then introduced to allow for left truncated and censored individual data, summarized as table data. The waiting model suggested gives better understanding of marital fertility and by a simulation study it is shown that the waiting model outperforms the Coale-Trussell model when it comes to estimating the fertility intensity and to predict the mean and variance of the number of births for a population. The second part of the thesis focus on developing functional clustering methods.The methods are motivated by and applied to varved (annually laminated) sediment data from lake Kassj\"on in northern Sweden. The rich but complex information (with respect to climate) in the varves, including the shapes of the seasonal patterns, the varying varve thickness, and the non-linear sediment accumulation rates makes it non-trivial to cluster the varves. Functional representations, smoothing and alignment are functional data tools used to make the seasonal patterns comparable.Functional clustering is used to group the seasonal patterns into different types, which can be associated with different weather conditions. A new non-parametric functional clustering method is suggested, the Bagging Voronoi K-mediod Alignment algorithm, (BVKMA), which simultaneously clusters and aligns spatially dependent curves. BVKMA is used on the varved lake sediment, to infer on climate, defined as frequencies of different weather types, over longer time periods. Furthermore, a functional model-based clustering method is proposed that clusters subjects for which both functional data and covariates are observed, allowing different covariance structures in the different clusters. The model extends a model-based functional clustering method proposed by James and Suger (2003). An EM algorithm is derived to estimate the parameters of the model.
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Zhao, Meng. "Treatment Comparison in Biomedical Studies Using Survival Function." Digital Archive @ GSU, 2011. http://digitalarchive.gsu.edu/math_diss/4.
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In the dissertation, we study the statistical evaluation of treatment comparisons by evaluating the relative comparison of survival experiences between two treatment groups. We construct confidence interval and simultaneous confidence bands for the ratio and odds ratio of two survival functions through both parametric and nonparametric approaches.We first construct empirical likelihood confidence interval and simultaneous confidence bands for the odds ratio of two survival functions to address small sample efficacy and sufficiency. The empirical log-likelihood ratio is developed, and the corresponding asymptotic distribution is derived. Simulation studies show that the proposed empirical likelihood band has outperformed the normal approximation band in small sample size cases in the sense that it yields closer coverage probabilities to chosen nominal levels.Furthermore, in order to incorporate prognostic factors for the adjustment of survival functions in the comparison, we construct simultaneous confidence bands for the ratio and odds ratio of survival functions based on both the Cox model and the additive risk model. We develop simultaneous confidence bands by approximating the limiting distribution of cumulative hazard functions by zero-mean Gaussian processes whose distributions can be generated through Monte Carlo simulations. Simulation studies are conducted to evaluate the performance for proposed models. Real applications on published clinical trial data sets are also studied for further illustration purposes.In the end, the population attributable fraction function is studied to measure the impact of risk factors on disease incidence in the population. We develop semiparametric estimation of attributable fraction functions for cohort studies with potentially censored event time under the additive risk model.
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Bhering, Felipe Lunardi. "Confiabilidade em sistemas coerentes: um modelo bayesiano Weibull." Universidade de São Paulo, 2013. http://www.teses.usp.br/teses/disponiveis/45/45133/tde-01122013-155316/.
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O principal objetivo desse trabalho é introduzir um modelo geral bayesiano Weibull hierárquico para dados censurados que estima a função de confiabilidade de cada componente para sistemas de confiabilidade coerentes. São introduzidos formas de estimação mais sólidas, sem a inserção de estimativas médias nas funções de confiabilidade (estimador plug-in). Através desse modelo, são expostos e solucionados exemplos na área de confiabilidade como sistemas em série, sistemas em paralelo, sistemas k-de-n, sistemas bridge e um estudo clínico com dados censurados intervalares. As soluções consideram que as componentes tem diferentes distribuições, e nesse caso, o sistema bridge ainda não havia solução na literatura. O modelo construído é geral e pode ser utilizado para qualquer sistema coerente e não apenas para dados da área de confiabilidade, como também na área de sobrevivência, dentre outros. Diversas simulações com componentes com diferentes proporções de censura, distintas médias, três tipos de distribuições e tamanhos de amostra foram feitas em todos os sistemas para avaliar a eficácia do modelo.The main purpose of this work is to introduce a general bayesian Weibull hierarchical model for censored data which estimates each reliability components function from coherent systems. Its introduced estimation procedures which do not consider plug-in estimators. Also, its exposed and solved with this model examples in reliability area such as series systems, parallel systems, k-out-of-n systems, bridge systems and a clinical study with interval censoring data. The problem of bridge system hadnt a solution before for the case of each component with different distribution. Actually, this model is general and can be used to analyse any kind of coherent system and censored data, not only reliability ones, but also survival data and others. Several components simulations with different censored proportions, distinct means, three kinds of distributions and sample size were made in all systems to evaluate model efficiency.
