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Автор: Grafiati

Опубліковано: 10 грудня 2022

Оновлено: 28 січня 2023

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1

Wey, Andrew, John Connett, and Kyle Rudser. "Combining parametric, semi-parametric, and non-parametric survival models with stacked survival models." Biostatistics 16, no. 3 (February 5, 2015): 537–49. http://dx.doi.org/10.1093/biostatistics/kxv001.

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2

H, Alexis Selvaraj. "Non-Parametric Survival Models." INTERNATIONAL JOURNAL OF COMPUTING ALGORITHM 3, no. 3 (December 31, 2014): 232–35. http://dx.doi.org/10.20894/ijcoa.101.003.003.016.

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3

Liu, Xing-Rong, Yudi Pawitan, and Mark Clements. "Parametric and penalized generalized survival models." Statistical Methods in Medical Research 27, no. 5 (September 1, 2016): 1531–46. http://dx.doi.org/10.1177/0962280216664760.

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Анотація:

We describe generalized survival models, where g( S( t| z)), for link function g, survival S, time t, and covariates z, is modeled by a linear predictor in terms of covariate effects and smooth time effects. These models include proportional hazards and proportional odds models, and extend the parametric Royston–Parmar models. Estimation is described for both fully parametric linear predictors and combinations of penalized smoothers and parametric effects. The penalized smoothing parameters can be selected automatically using several information criteria. The link function may be selected based on prior assumptions or using an information criterion. We have implemented the models in R. All of the penalized smoothers from the mgcv package are available for smooth time effects and smooth covariate effects. The generalized survival models perform well in a simulation study, compared with some existing models. The estimation of smooth covariate effects and smooth time-dependent hazard or odds ratios is simplified, compared with many non-parametric models. Applying these models to three cancer survival datasets, we find that the proportional odds model is better than the proportional hazards model for two of the datasets.

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4

TSIATIS, A. A., H. BOUCHER, and K. KIM. "Sequential methods for parametric survival models." Biometrika 82, no. 1 (March 1, 1995): 165–73. http://dx.doi.org/10.1093/biomet/82.1.165.

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5

Adeboye, Nureni Olawale, Ilesanmi A. Ajibode, and Olubisi L. Aako. "On the Survival Assessment of Asthmatic Patients Using Parametric and Semi-Parametric Survival Models." Occupational Diseases and Environmental Medicine 08, no. 02 (2020): 50–63. http://dx.doi.org/10.4236/odem.2020.82004.

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6

Hjort, Nils Lid. "On Inference in Parametric Survival Data Models." International Statistical Review / Revue Internationale de Statistique 60, no. 3 (December 1992): 355. http://dx.doi.org/10.2307/1403683.

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7

Gutierrez, Roberto G. "Parametric Frailty and Shared Frailty Survival Models." Stata Journal: Promoting communications on statistics and Stata 2, no. 1 (March 2002): 22–44. http://dx.doi.org/10.1177/1536867x0200200102.

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8

Hemming, K., and J. E. H. Shaw. "A Class of Parametric Dynamic Survival Models." Lifetime Data Analysis 11, no. 1 (March 2005): 81–98. http://dx.doi.org/10.1007/s10985-004-5641-5.

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9

Slud, Eric V., and Jiraphan Suntornchost. "Parametric survival densities from phase-type models." Lifetime Data Analysis 20, no. 3 (August 22, 2013): 459–80. http://dx.doi.org/10.1007/s10985-013-9278-0.

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10

Jakobsen, Lasse Hjort, Martin Bøgsted, and Mark Clements. "Generalized parametric cure models for relative survival." Biometrical Journal 62, no. 4 (January 20, 2020): 989–1011. http://dx.doi.org/10.1002/bimj.201900056.

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11

GANAKA KUBI, MUSA,, LASISI K. E, BELLO ABDULKADR RASHEED, USMAN Y. B, and ABDULLAHI LAWAN. "PARAMETRIC AND SEMI-PARAMETRIC SURVIVAL MODELS WITH APPLICATION TO HYPERTENSION DATA." BIMA JOURNAL OF SCIENCE AND TECHNOLOGY (2536-6041) 6, no. 01 (April 30, 2022): 50–64. http://dx.doi.org/10.56892/bimajst.v6i01.313.

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Анотація:

Correlated survival data with possible censoring are frequently encountered in survival analysis.When there are dependencies among observed survival times, conventional Cox proportionalhazards model (CPHM) and Accelerated Failure Time (AFT) models that assumes independentresponses may not be appropriate. In this study, we compare the performance of parametric andsemi-parametric survival models with application to clinical data. Specifically, the AFT modeland the CPHM with and without Random effect were compared. Data on hypertension wascollected from Federal Medical Centre Keffi and General Hospital Nasarawa for the period offive years (2016 – 2020). The results from the analysis revealed that the Weibull AFT modelwith Gamma Random effect distribution had the least AIC and BIC values indicating that itoutperformed the other models considered in this study. Hence, the interpretation of the resultswas based on the most efficient model. Based on our results, it was found that hypertensionpatient that were giving drugs on the visit to the hospital has longer survival time compared tothose that were not giving drugs. Also, Hypertension patient with blood group AB and Obesedhave lesser survival time as compared to those with blood group o+ and normal weightrespectively. The study recommend that health expert can use the Weibull AFT model withGamma Random effect for predicting the risk factors of Hypertension especially when the dataare correlated.Keywords: AFT, CPHM, Hazard, Hypertension, Survival,

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12

Petersen, Trond. "Fitting Parametric Survival Models with Time-Dependent Covariates." Applied Statistics 35, no. 3 (1986): 281. http://dx.doi.org/10.2307/2348028.

