Academic literature on the topic 'Proportional hazards (PH)'
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Journal articles on the topic "Proportional hazards (PH)"
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Xu, Ronghui. "Proportional hazards mixed models." Advances in Methodology and Statistics 1, no. 1 (January 1, 2004): 205–12. http://dx.doi.org/10.51936/lmzi2020.
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We describe our recent work on mixed effects models for right-censored data. Vaida and Xu (2000) provided a general framework for handling random effects in proportional hazards (PH) regression, in a way similar to the linear, non-linear and generalized linear mixed effects models that allow random effects of arbitrary covariates. This general framework includes the frailty models as a special case. Maximum likelihood estimates of the regression parameters, the variance components and the baseline hazard, and empirical Bayes estimates of the random effects can be obtained via an MCEM algoritm. Variances of the parameter estimates are approximated using Louis' formula. We show interesting applications of the PH mixed effects model (PHMM) to a US Vietnam Era Twin Registry study on alcohol abuse, with the primary goal of identifying genetic contributions to such events. The twin pairs in the registry consist of monozygotic and dizygotic twins. After model fitting and for interpretation purposes, the proportional hazards formulation is converted to a linear transformation model before the results on genetic contributions are reported. The model also allows examination of gene and covariate interactions, as well as the modelling of multivariate outcomes (comorbidities).
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Asadi, Majid, Nader Ebrahimi, and Ehsan S. Soofi. "Connections of Gini, Fisher, and Shannon by Bayes risk under proportional hazards." Journal of Applied Probability 54, no. 4 (November 30, 2017): 1027–50. http://dx.doi.org/10.1017/jpr.2017.51.
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Abstract The proportional hazards (PH) model and its associated distributions provide suitable media for exploring connections between the Gini coefficient, Fisher information, and Shannon entropy. The connecting threads are Bayes risks of the mean excess of a random variable with the PH distribution and Bayes risks of the Fisher information of the equilibrium distribution of the PH model. Under various priors, these Bayes risks are generalized entropy functionals of the survival functions of the baseline and PH models and the expected asymptotic age of the renewal process with the PH renewal time distribution. Bounds for a Bayes risk of the mean excess and the Gini's coefficient are given. The Shannon entropy integral of the equilibrium distribution of the PH model is represented in derivative forms. Several examples illustrate implementation of the results and provide insights for potential applications.
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Farooq, Fabiha Binte, and Md Jamil Hasan Karami. "Model Selection Strategy for Cox Proportional Hazards Model." Dhaka University Journal of Science 67, no. 2 (July 30, 2019): 111–16. http://dx.doi.org/10.3329/dujs.v67i2.54582.
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Often in survival regression modelling, not all predictors are relevant to the outcome variable. Discarding such irrelevant variables is very crucial in model selection. In this research, under Cox Proportional Hazards (PH) model we study different model selection criteria including Stepwise selection, Least Absolute Shrinkage and Selection Operator (LASSO), Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and the extended versions of AIC and BIC to the Cox model. The simulation study shows that varying censoring proportions and correlation coefficients among the covariates have great impact on the performances of the criteria to identify a true model. In the presence of high correlation among the covariates, the success rate for identifying the true model is higher for LASSO compared to other criteria. The extended version of BIC always shows better result than the traditional BIC. We have also applied these techniques to real world data.
Dhaka Univ. J. Sci. 67(2): 111-116, 2019 (July)
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ZHANG, HAO, and ELSAYED A. ELSAYED. "NONPARAMETRIC ACCELERATED LIFE TESTING BASED ON PROPORTIONAL ODDS MODEL." International Journal of Reliability, Quality and Safety Engineering 13, no. 04 (August 2006): 365–78. http://dx.doi.org/10.1142/s0218539306002318.
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Accelerated life testing (ALT) is used to obtain failure time data in short duration under high stress levels in order to predict product life and performance under design conditions. The proportional hazards (PH) model, a widely used reliability prediction model, assumes constant ratio between the failure rate at high stress levels and the failure rate at the normal operating conditions. However, this assumption might be violated under some conditions and the prediction of the failure rate at normal conditions becomes inaccurate. We investigate the proportional odds (PO) model, which assumes that the odds ratio under different stress levels is constant, for accelerating life testing. In this research, we propose a nonparametric ALT approach based on the proportional odds model to predict reliability at normal operating conditions. We estimate the parameters of the proposed ALT model using the maximum likelihood estimation method. To verify the new approach, we fit the PO model with simulated failure time datasets and experimental failure data and compare its performance with the PH model. The results show that the new approach based on the PO model is a viable complement to the PH model in estimating reliability of products possessing property of converging hazard rate functions.