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Santos, Daiane de Souza. "Comparações múltiplas para dados censurados." Universidade de São Paulo, 2013. http://www.teses.usp.br/teses/disponiveis/55/55134/tde-11072013-143209/.
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O objetivo deste trabalho é estudar a performance de alguns métodos de comparações múltiplas (MCMs) que ajustam o valor-p quando as estatísticas empregadas nos testes são a log-rank e a Cramér-von Mises, ambas não paramétricas e com estrutura de dependência. A vantagem dos MCMs que ajustam o valor-p é que eles controlam as taxas de erro tipo I e tipo II para cada hipótese, afim de atingir um poder estatístico elevado, mantendo a taxa de erro da família dos testes (FWER) menor ou igual ao nível de significância escolhido. Trabalhamos com o procedimento clássico de Bonferroni e com outros métodos vistos como seu melhoramento, com especial atenção a certos procedimentos derivados do método de Simes que permitem realizar inferências sob as hipóteses individuais. Foi verificado teoricamente que a estatística log-rank pertence à classe multivariada totalmente positiva de ordem 2 (\'MTP IND. 2\'), uma vez que o método de Simes garante o controle da FWER quando as estatísticas dependentes assumem esta condição. O controle da FWER empregando a estatística de Cramér-von Mises foi observado apenas por meio de simulações. Os MCMs foram analisados através de estudos computacionais em modelos discretos e contínuos sob censura com foco no problema de comparar um tratamento versus controleThe aim of this work is to study the performance of some Multiple Comparison Methods (MCMs) that adjust the p-value when the log-rank-type and Cramér-von Mises statistics are used, both nonparametric and with dependency structure. The advantage of these methods is that they control the error rates of type I and type II for each hypothesis in order to achieve high statistical power while keeping the Family Wise Error Rate (FWER) lower or equal than a given significance level. The classical Bonferroni procedure is used as well as others seen as its improvement, with special attention to certain procedures derived from Simes\' method for making inferences on individual hypothesis. It is theoretically proved that the weighted Log-Rank statistics belongs to the multivariate totally positive of order 2 (\'MTP IND. 2\') class, which is needed in order to apply Simes\' method, that guarantees control of the FWER of dependent statistics in this case. The control of the FWER when the Cramér-von Mises statistics is used is only veried by means of computational simulations. The MCMs are also analyzed by means of computational experiments with discrete and continuous data under censoring with focus on the problem of comparisons of treatment versus a control
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Santos, Carlos Aparecido dos. "Dados de sobrevivência multivariados na presença de covariáveis e observações censuradas: uma abordagem bayesiana." Universidade Federal de São Carlos, 2010. https://repositorio.ufscar.br/handle/ufscar/4483.
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Previous issue date: 2010-03-04In this work, we introduce a Bayesian Analysis for survival multivariate data in the presence of a covariate vector and censored observations. Different frailties or latent variables are considered to capture the correlation among the survival times for the same individual. We also introduce a Bayesian analysis for some of the most popular bivariate exponential distributions introduced in the literature. A Bayesian analysis is also introduced for the Block & Basu bivariate exponential distribution using Markov Chain Monte Carlo (MCMC) methods and considering lifetimes in presence of covariates and censored data. In another topic, we introduce a Bayesian Analysis for bivariate lifetime data in the presence of covariates and censoring data assuming different bivariate Weibull distributions derived from some existing copula functions. A great computational simplification to simulate samples for the joint posterior distribution is obtained using the WinBUGS software. Numerical illustrations are introduced considering real data sets considering every proposed methodology.