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13

Federico Paly, Victoria, Murat Kurt, Lirong Zhang, Marcus O. Butler, Olivier Michielin, Adenike Amadi, Emma Hernlund, et al. "Heterogeneity in Survival with Immune Checkpoint Inhibitors and Its Implications for Survival Extrapolations: A Case Study in Advanced Melanoma." MDM Policy & Practice 7, no. 1 (January 2022): 238146832210896. http://dx.doi.org/10.1177/23814683221089659.

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Background Survival heterogeneity and limited trial follow-up present challenges for estimating lifetime benefits of oncology therapies. This study used CheckMate 067 (NCT01844505) extended follow-up data to assess the predictive accuracy of standard parametric and flexible models in estimating the long-term overall survival benefit of nivolumab plus ipilimumab (an immune checkpoint inhibitor combination) in advanced melanoma. Methods Six sets of survival models (standard parametric, piecewise, cubic spline, mixture cure, parametric mixture, and landmark response models) were independently fitted to overall survival data for treatments in CheckMate 067 (nivolumab plus ipilimumab, nivolumab, and ipilimumab) using successive data cuts (28, 40, 52, and 60 mo). Standard parametric models allow survival extrapolation in the absence of a complex hazard. Piecewise and cubic spline models allow additional flexibility in fitting the hazard function. Mixture cure, parametric mixture, and landmark response models provide flexibility by explicitly incorporating survival heterogeneity. Sixty-month follow-up data, external ipilimumab data, and clinical expert opinion were used to evaluate model estimation accuracy. Lifetime survival projections were compared using a 5% discount rate. Results Standard parametric, piecewise, and cubic spline models underestimated overall survival at 60 mo for the 28-mo data cut. Compared with other models, mixture cure, parametric mixture, and landmark response models provided more accurate long-term overall survival estimates versus external data, higher mean survival benefit over 20 y for the 28-mo data cut, and more consistent 20-y mean overall survival estimates across data cuts. Conclusion This case study demonstrates that survival models explicitly incorporating survival heterogeneity showed greater accuracy for early data cuts than standard parametric models did, consistent with similar immune checkpoint inhibitor survival validation studies in advanced melanoma. Research is required to assess generalizability to other tumors and disease stages. Highlights Given that short clinical trial follow-up periods and survival heterogeneity introduce uncertainty in the health technology assessment of oncology therapies, this study evaluated the suitability of conventional parametric survival modeling approaches as compared with more flexible models in the context of immune checkpoint inhibitors that have the potential to provide lasting survival beneﬁts. This study used extended follow-up data from the phase III CheckMate 067 trial (NCT01844505) to assess the predictive accuracy of standard parametric models in comparison with more flexible methods for estimating the long-term survival benefit of the immune checkpoint inhibitor combination of nivolumab plus ipilimumab in advanced melanoma. Mixture cure, parametric mixture, and landmark response models provided more accurate estimates of long-term overall survival versus external data than other models tested. In this case study with immune checkpoint inhibitor therapies in advanced melanoma, extrapolation models that explicitly incorporate differences in cancer survival between observed or latent subgroups showed greater accuracy with both early and later data cuts than other approaches did.

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14

Mulayath Variyath, Asokan, and P. G. Sankaran. "Parametric Regression Models Using Reversed Hazard Rates." Journal of Probability and Statistics 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/645719.

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Proportional hazard regression models are widely used in survival analysis to understand and exploit the relationship between survival time and covariates. For left censored survival times, reversed hazard rate functions are more appropriate. In this paper, we develop a parametric proportional hazard rates model using an inverted Weibull distribution. The estimation and construction of confidence intervals for the parameters are discussed. We assess the performance of the proposed procedure based on a large number of Monte Carlo simulations. We illustrate the proposed method using a real case example.

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15

Vijai, B., P. R. Jayashree, and C. Ponnuraja. "Flexible Parametric Survival Cure Rate Models for Pulmonary Tuberculosis Data." Asian Pacific Journal of Health Sciences 9, no. 3 (April 16, 2022): 175–80. http://dx.doi.org/10.21276/apjhs.2022.9.3.35.

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This article mainly aims to compare Flexible parametric cure rate models using relative survival function and to predict cure fraction for tuberculosis (TB) data. In survival analysis, the Cox proportional-hazards model of time-to-event data is effective, but still there may be some benefits of using parametric models than non-parametric or semi-parametric models. Sometimes, it happens that a certain fraction of the data corresponds to subjects who are never involved in the event when assessing time-to-event data. Survival models that take this characteristic into account are typically referred to as cure rate models. Hence, in this article the parametric cure model to time-to-event (sputum conversion) on pulmonary TB data with the survival time distribution such as Weibull, Gamma, Exponential and Lognormal is developed. The objective of this article is to compare cure rate models to find the best model fitting survival time using the relative survival function and to predict cure fraction of TB data. The data were analyzed using “R-4.0.2” and STATA 15.0.0 statistical tools.

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16

Liaqat, Madiha, Shahid Kamal, Florian Fischer, and Waqas Fazil. "Survival models for right censored breast cancer data: theory, application and comparison." F1000Research 10 (October 13, 2021): 1042. http://dx.doi.org/10.12688/f1000research.73507.1.