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Equeter, Lucas, François Ducobu, Edouard Rivière-Lorphèvre, Roger Serra, and Pierre Dehombreux. "An Analytic Approach to the Cox Proportional Hazards Model for Estimating the Lifespan of Cutting Tools." Journal of Manufacturing and Materials Processing 4, no. 1 (March 24, 2020): 27. http://dx.doi.org/10.3390/jmmp4010027.
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The machining industry raises an ever-growing concern for the significant cost of cutting tools in the production process of mechanical parts, with a focus on the replacement policy of these inserts. While an early maintenance induces lower tool return on investment, scraps and inherent costs stem from late replacement. The framework of this paper is the attempt to predict the tool inserts Mean Up Time, based solely on the value of a cutting parameter (the cutting speed in this particular turning application). More specifically, the use of the Cox Proportional Hazards (PH) Model for this prediction is demonstrated. The main contribution of this paper is the analytic approach that was conducted about the relevance on data transformation prior to using the Cox PH Model. It is shown that the logarithm of the cutting speed is analytically much more relevant in the prediction of the Mean Up Time through the Cox PH model than the raw cutting speed value. The paper also covers a numerical validation designed to show and discuss the benefits of this data transformation and the overall interest of the Cox PH model for the lifetime prognosis. This methodology, however, necessitates the knowledge of an analytical law linking the covariate to the Mean Up Time. It also shows how the necessary data for the numerical experiment was obtained through a gamma process simulating the degradation of cutting inserts. The results of this paper are expected to help manufacturers in the assessment of tool lifespan.
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Telford, Claire, Shweta Takyar, Parth Joshi, Mattias Ekman, and Nick Jones. "A network meta-analysis of fulvestrant vs alternative first-line endocrine therapies for endocrine therapy-naive postmenopausal hormone receptor-positive advanced or metastatic breast cancer." Journal of Clinical Oncology 35, no. 15_suppl (May 20, 2017): e12545-e12545. http://dx.doi.org/10.1200/jco.2017.35.15_suppl.e12545.
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e12545 Background: Fulvestrant (F) is a selective estrogen degrader for hormone receptor-positive (HR+) locally advanced or metastatic breast cancer (LA/MBC). This network meta-analysis examined the efficacy of F (500 mg) vs alternative endocrine therapies (ETs) for first-line treatment of ET-naïve HR+ LA/MBC. Methods: Randomized controlled trials of first-line F, tamoxifen (Tam), anastrozole (A), exemestane (E), letrozole (L), and toremifene (T) for women (≥18 years) with HR+ LA/MBC and no prior ET were identified in a systematic review of MEDLINE, EMBASE, and Cochrane databases from inception to October 2016. Conference proceedings of the American Society of Clinical Oncology, European Society of Medical Oncology, and San Antonio Breast Cancer Symposium from 2013-2016 were hand searched. Trials of targeted combination therapies were excluded. Studies were checked for heterogeneity. A standard fixed-effect Bayesian network meta-analysis was conducted based on hazard ratios (HRs) and assuming proportional hazards for progression-free and overall survival (PFS/OS). Results: Seven eligible studies (1 Phase [Ph] 2, 5 Ph 3, 1 Ph 2/3) were identified. All had PFS data; five had OS data. Two trials compared F vs A; PFS data were available for both trials; sufficiently mature OS data for F were available from Ph 2 only. The proportional hazards assumption was met for PFS only.F had significantly improved PFS vs Tam (HR 0.57, 95% credibility interval [Crl] 0.44-0.73), A (HR 0.75, 95% Crl 0.62-0.91), E (HR 0.65, 95% Crl 0.47-0.91), and T (HR 0.53, 95% Crl 0.37-0.78). Numerically improved PFS was observed for F vs L (HR 0.81, 95% Crl 0.59-1.11). F had significantly improved OS vs Tam (HR 0.63, 95% Crl 0.40-0.98), A (HR 0.63, 95% Crl 0.42-0.94), and E (HR 0.56, 95% Crl 0.33-0.95). OS was numerically improved with F vs L (HR 0.66, 95% Crl 0.41-1.04). Conclusions: This analysis suggests improved PFS and OS for fulvestrant vs tamoxifen, anastrozole, exemestane, and letrozole, and PFS for fulvestrant vs toremifene. Further analysis should be conducted, using non-proportional hazard methods and more mature OS data, to confirm the OS results.