Nesta tese introduzimos uma an´alise Bayesiana para dados de sobreviv encia multivariados, na presen¸ca de um vetor de covari´aveis e observa¸c oes censuradas. Diferentes fragilidades ou vari´aveis latentes s ao consideradas para capturar a correla¸c ao existente entre os tempos de sobreviv encia, para o mesmo indiv´ıduo. Tamb´em apresentamos uma an´alise Bayesiana para algumas das mais populares distribui¸c oes exponenciais bivariadas introduzidas na literatura. Uma an´alise Bayesiana tamb´em ´e introduzida para a distribui¸c ao exponencial bivariada de Block & Basu, usando m´etodos MCMC (Monte Carlo em Cadeias de Markov) e considerando os tempos de sobreviv encia na presen¸ca de covari´aveis e dados censurados. Em outro t´opico, introduzimos uma an´alise Bayesiana para dados de sobreviv encia bivariados na presen¸ca de covari´aveis e observa¸c oes censuradas, assumindo diferentes distribui¸c oes bivariadas Weibull derivadas de algumas fun¸c oes c´opulas existentes. Uma grande simplifica¸c ao computacional para simular amostras da distribui¸c ao a posteriori conjunta de interesse ´e obtida usando o software WinBUGS. Ilustra¸c oes num´ericas s ao introduzidas considerando conjunto de dados reais, para cada uma das metodologias propostas.
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KALLAS, KASSEM. "A Game-Theoretic Approach for Adversarial Information Fusion in Distributed Sensor Networks." Doctoral thesis, Università di Siena, 2017. http://hdl.handle.net/11365/1005735.
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Every day we share our personal information through digital systems which are constantly exposed to threats. For this reason, security-oriented disciplines of signal processing have received increasing attention in the last decades: multimedia forensics, digital watermarking, biometrics, network monitoring, steganography and steganalysis are just a few examples. Even though each of these fields has its own peculiarities, they all have to deal with a common problem: the presence of one or more adversaries aiming at making the system fail. Adversarial Signal Processing lays the basis of a general theory that takes into account the impact that the presence of an adversary has on the design of effective signal processing tools.
By focusing on the application side of Adversarial Signal Processing, namely adversarial information fusion in distributed sensor networks, and adopting a game-theoretic approach, this thesis contributes to the above mission by addressing four issues. First, we address decision fusion in distributed sensor networks by developing a novel soft isolation defense scheme that protects the
network from adversaries, specifically, Byzantines. Second, we develop an optimum decision fusion strategy in the presence of Byzantines. In the next step, we propose a technique to reduce the complexity of the optimum fusion by relying on a novel nearly-optimum message passing algorithm based on factor graphs. Finally, we introduce a defense mechanism to protect decentralized networks running consensus algorithm against data falsification attacks.
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Pantoja, Galicia Norberto. "Interval Censoring and Longitudinal Survey Data." Thesis, 2007. http://hdl.handle.net/10012/3224.
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Being able to explore a relationship between two life events is of great interest to scientists from different disciplines. Some issues of particular concern are, for example, the connection between smoking cessation and pregnancy (Thompson and Pantoja-Galicia 2003), the interrelation between entry into marriage for individuals in a consensual union and first pregnancy (Blossfeld and Mills 2003), and the association between job loss and divorce (Charles and Stephens 2004, Huang 2003 and Yeung and Hofferth 1998).
Establishing causation in observational studies is seldom possible. Nevertheless, if one of two events tends to precede the other closely in time, a causal interpretation of an association between these events can be more plausible. The role of longitudinal surveys is crucial, then, since they allow sequences of events for individuals to be observed. Thompson and Pantoja-Galicia (2003) discuss in this context several notions of temporal association and ordering, and propose an approach to investigate a possible relationship between two lifetime events.
In longitudinal surveys individuals might be asked questions of particular interest about two specific lifetime events. Therefore the joint distribution might be advantageous for answering questions of particular importance. In follow-up studies, however, it is possible that interval censored data may arise due to several reasons. For example, actual dates of events might not have been recorded, or are missing, for a subset of (or all) the sampled population, and can be established only to within specified intervals.
Along with the notions of temporal association and ordering, Thompson and Pantoja-Galicia (2003) also discuss the concept of one type of event "triggering" another. In addition they outline the construction of tests for these temporal relationships.
The aim of this thesis is to implement some of these notions using interval censored data from longitudinal complex surveys. Therefore, we present some proposed tools that may be used for this purpose.
This dissertation is divided in five chapters, the first chapter presents a notion of a temporal relationship along with a formal nonparametric test. The mechanisms of right censoring, interval censoring and left truncation are also overviewed. Issues on complex surveys designs are discussed at the end of this chapter.