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Background: Censoring frequently occurs in disease data analysis, which is a key characteristic of time to failure modeling. Typically, time to failure studies are conducted through non-parametric and semi-parametric modelling techniques. Parametric models provide more efficient estimates, but are seldomly used, because of some of the limitations and assumptions which need to be fulfilled to apply them. The aim of this study is to illustrate the theoretical and application limitations and performance of different flexible and standard parametric models to evaluate the prognostic value for mortality risk of breast cancer after recurrence among women. Methods: This article describes the theoretical properties of flexible parametric models and compares their performances to standard parametric models, by studying mortality in women diagnosed with breast cancer. We describe how time to failure data may be analyzed with nonlinear flexible models. In this regard, we apply fractional polynomials, spline models, piecewise exponential models, and piecewise exponential additive mixed models. We also illustrate properties of standard parametric models. All analyses have been conducted with multiple covariates to identify significant predictors. Information criteria have been used to evaluate performances of models. Results: Fractional polynomial and spline-based generalized additive models work well in capturing local fluctuations. Parameter estimation with a piecewise exponential additive mixed model (PAMM) as an extension of the piecewise exponential modelling (PEM) approach automatically penalizes model complexity, which is very helpful to avoid over fitting. Conclusions: Flexible parametric time to failure models are more efficient than standard parametric time to failure models. By incorporating time dependent covariates, PAMM is a good approach to perform in-depth studies of predictors over different finite intervals of follow-up time. Until now, this approach is rarely used in time to failure right censored studies.

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17

Mokarram, Reza, Mahdi Emadi, Arezou Habibi Rad, and Mahdi Jabbari Nooghabi. "A comparison of parametric and semi-parametric survival models with artificial neural networks." Communications in Statistics - Simulation and Computation 47, no. 3 (June 8, 2017): 738–46. http://dx.doi.org/10.1080/03610918.2017.1291961.

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18

Chopra, Sandeep, Lata Nautiyal, Preeti Malik, Mangey Ram, and Mahesh K. Sharma. "A Non-Parametric Approach for Survival Analysis of Component-Based Software." International Journal of Mathematical, Engineering and Management Sciences 5, no. 2 (April 1, 2020): 309–18. http://dx.doi.org/10.33889/ijmems.2020.5.2.025.

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Reliability of a software or system is the probability of system to perform its functions adequately for the stated time period under specific environment conditions. In case of component-based software development reliability estimation is a crucial factor. Existing reliability estimation model falls into two broad categories parametric and non-parametric models. Parametric models approximate the model parameters based on the assumptions of fundamental distributions. Non-parametric models enable parameter estimation of the software reliability growth models without any assumptions. We have proposed a novel non-parametric approach for survival analysis of components. Failure data is collected based on which we have calculated failure rate and reliability of the software. Failure rate increases with the time whereas reliability decreases with the time.

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19

Swihart, Bruce J., and Dipankar Bandyopadhyay. "Bridged parametric survival models: General paradigm and speed improvements." Computer Methods and Programs in Biomedicine 206 (July 2021): 106115. http://dx.doi.org/10.1016/j.cmpb.2021.106115.

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20

Ahmed, Layla A. "Parametric Models in Survival Analysis for Lung Cancer Patients." Ibn AL- Haitham Journal For Pure and Applied Sciences 34, no. 2 (April 20, 2021): 108–18. http://dx.doi.org/10.30526/34.2.2617.

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The aim of this study is to estimate the survival function for the data of lung cancer patients, using parametric methods (Weibull, Gumbel, exponential and log-logistic). Comparisons between the proposed estimation method have been performed using statistical indicator Akaike information Criterion, Akaike information criterion corrected and Bayesian information Criterion, concluding that the survival function for the lung cancer by using Gumbel distribution model is the best. The expected values of the survival function of all estimation methods that are proposed in this study have been decreasing gradually with increasing failure times for lung cancer patients, which means that there is an opposite relationship failure times and survival function.

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21

Richards, S. J. "A handbook of parametric survival models for actuarial use." Scandinavian Actuarial Journal 2012, no. 4 (December 2012): 233–57. http://dx.doi.org/10.1080/03461238.2010.506688.

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22

Lambert, Paul C., and Patrick Royston. "Further Development of Flexible Parametric Models for Survival Analysis." Stata Journal: Promoting communications on statistics and Stata 9, no. 2 (August 2009): 265–90. http://dx.doi.org/10.1177/1536867x0900900206.

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Royston and Parmar (2002, Statistics in Medicine 21: 2175–2197) developed a class of flexible parametric survival models that were programmed in Stata with the stpm command (Royston, 2001, Stata Journal 1: 1–28). In this article, we introduce a new command, stpm2, that extends the methodology. New features for stpm2 include improvement in the way time-dependent covariates are modeled, with these effects far less likely to be over parameterized; the ability to incorporate expected mortality and thus fit relative survival models; and a superior predict command that enables simple quantification of differences between any two covariate patterns through calculation of time-dependent hazard ratios, hazard differences, and survival differences. The ideas are illustrated through a study of breast cancer survival and incidence of hip fracture in prostate cancer patients.

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23

Siannis, F., J. Copas, and G. Lu. "Sensitivity analysis for informative censoring in parametric survival models." Biostatistics 6, no. 1 (December 23, 2004): 77–91. http://dx.doi.org/10.1093/biostatistics/kxh019.

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24

Remontet, Laurent, Nadine Bossard, Jean Iwaz, Jacques Estève, and Aurelien Belot. "Framework and optimisation procedure for flexible parametric survival models." Statistics in Medicine 34, no. 25 (October 4, 2015): 3376–77. http://dx.doi.org/10.1002/sim.6489.

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25

Macdonald, A. S. "An Actuarial Survey of Statistical Models for Decrement and Transition Data, III. Counting Process Models." British Actuarial Journal 2, no. 3 (August 1, 1996): 703–26. http://dx.doi.org/10.1017/s1357321700003524.

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ABSTRACTCounting processes and their compensators are introduced at a heuristic level. The martingale property of stochastic integrals with respect to a compensated counting process leads to moment estimates and asymptotic normal distributions for statistics arising in multiple state, non-parametric and semi-parametric models. The place of survival models in actuarial education is discussed.

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26

Gamel, John W., Edie A. Weller, Margaret N. Wesley, and Eric J. Feuer. "Parametric cure models of relative and cause-specific survival for grouped survival times." Computer Methods and Programs in Biomedicine 61, no. 2 (February 2000): 99–110. http://dx.doi.org/10.1016/s0169-2607(99)00022-x.

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27

Tutkun, Nihal Ata, Müge Yeldan, and Handan İlhan. "Flexible parametric survival models: An application to gastric cancer data." International Journal of ADVANCED AND APPLIED SCIENCES 4, no. 4 (April 2017): 91–95. http://dx.doi.org/10.21833/ijaas.2017.04.014.

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28

Wang, Dongliang, Alan D. Hutson, and Jeffrey C. Miecznikowski. "L-moment estimation for parametric survival models given censored data." Statistical Methodology 7, no. 6 (November 2010): 655–67. http://dx.doi.org/10.1016/j.stamet.2010.07.002.

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29

Abrams, Keith R., and Bruno Sansó. "30 Comparison of competing parametric survival models — a bayesian perspective." Controlled Clinical Trials 18, no. 3 (June 1997): S59. http://dx.doi.org/10.1016/s0197-2456(97)91015-1.

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30

Yeniew Enyew, Belaynesh, and Zeytu Gashaw Asfaw. "Comparison of survival models and assessment of risk factors for survival of cardiovascular patients at Addis Ababa Cardiac Center, Ethiopia: a retrospective study." African Health Sciences 21, no. 3 (September 27, 2021): 1201–13. http://dx.doi.org/10.4314/ahs.v21i3.29.

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Background: Cardiovascular diseases (CVDs) is disorders of heart and blood vessels. It is a major health problem across the world,and 82% of CVD deaths is contributed by countries with low and middle income. The aim of this study was to choose appropriate model for the survival of cardiovascular patients data and identify the factors that affect the survival of cardiovascular patients at Addis Ababa Cardiac Center. Method: A Retrospective study was conducted on patients under follow-up at Addis Ababa Cardiac Center between Sep- tember 2010 to December 2018. The patients included have made either post operation or pre-operation. Out of 1042 car- diac patients, a sample of 332 were selected for the current study using simple random sampling technique. Non-parametric, semi-parametric and parametric survival models were used and comparisons were made to select the appropriate predicting model. Results: Among the sample of 332 cardiac patients, only 67(20.2%) experienced CVD and the remaining 265(79.8%) were censored. The median and the maximum survival time of cardiac patients was 1925 and 1403 days respectively.The estimated hazard ratio of male patients to female patients is 1.926214 (95%CI: 1.111917-3.336847; p = 0.019) implying that the risk of death of male patients is 1.926214 times higher than female cardiac patients keeping the other covariates constant in the model. Even if, all semi parametric and parametric survival models ﬁtted to the current data well, various model comparison criteria showed that parametric/weibull AFT survival model is better than the other. Conclusions: The governmental and non-governmental stakeholders should pay attention to give training on the risk fac- tors identiﬁed on the current study to optimize individual’s knowledge and awareness so that death due to CVDs can be minimized. Keywords: Cardiovascular patient; survival analysis; non-parametric; semi-parametric; parametric.

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31

Kearns, Benjamin, Matt D. Stevenson, Kostas Triantafyllopoulos, and Andrea Manca. "Generalized Linear Models for Flexible Parametric Modeling of the Hazard Function." Medical Decision Making 39, no. 7 (September 26, 2019): 867–78. http://dx.doi.org/10.1177/0272989x19873661.

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Background. Parametric modeling of survival data is important, and reimbursement decisions may depend on the selected distribution. Accurate predictions require sufficiently flexible models to describe adequately the temporal evolution of the hazard function. A rich class of models is available among the framework of generalized linear models (GLMs) and its extensions, but these models are rarely applied to survival data. This article describes the theoretical properties of these more flexible models and compares their performance to standard survival models in a reproducible case study. Methods. We describe how survival data may be analyzed with GLMs and their extensions: fractional polynomials, spline models, generalized additive models, generalized linear mixed (frailty) models, and dynamic survival models. For each, we provide a comparison of the strengths and limitations of these approaches. For the case study, we compare within-sample fit, the plausibility of extrapolations, and extrapolation performance based on data splitting. Results. Viewing standard survival models as GLMs shows that many impose a restrictive assumption of linearity. For the case study, GLMs provided better within-sample fit and more plausible extrapolations. However, they did not improve extrapolation performance. We also provide guidance to aid in choosing between the different approaches based on GLMs and their extensions. Conclusions. The use of GLMs for parametric survival analysis can outperform standard parametric survival models, although the improvements were modest in our case study. This approach is currently seldom used. We provide guidance on both implementing these models and choosing between them. The reproducible case study will help to increase uptake of these models.