For the remaining chapters of the thesis, we note that the corresponding formal nonparametric test requires estimation of a joint density, therefore in the second chapter a nonparametric approach for bivariate density estimation with interval censored survey data is provided. The third chapter is devoted to model shorter term triggering using complex survey bivariate data. The semiparametric models in Chapter 3 consider both noncensoring and interval censoring situations. The fourth chapter presents some applications using data from the National Population Health Survey and the Survey of Labour and Income Dynamics from Statistics Canada. An overall discussion is included in the fifth chapter and topics for future research are also addressed in this last chapter.
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盧亭妤. "panel count data under informative censoring with measurement error." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/50106381035793176592.
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Hsu, Wen-Chih, and 許文志. "The MCMC Approach to Progressive Type-I Interval Censoring Data." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/20140748612618571263.
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碩士中原大學
應用數學研究所
98
Assume the progressive type-I interval censoring data come from two parameter generalized exponential distribution. We first introduce some existing methods, such as the Maximum likelihood estimate (MLE) and the Expectation-Maximization (EM) algorithm, to do statistical estimation. Then, we study progressively type-I interval censoring data by the Markov chain Monte Carlo (MCMC) method. Simulated data are generated to investigate the performances of all estimation methods. It shows that the estimation obtained by our MCMC method with non-informative priors is about as good as that by the MLE, but its disadvantage is that it takes longer time to run the MCMC samplers. However, if some prior information about the parameters is given, the Bayesian approach is better. Finally, a real data set, Carbone et al. (1967), is applied by our developed MCMC approach.
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Zheng, Lifu, and 鄭立夫. "Statistical Analysis of Multivariate Current Status Data with Informative censoring." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/91640479926102760077.
Full textAbstract:
碩士靜宜大學
財務與計算數學系
100
The multivariate current status failure time data consist several possibly related event times of interest, in which the status of each event is determined at an examination time. If the examination time is intrinsically related to the event times, the examination is referred to as informative censoring and needed to be taken into account. Such data often occur in, for example, epidemiological survey, cancer research and animal carcinogenicity experiment. This thesis proposes a frailty model, which characterizes the correlation among the event times by a shared random effect. The frailty also accounts for the informative censoring simultaneously. Likelihood approach is proposed, in which the likelihood is approximated by the Gaussian quadrature techniques. Thus, maximum likelihood estimation is derived. To investigate finite sample properties of the proposed method, extensive simulation studies are conducted.
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Yu, Hsiang, and 游翔. "Recurrent event data analysis with informative censoring and measurement error." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/vf965y.
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博士國立清華大學
統計學研究所
105
Recurrent event data are frequently observed in many longitudinal and clinical studies. In the literature, various methods have been proposed to analyze covariate effects on the occurrence rate of a recurrent event, yet these methods usually require the assumption of independent censoring and accurately measured covariates. However, in many real data applications, informative censoring occurs when the recurrent event process is stopped by some terminal events that are related to the recurrent event (e.g. death). Additionally, the covariates could be measured with errors and need to be corrected. In this doctoral dissertation, we develop semi-parametric estimation to deal with informative censoring and measurement errors for recurrent event data. This dissertation contains two works. In the first work, we propose two approaches to estimate regression parameters for univariate recurrent event data in the presence of informative censoring and measurement errors. Explicitly, we impose a shared frailty model on the intensity function of a Poisson process to characterize the informative censoring and the dependence of the events within a subject without specifying the frailty distribution. To estimate the regression parameters, a regression calibration method and a moment corrected method are proposed for adjusting measurement errors. Both methods are referred to as the parametric correction because they assume that the underlying covariates and error terms are normally distributed. Moreover, the replicated data is needed to estimate the measurement error variance. In the second work, we extend the first work to accommodate informative censoring and measurement errors in multivariate recurrent event data, in which more than one type of events is of interest. Also, we consider a situation that a surrogate is available for all subjects but an instrumental variable is obtained only for a fraction of subjects. No replicated data or a validation set is available. To formulate the dependence of the informative censoring on the recurrent event processes, a shared frailty model is imposed on the rate function for each type of recurrent event, where the frailty distribution is unspecified. The shared frailty model also characterizes the association among different types of recurrent events. For regression parameter estimation, we first construct a simple correction approach, in which only subjects with an observed instrumental variable are involved in the estimation. To gain the efficiency of the simple correction estimator, we further develop a new correction approach to incorporate the information from the whole cohort. Distinct from the approaches in our first work, the approaches in the second work require neither the assumption of a Poisson process nor the distributional assumption of the underlying covariates and measurement errors. The asymptotic properties of the four proposed estimators are established. The performance of all proposed methods is investigated through simulation studies. We illustrate the proposed methods with the Nutritional Prevention of Cancer data, which aims to assess the effect of plasma selenium supplement on recurrences of squamous cell carcinoma and basal cell carcinoma.