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Hameed, Hevi J., and Mohammad M. Faqe. "Apply Parametric Shared Frailty Models to Colorectal Cancer Patients." Cihan University-Erbil Scientific Journal 6, no. 2 (November 1, 2022): 119–24. http://dx.doi.org/10.24086/cuesj.v6n2y2022.pp119-124.

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Colorectal cancer is a combination of colon and rectal cancer that indicates an abnormal growth of cells in either the colon or rectum and is named according to its original location. After treatment, cancer may return to the primary site of the original tumor or to a different location in the body once or more, which is called recurrent. This paper aimed to model this type of data from 128 colorectal cancer patients collected at Hiwa hospital in Sulaimani considering the gamma shared and inverse Gaussian shared frailty models for analyzing the patient’s survival times with colorectal cancer recurrence and estimate the prognostic factor’s impact on their survival. Comparison of the results of these models with those without a frailty model using Weibull, log-logistic, and lognormal as a baseline distribution. To identify the best model for the data the (AIC) Akaike Information Criterion and (BIC) Bayesian Information Criterion were also used. Results showed that the cancer stage was the only significant factor affecting survival in recurrent events, as well as evidence of existing heterogeneity in colorectal patients. According to (AIC) and (BIC), the Weibull as baseline distribution with shared Gamma frailty model proved the most efficient model for the colorectal recurrent data. In Conclusion, the shared frailty model is better than no frailty when analyzing this type of data.

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Muse, Abdisalam Hassan, Christophe Chesneau, Oscar Ngesa, and Samuel Mwalili. "Flexible Parametric Accelerated Hazard Model: Simulation and Application to Censored Lifetime Data with Crossing Survival Curves." Mathematical and Computational Applications 27, no. 6 (November 30, 2022): 104. http://dx.doi.org/10.3390/mca27060104.

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This study aims to propose a flexible, fully parametric hazard-based regression model for censored time-to-event data with crossing survival curves. We call it the accelerated hazard (AH) model. The AH model can be written with or without a baseline distribution for lifetimes. The former assumption results in parametric regression models, whereas the latter results in semi-parametric regression models, which are by far the most commonly used in time-to-event analysis. However, under certain conditions, a parametric hazard-based regression model may produce more efficient estimates than a semi-parametric model. The parametric AH model, on the other hand, is inappropriate when the baseline distribution is exponential because it is constant over time; similarly, when the baseline distribution is the Weibull distribution, the AH model coincides with the accelerated failure time (AFT) and proportional hazard (PH) models. The use of a versatile parametric baseline distribution (generalized log-logistic distribution) for modeling the baseline hazard rate function is investigated. For the parameters of the proposed AH model, the classical (via maximum likelihood estimation) and Bayesian approaches using noninformative priors are discussed. A comprehensive simulation study was conducted to assess the performance of the proposed model’s estimators. A real-life right-censored gastric cancer dataset with crossover survival curves is used to demonstrate the tractability and utility of the proposed fully parametric AH model. The study concluded that the parametric AH model is effective and could be useful for assessing a variety of survival data types with crossover survival curves.

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Yakubu, Othman Musa, Yusuf Abbakar Mohammed, and Akeyede Imam. "A Mixture of Gamma-Gamma, Loglogistic-Gamma Distributions for the Analysis of Heterogenous Survival Data." International Journal of Mathematical Research 11, no. 1 (February 15, 2022): 1–9. http://dx.doi.org/10.18488/24.v11i1.2924.

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Survival analysis deals with failure time data. The presence of censoring makes the application of the classical parametric and nonparametric methods of survival analysis inadequate and as such need’s modifications. Parametric mixture models are applied where a single classical model may not suffice. The parametric mixture needs to be made more robust to address the heterogeneity of survival data. This paper proposed a mixture of two distributions for the analysis of survival data, the models consist of Gamma-Gamma, and Loglogistic-Gamma distributions. Data was simulated to investigate the performance of the models, and used to estimate the maximum likelihood parameters of the models by employing Expectation Maximization (EM). Parameters of the models were estimated and were all close the postulated values. Simulations were repeated to test the consistency and stability of the models through mean square error (MSE) and root mean square error (RMSE), and were all found to be stable and consistent. Real data was applied to determine the best fit among the mixture models and classical distributions using information criteria. Mixture models were found to model the data and the mixture of two different distributions gives the best fit.

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35

Selingerova, Iveta, Stanislav Katina, and Ivanka Horova. "Comparison of parametric and semiparametric survival regression models with kernel estimation." Journal of Statistical Computation and Simulation 91, no. 13 (April 8, 2021): 2717–39. http://dx.doi.org/10.1080/00949655.2021.1906875.

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36

May, M. "Parametric survival models may be more accurate than Kaplan-Meier estimates." BMJ 326, no. 7393 (April 12, 2003): 822. http://dx.doi.org/10.1136/bmj.326.7393.822.

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37

Chavez, G., C. Proescholdt, and G. Lavy-Shahaf. "PCN287 RESPONDER-BASED PARAMETRIC MODELS UNDERESTIMATE LONG-TERM SURVIVAL IN GLIOBLASTOMA." Value in Health 23 (May 2020): S74. http://dx.doi.org/10.1016/j.jval.2020.04.1753.