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FAN, MIN-CHI, and 范旻琪. "Two Sample Test of Current Status Data with Dependent Censoring." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/gjr58a.
Full textAbstract:
碩士國立中正大學
數學系統計科學研究所
106
This article focus on current status data with dependent censoring between the failure time and the observation time. According to Hsieh and Chen (2014), we estimate the two survival functions of the failure time. Our main purpose is to identify whether the two survival curves are the same or not through the two sample test statistics. Based on two sample survival function estimations, we construct several test statistics. For the p-value computation, we apply the bootstrap method to construct the distribution under the null hypothesis. Then, compare the two sample test statistics of the two survival curves in the different configurations via simulations. Finally, we analyze the tumorigenicity data from Hoel and Walburg (1972) by our proposed methodology.
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Lin, Ko-Hung, and 林科宏. "Semiparametric Analysis of Survival Data with Left Truncation and Right Censoring." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/40725588599192812379.
Full textAbstract:
碩士東海大學
統計學系
94
In this note, for LTRC data, two semiparametric estimates are proposed for the semiparametric model. A simulation study is conducted to compare the performances of the two semiparametric estimators against that of parametric estinate.
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Chen, Yung-Yu, and 陳永諭. "The survival function estimation of current status data with dependent censoring." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/zq8bd6.
Full textAbstract:
碩士國立中正大學
數學系統計科學研究所
102
This thesis focuses on the estimation of the survival function of the failure time under the current status data. Because the failure time may be correlated with the observation time in the practice, we would like to investigate the estimation of the survival function of the failure time under dependent censoring. We use the Archimedean Copula model to specify the dependency between the failure time and the observation time. Under the Archimedean Copula model assumption, we adopt a redistribution algorithm to estimate the survival function of the failure time. We examine the finite-sample performance of the proposed approach by simulation studies and compared it with a pool-adjacent-violators type algorithm (Titman, 2013). We also apply our proposed methodology to analyze a practical tumorigenicity data.
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Liu, Shi Rong, and 劉士榮. "A study on Bayesian methods for categorical data under informative censoring." Thesis, 1996. http://ndltd.ncl.edu.tw/handle/07337660319169521297.
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SHI, MING-YU, and 石銘語. "Method of dealing with type Ⅱ censoring data from lognormal distribution." Thesis, 1993. http://ndltd.ncl.edu.tw/handle/61573531963391778068.
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Pei-Lan, Su, and 蘇佩蘭. "Reliability Estimation of Components of Censoring Data in a masked system." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/97331210598873843977.
Full textAbstract:
碩士元智大學
工業工程與管理學系
90
Life-test data from a multi-component system is often used to estimate the reliability of each component. In practice, due to cost and time constraints, the exact cause of system failure may be unknown for which is known as masked data. In this thesis, we use likelihood approach to find the reliability under series system of two components, and assume that components are independent with each other and the lifetimes follow exponentially distribution. We focus on the effect of component’s reliability when the data are collected based on the two different types of censoring-type Ⅰ and type Ⅱ. Type Ⅰ censoring means the observed period terminated at a specified time and type Ⅱ censoring means observation terminated at a specified number of failures. The contribution of this paper is to derive the maximum likelihood estimators of the parameters. Meanwhile, the expectation and variance of the MLEs are derived and verified the correctness by the simulated data. Simulation studies show that MLE of parameters at Type Ⅰ censoring case is biased. The biasedness of estimators may be affected by sample size and total observed length. For the type Ⅱ censoring case, MLEs of parameters also biased which is affected only by a specified number of failures.
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Li, Ling-Yu, and 李令璵. "Statistical Analysis of Recurrent Birth Data Subject to Truncation and Censoring." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/7d7m58.
Full textAbstract:
碩士國立交通大學
統計學研究所
106
In the thesis, we study the birth patterns for women in Bangladesh which is notorious for its custom of child marriage. In particular, we focus on serial birth intervals which can reflect how frequent a woman gives births, another sign of women’s right. We find that Kaplan-Meier estimator actually underestimates the true survival function due to the mixed effects of right truncation and right censoring. We figure out the bias term after some mathematical derivations and propose a modified estimator which is shown to be a valid estimator based on simulations. The modified method is then applied to analyze the data. The result shows that there are obvious generation and regional differences.
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Lin, Ying-Po, and 林英博. "Optimal Step-Stress Test under Progressive Type I Censoring with Grouped Data." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/74396472995776456245.
Full textAbstract:
碩士淡江大學
統計學系
91
In the study of product reliability, a life test usually has to be conducted. There are several types of life testing experiments. Type I and Type II censoring schemes have been studied rather extensively by lots of researchers in order to obtain the lifetimes of products. These two schemes do not allow for units to be removed from the test at points other than the final termination point. However, this allowance will be desirable for some experimenters. Therefore, a progressive censoring scheme is proposed to handle this problem. With today's high technology, many products are designed to work without failure for years. Thus, some life tests result in few or no failures in a short life testing time. One approach to solve this problem is to accelerate the life of products by increasing the levels of stress in order to obtain failures quickly. Moreover, in practice, it is often impossible continuously to observe or inspect the testing process, even with censoring. We might only be able to inspect the test units intermittently. Hence, we observe only the number of failures within the time period, but not the ssociated failure times. Data of this type are called grouped data. In this thesis, we are going to combine progressive censoring, accelerated life test and grouped data to develop a step-stress accelerated life-testing scheme with type I progressive group-censoring. We will obtain the estimators of the parameter in the proposed model when the failure time distribution is exponential. The problem of choosing the optimal length of the inspection interval will also be addressed using the variance and the D-optimality criteria.
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Peng, Lun-Chung, and 彭倫忠. "Data Censoring at Relay and Signal Combining at Destination in Cooperative Communications." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/07183257319933124784.
Full textAbstract:
博士國立臺灣科技大學
電子工程系
101
To provide robust wireless data transmission over fading channels, various schemes which involve the use of relays have been proposed. In some of those schemes, the relay chooses not to forward the received message if its reliability is deemed as too low. Some researchers refer to such schemes as selective decode-and-forward. It can be used to suppress the error propagation and hence improve the diversity gain in the cooperative network. Our work in this dissertation falls into such a category. More specifically speaking, the relay in our system is a censorial relay (a relay that performs censorial task). It evaluates the reliability, in terms of log likelihood ratio (LLR) or signal-to-noise ratio (SNR), of a received data bit (from the source). If its LLR or SNR magnitude is below some preset threshold, then it is censored (i.e. not sent to the destination). The diversity combining schemes are another issue in the cooperative relaying network. Diversity combining strategy can affect the result of decoding in the destination. Previous works that address the performance of censorial relays with LLR or SNR thresholds often adopt maximum ratio combining (MRC) for signal combining at the destination. However, it should be noted that MRC is not optimal for relay-assisted cooperative diversity systems, because the relay can make wrong decisions sometimes. Hence, instead of adopting MRC at the destination, an optimal diversity combining weights is sought in this research. When the channel is Rayleigh faded, closed-form bit error rate (BER) expressions for the proposed system are derived for several scenarios. Those scenarios are differentiated by the availability of an energy detector (ED) and the various degrees of knowledge regarding the channel state information (CSI). Aided by those closed-form BER expressions, the system parameters can be efficiently optimized to achieve the minimum BER. More specifically speaking, these system parameters include censoring-thresholds, weighted combining factors and power allocation index. Simulation results are observed to closely match theoretical values, as computed by the afore-mentioned closed-form BER expressions. It is observed that the incorporation of power allocation into the proposed censor-and-relaying cooperative communication system greatly improves the BER performance. Moreover, the power allocation task can be carried out fast with low computing complexity, because the proposed scheme only require the statistical CSI. As compared to some existing relay-assisted systems in which censoring is incorporated, the performance of our system is better in terms of BER and also in terms of the requirement on the knowledge about the CSI.
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Chen, Hsin-Hao, and 陳信豪. "Acceptance Sampling Plans under Step-stress Test and Type Ⅰ Interval Censoring Data." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/92860141347330162235.