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38

Vahedi, Mohsen, Mahmood Mahmoodi, Kazem Mohammad, Sharzad Ossareh, and Hojjat Zeraati. "What Is the Best Parametric Survival Models for Analyzing Hemodialysis Data?" Global Journal of Health Science 8, no. 10 (February 24, 2016): 118. http://dx.doi.org/10.5539/gjhs.v8n10p118.

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<p><strong>Background: </strong>Chronic kidney disease (CKD) and end-stage renal disease (ESRD) are both common public health problems worldwide. Hemodialysis (HD) is one of the main ultimate modalities of renal replacement therapy in these patients. The aim of this study was to compare the different parametric (Weibull, Gamma, Gompertz, Log-logistic and Lognormal) survival models, in maintenance HD (MHD) patients.</p><p><strong>Method: </strong>This study was conducted from March 2004 to October 2013 and encompassed 544 ESRD patients under MHD in Hasheminejad Kidney Center, Tehran, Iran. Laboratory, clinical and demographic data were extracted from the Hemodialysis Data Processor Software, which had been designed for data collection in Hasheminejad Kidney Center. Exponential, Weibull, Gompertz, lognormal and log-logistic were used for analyzing survival of hemodialysis patient using STATA software. To compare these models Akaike Information criterion (AIC) and Cox-Snell residual were utilized.</p><p><strong>Results: </strong>According to the both criteria (AIC and Cox-Snell residual), Weibull survival model manifested better results as compared with other models. According to this model, age at the time of admission (HR=1.015, p-value=0.018), walking ability (HR=0.656, p-value=0.010), diabetes mellitus as the underlying disease (HR=1.392, p-value=0.038), hemoglobin level (HR=0.790, p-value<0.001), serum creatinine (HR=0.803, p-value<0.001), serum protein (HR=0.747, p-value=0.010) and Single pool Kt/V(HR=0.092, p-value<0.001), had significant effect on survival of the hemodialysis patient</p><p><strong>Conclusion: </strong>In our analysis Weibull distribution, which had the lowest AIC value, was selected as the most suitable model. </p>

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39

Sparling, Y. H. "Parametric survival models for interval-censored data with time-dependent covariates." Biostatistics 7, no. 4 (February 16, 2006): 599–614. http://dx.doi.org/10.1093/biostatistics/kxj028.

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40

Gallacher, Daniel, Peter Kimani, and Nigel Stallard. "Extrapolating Parametric Survival Models in Health Technology Assessment: A Simulation Study." Medical Decision Making 41, no. 1 (December 7, 2020): 37–50. http://dx.doi.org/10.1177/0272989x20973201.

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Extrapolations of parametric survival models fitted to censored data are routinely used in the assessment of health technologies to estimate mean survival, particularly in diseases that potentially reduce the life expectancy of patients. Akaike’s information criterion (AIC) and Bayesian information criterion (BIC) are commonly used in health technology assessment alongside an assessment of plausibility to determine which statistical model best fits the data and should be used for prediction of long-term treatment effects. We compare fit and estimates of restricted mean survival time (RMST) from 8 parametric models and contrast models preferred in terms of AIC, BIC, and log-likelihood, without considering model plausibility. We assess the methods’ suitability for selecting a parametric model through simulation of data replicating the follow-up of intervention arms for various time-to-event outcomes from 4 clinical trials. Follow-up was replicated through the consideration of recruitment duration and minimum and maximum follow-up times. Ten thousand simulations of each scenario were performed. We demonstrate that the different methods can result in disagreement over the best model and that it is inappropriate to base model selection solely on goodness-of-fit statistics without consideration of hazard behavior and plausibility of extrapolations. We show that typical trial follow-up can be unsuitable for extrapolation, resulting in unreliable estimation of multiple parameter models, and infer that selecting survival models based only on goodness-of-fit statistics is unsuitable due to the high level of uncertainty in a cost-effectiveness analysis. This article demonstrates the potential problems of overreliance on goodness-of-fit statistics when selecting a model for extrapolation. When follow-up is more mature, BIC appears superior to the other selection methods, selecting models with the most accurate and least biased estimates of RMST.

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Jin, Xiaoping, and Bradley P. Carlin. "Multivariate Parametric Spatiotemporal Models for County Level Breast Cancer Survival Data." Lifetime Data Analysis 11, no. 1 (March 2005): 5–27. http://dx.doi.org/10.1007/s10985-004-5637-1.

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42

Cortese, Giuliana, and Nicola Sartori. "Integrated likelihoods in parametric survival models for highly clustered censored data." Lifetime Data Analysis 22, no. 3 (July 26, 2015): 382–404. http://dx.doi.org/10.1007/s10985-015-9337-9.

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43

Takeuchi, Yoshinori, Mitsunori Ogawa, Yasuhiro Hagiwara, and Yutaka Matsuyama. "Non-parametric approach for frequentist multiple imputation in survival analysis with missing covariates." Statistical Methods in Medical Research 30, no. 7 (June 10, 2021): 1691–707. http://dx.doi.org/10.1177/09622802211011197.

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In clinical and epidemiological studies using survival analysis, some explanatory variables are often missing. When this occurs, multiple imputation (MI) is frequently used in practice. In many cases, simple parametric imputation models are routinely adopted without checking the validity of the model specification. Misspecified imputation models can cause biased parameter estimates. In this study, we describe novel frequentist type MI procedures for survival analysis using proportional and additive hazards models. The procedures are based on non-parametric estimation techniques and do not require the correct specification of parametric imputation models. For continuous missing covariates, we first sample imputation values from a parametric imputation model. Then, we obtain estimates by solving the estimating equation modified by non-parametrically estimated conditional densities. For categorical missing covariates, we directly sample imputation values from a non-parametrically estimated conditional distribution and then obtain estimates by solving the corresponding estimating equation. We evaluate the performance of the proposed procedures using simulation studies: one uses simulated data; another uses data informed by parameters generated from a real-world medical claims database. We also applied the procedures to a pharmacoepidemiological study that examined the effect of antihyperlipidemics on hyperglycemia incidence.

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44

Yabaci, Aysegul, and Deniz Sigirli. "Comparison of tree-based methods used in survival data." Statistics in Transition New Series 23, no. 1 (March 1, 2022): 21–38. http://dx.doi.org/10.2478/stattrans-2022-0002.

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Abstract Survival trees and forests are popular non-parametric alternatives to parametric and semi-parametric survival models. Conditional inference trees (Ctree) form a non-parametric class of regression trees embedding tree-structured regression models into a well-defined theory of conditional inference procedures. The Ctree is applicable in a varietyof regression-related issues, involving nominal, ordinal, numeric, censored, as well as multivariate response variables and arbitrary measurement scales of covariates. Conditional inference forests (Cforest) consitute a survival forest method which combines a large number of Ctrees. The Cforest provides a unified and flexible framework for ensemble learning in the presence of censoring. The random survival forests (RSF) methodology extends the random forests method enabling the approximation of rich classes of functions while maintaining generalisation errors low. In the present study, the Ctree, Cforest and RSF methods are discussed in detail and the performances of the survival forest methods, namely the Cforest and RSF have been compared with a simulation study. The results of the simulation demonstrate that the RSF method with a log-rank score distinction criteria outperforms the Cforest and the RSF with log-rank distinction criteria.

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45

Bai, Lu, and Daniel Gillen. "Survival analysis via cox proportional hazards additive models." Encyclopedia with Semantic Computing and Robotic Intelligence 01, no. 01 (March 2017): 1650003. http://dx.doi.org/10.1142/s2425038416500036.

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The Cox proportional hazards model is commonly used to examine the covariate-adjusted association between a predictor of interest and the risk of mortality for censored survival data. However, it assumes a parametric relationship between covariates and mortality risk though a linear predictor. Generalized additive models (GAMs) provide a flexible extension of the usual linear model and are capable of capturing nonlinear effects of predictors while retaining additivity between the predictor effects. In this paper, we provide a review of GAMs and incorporate bivariate additive modeling into the Cox model for censored survival data with applications to estimating geolocation effects on survival in spatial epidemiologic studies.

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46

Chandra, Novita Eka, and Siti Alfiatur Rohmaniah. "Analisis Survival Model Regresi Parametrik Lama Studi Mahasiswa." Jurnal Matematika 9, no. 1 (June 30, 2019): 01. http://dx.doi.org/10.24843/jmat.2019.v09.i01.p106.

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Timely graduation of students can be used as an indicator to show the quality of a university. Students are said to graduate on time if they have a short study period of 4 years. The duration of the study of students varies because it is influenced by several factors. The purpose of this study is to determine the factors that have a significant effect on the duration of student studies. The factors studied included gender, GPA, school origin, joining the organization and working in college. The method used in this study is survival analysis. Survival analysis in this study used Log-normal and Weibull, parametric regression models. From the two models, it was found that the GPA and organizational factors significantly influence the duration of student studies. Next, to determine the best model is determined based on the minimum AIC value. Based on the comparison of the two models, the parametric Weibull model has a minimum AIC value, so this model is the best model. Based on HR values ??obtained by students who have a higher GPA and are more active in graduating faster or can be said to have fewer studies. Keywords: survival, regression, parametric, time of study.

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47

Dyer, Matthew, Matthew Green, simon jones, and Rachel Hodge. "Estimating long-term survival of previously untreated patients with EGFR mutation-positive (EGFRm) advanced non-small cell lung cancer (NSCLC) who received osimertinib in the FLAURA study." Journal of Clinical Oncology 37, no. 15_suppl (May 20, 2019): e20560-e20560. http://dx.doi.org/10.1200/jco.2019.37.15_suppl.e20560.

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e20560 Background: In the Phase III FLAURA trial (NCT02296125), osimertinib, a third-generation EGFR-TKI, provided clinically and statistically significantly longer progression-free survival versus gefitinib/erlotinib as first-line treatment for patients with EGFRm advanced NSCLC. At the time of analysis, data on overall survival (OS) were immature (25% maturity). To better understand the long-term survival potential of osimertinib beyond the observed trial follow-up period, mathematical parametric survival models were used to estimate clinically plausible survival rates up to 5 years from FLAURA. Methods: Following published best-practice guidelines, candidate parametric survival models were evaluated based on both statistical and visual goodness-of-fit to the observed FLAURA OS data. Two modeling approaches were considered: single models with treatment included as a covariate; and separate models fitted to the osimertinib and gefitinib/erlotinib arms. Point estimates of 5-year survival rates with 95% confidence intervals (CIs) are reported for the best fitting model. Results: The best fitting parametric survival model to the FLAURA OS data was the Weibull model with treatment included as a covariate. Based on this model, estimated median OS was longer with osimertinib than with gefitinib/erlotinib (41.4 months vs 30.6 months). The estimated 3- and 5-year survival rates with osimertinib were 57.3% (95% CI 46.6%, 69.2%) and 31.1% (95% CI 23.7%, 41.8%), respectively. In comparison, the estimated 3- and 5-year survival rates with gefitinib/erlotinib were 41.1% (95% CI 31.9%, 52.9%) and 15.5% (95% CI 11.6%, 22.1%), respectively. Conclusions: Based on the best fitting parametric survival model to FLAURA OS data, the estimated 5-year survival rate with osimertinib was double that with gefitinib/erlotinib (31.1% vs 15.5%) in patients with EGFRm advanced NSCLC. Long-term follow-up data from FLAURA (60% OS maturity) will further validate this finding. Clinical trial information: NCT02296125.