Full textAbstract:
碩士國立政治大學
統計研究所
94
In life test experiment we use interval censoring to complete it when we can not inspect the experiment units continuously due to some accidents or for convenience. Furthermore, it is difficult to obtain enough units of breakdown products for many long life components and products. At this moment we can adopt step-stress life test to proceed the experiment. Using this method we can make the test units breakdown early for reducing the time test needed effectively and save prime cost. In this thesis, acceptance sampling plans are established for Rayleigh lifetime data under step-stress and type I interval censoring scheme. The minimum sample sizes and the corresponding critical values of lifetime needed for test plans are found. Some tables are provided for the use of the proposed test plans.
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Chu, Chenghao. "Modeling longitudinal data with interval censored anchoring events." Diss., 2018. https://doi.org/10.7912/C2XD2Q.
Full textAbstract:
Indiana University-Purdue University Indianapolis (IUPUI)In many longitudinal studies, the time scales upon which we assess the primary outcomes are anchored by pre-specified events. However, these anchoring events are often not observable and they are randomly distributed with unknown distribution. Without direct observations of the anchoring events, the time scale used for analysis are not available, and analysts will not be able to use the traditional longitudinal models to describe the temporal changes as desired. Existing methods often make either ad hoc or strong assumptions on the anchoring events, which are unveri able and prone to biased estimation and invalid inference. Although not able to directly observe, researchers can often ascertain an interval that includes the unobserved anchoring events, i.e., the anchoring events are interval censored. In this research, we proposed a two-stage method to fit commonly used longitudinal models with interval censored anchoring events. In the first stage, we obtain an estimate of the anchoring events distribution by nonparametric method using the interval censored data; in the second stage, we obtain the parameter estimates as stochastic functionals of the estimated distribution. The construction of the stochastic functional depends on model settings. In this research, we considered two types of models. The first model was a distribution-free model, in which no parametric assumption was made on the distribution of the error term. The second model was likelihood based, which extended the classic mixed-effects models to the situation that the origin of the time scale for analysis was interval censored. For the purpose of large-sample statistical inference in both models, we studied the asymptotic properties of the proposed functional estimator using empirical process theory. Theoretically, our method provided a general approach to study semiparametric maximum pseudo-likelihood estimators in similar data situations. Finite sample performance of the proposed method were examined through simulation study. Algorithmically eff- cient algorithms for computing the parameter estimates were provided. We applied the proposed method to a real data analysis and obtained new findings that were incapable using traditional mixed-effects models.
2 years
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Chu, Szu-Wei, and 褚思暐. "The Bayesian Approach to Progressive Type-I Interval Censoring Data under Generalized Gamma Distribution." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/98630161587575559098.
Full textAbstract:
碩士中原大學
應用數學研究所
99
In the survival analysis, the experimental changes may not be continuously observed all the time.Hence complete observations are sometimes not available.In practice, only censored interval data can be obtained. In this research, we assume data come from the generalized gamma distribution and they are collected in progressive type-I interval ensoring. We then apply Bayesian analysis via MCMC to do the statistical estimation. Simulation studies, along with the mean square errors of parameters of interest, are shown.Moreover, we analyze the real data set, Carbone et al.(1967), and compare the results with previously done MLE and EM methods.
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Shen, Yan-Quan, and 沈晏全. "Semiparametric Estimation of Survival Function When Data are Subject to Dependent Censoring and Left Truncation." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/35547535353942928669.
Full textAbstract:
碩士東海大學
統計學系
96
Satten, Datta and Robins (2001) proposed an estimator of survival function (denoted by S(t)) of failure times that is in the class of survival function estimators proposed by Robins (1993). The estimator is appropriate when data are subject to dependent censoring. In this article, we consider the case when data is subject to dependent censoring and left truncation, where the distribution function of the truncation variables is parameterized as G(x). We propose two estimators of survival function by simultaneously estmating G(x) and S(t). The first estimator, denoted by Sw(t), is represented as an inverse-probabilityweighted average (Satten and Datta 2001). The other estimator, denoted by S(t), is an extension of the estimator proposed by Satten et al. (2001). Simulation results show that when truncation is not severe the mean-squared error of S(t) is smaller than that of Sw(t). However, when truncation is severe and censoring is light, the situation can be reverse.