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Eckel, K. T., A. Pfahlberg, O. Gefeller, and T. Hothorn. "Flexible Modeling of Malignant Melanoma Survival." Methods of Information in Medicine 47, no. 01 (2008): 47–55. http://dx.doi.org/10.3414/me0450.

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Summary Objectives: This paper compares the diagnostic capabilities of flexible ensemble methods modeling the survival time of melanoma patients in comparison to the well established proportional hazards model. Both a random forest type algorithm for censored data as well as a model combination of the proportional hazards model with recursive partitioning are investigated. Methods: Benchmark experiments utilizing the integrated Brier score as a measure for goodness of prediction are the basis of the performance assessment for all competing algorithms. For the purpose of comparing regression relationships represented by the models under test, we describe fitted conditional survival functions by a univariate measure derived from the area under the curve. Based on this measure, we adapt a visualization technique useful for the inspection and comparison of model fits. Results: For the data of malignant melanoma patients the predictive performance of the competing models is on par, allowing for a fair comparison of the fitted relationships. Newly introduced MODplots visualize differences in the fitting structure of the underlying models. Conclusion: The paper provides a framework for comparing the predictive and diagnostic performance of a parametric, a non-parametric and a combined approach.

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Kvamme, Håvard, and Ørnulf Borgan. "Continuous and discrete-time survival prediction with neural networks." Lifetime Data Analysis 27, no. 4 (October 2021): 710–36. http://dx.doi.org/10.1007/s10985-021-09532-6.

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AbstractDue to rapid developments in machine learning, and in particular neural networks, a number of new methods for time-to-event predictions have been developed in the last few years. As neural networks are parametric models, it is more straightforward to integrate parametric survival models in the neural network framework than the popular semi-parametric Cox model. In particular, discrete-time survival models, which are fully parametric, are interesting candidates to extend with neural networks. The likelihood for discrete-time survival data may be parameterized by the probability mass function (PMF) or by the discrete hazard rate, and both of these formulations have been used to develop neural network-based methods for time-to-event predictions. In this paper, we review and compare these approaches. More importantly, we show how the discrete-time methods may be adopted as approximations for continuous-time data. To this end, we introduce two discretization schemes, corresponding to equidistant times or equidistant marginal survival probabilities, and two ways of interpolating the discrete-time predictions, corresponding to piecewise constant density functions or piecewise constant hazard rates. Through simulations and study of real-world data, the methods based on the hazard rate parametrization are found to perform slightly better than the methods that use the PMF parametrization. Inspired by these investigations, we also propose a continuous-time method by assuming that the continuous-time hazard rate is piecewise constant. The method, named PC-Hazard, is found to be highly competitive with the aforementioned methods in addition to other methods for survival prediction found in the literature.

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Hashemian, A. H., M. Garshasbi, M. A. Pourhoseingholi, and S. Eskandari. "A Comparative Study of Cox Regression vs. Log-Logistic Regression (with and without its frailty) in Estimating Survival Time of Patients with Colorectal Cancer." Journal of Medical and Biomedical Sciences 6, no. 1 (June 13, 2017): 35–43. http://dx.doi.org/10.4314/jmbs.v6i1.5.

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Colorectal cancer is common and lethal disease with different incidence rate in different parts of the world which is taken into account as the third cause of cancer-related deaths. In the present study, using non-parametric Cox model and parametric Log-logistic model, factors influencing survival of patients with colorectal cancer were evaluated and the models efficiency were compared to provide the best model. This study is conducted on medical records of 1,127 patients with colorectal cancer referred to Taleghani Medical and Training Center of Tehran between 2001 - 2007 and were definitely diagnosed with cancer, pathologically. Semi-parametric Cox model and parametric log-logistic model were fitted. Akaike’s criterion of Cox Snell graph was used to compare the models. To take into account non-measured individual characteristics, frailty was added to Cox and log-logistic models. All calculations were carried out using STATA software version 12 and SPSS version 20.0, at the 0.05 level of significance. From a total of 1,127 patients studied in this research, there were 690 men and 437 women. According to non-parametric Kaplan-Meier method, chances of surviving for 1, 3, 5 and 7 years were 91.16, 73.20, 61.00, and 54.94, respectively. Addition of frailty parameter did not change the model outcome. The results of fitting classified Cox and log-logistic models showed that body mass index (BMI), tumor grade, tumor size, and spread to lymph nodes, were the factors affecting survival time. Based on comparisons, and according to Cox Snell residuals, Cox and log-logistic models had almost identical results; however, because of the benefits of parametric models, in surveying survival time of patients with colorectal cancer, log-logistic can be replaced, as a parametric model, with Cox model.Journal of Medical and Biomedical Sciences (2017) 6(1), 35-43Keywords: Colorectal cancer, Cox regression, Log-logistic model, Cox Snell residual

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