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Sharma, Reema, Richa Srivastava, and Satyanshu K. Upadhyay. "A Hierarchical Bayes Analysis and Comparison of PH Weibull and PH Exponential Models for One-Shot Device Testing Experiment." International Journal of Reliability, Quality and Safety Engineering 28, no. 05 (July 30, 2021): 2150036. http://dx.doi.org/10.1142/s0218539321500364.
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The one-shot devices are highly reliable and, therefore, accelerated life tests are often employed to perform the experiments on such devices. Obviously, in the process, some covariates are introduced. This paper considers the proportional hazards model to observe the effect of covariates on the failure rates under the assumption of two commonly used models, namely the exponential and the Weibull for the lifetimes. The Bayes implementation is proposed using the hybridization of Gibbs and Metropolis algorithms that routinely extend to missing data situations as well. The entertained models are compared using the Bayesian and deviance information criteria and the expected posterior predictive loss criterion. Finally, the results based on two real data examples are given as an illustration.
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Spirko-Burns, Lauren, and Karthik Devarajan. "Unified methods for feature selection in large-scale genomic studies with censored survival outcomes." Bioinformatics 36, no. 11 (March 10, 2020): 3409–17. http://dx.doi.org/10.1093/bioinformatics/btaa161.
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Abstract Motivation One of the major goals in large-scale genomic studies is to identify genes with a prognostic impact on time-to-event outcomes which provide insight into the disease process. With rapid developments in high-throughput genomic technologies in the past two decades, the scientific community is able to monitor the expression levels of tens of thousands of genes and proteins resulting in enormous datasets where the number of genomic features is far greater than the number of subjects. Methods based on univariate Cox regression are often used to select genomic features related to survival outcome; however, the Cox model assumes proportional hazards (PH), which is unlikely to hold for each feature. When applied to genomic features exhibiting some form of non-proportional hazards (NPH), these methods could lead to an under- or over-estimation of the effects. We propose a broad array of marginal screening techniques that aid in feature ranking and selection by accommodating various forms of NPH. First, we develop an approach based on Kullback–Leibler information divergence and the Yang–Prentice model that includes methods for the PH and proportional odds (PO) models as special cases. Next, we propose R2 measures for the PH and PO models that can be interpreted in terms of explained randomness. Lastly, we propose a generalized pseudo-R2 index that includes PH, PO, crossing hazards and crossing odds models as special cases and can be interpreted as the percentage of separability between subjects experiencing the event and not experiencing the event according to feature measurements. Results We evaluate the performance of our measures using extensive simulation studies and publicly available datasets in cancer genomics. We demonstrate that the proposed methods successfully address the issue of NPH in genomic feature selection and outperform existing methods. Availability and implementation R code for the proposed methods is available at github.com/lburns27/Feature-Selection. Contact karthik.devarajan@fccc.edu Supplementary information Supplementary data are available at Bioinformatics online.
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Tebbi, O., F. Guérin, and B. Dumon. "Standard Accelerated Life Testing Model Applied to Mechanical Components." Journal of the IEST 48, no. 1 (September 1, 2005): 103–14. http://dx.doi.org/10.17764/jiet.48.1.b0640u145jw81346.
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This paper provides an overview of the application of accelerated life testing (ALT) models to mechanical components. Estimates are based upon a classical test plan using a sample system tested under accelerated conditions (not under operating conditions). The time transfer regression model is considered log-linear. The parametric model, proportional hazards (PH) model, and semiparametric model are studied. This paper illustrates an experimental example on a paper clip.
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Khajehpiri, Boshra, Hamid Abrishami Moghaddam, Mohamad Forouzanfar, Reza Lashgari, Jaime Ramos-Cejudo, Ricardo S. Osorio, and Babak A. Ardekani. "Survival Analysis in Cognitively Normal Subjects and in Patients with Mild Cognitive Impairment Using a Proportional Hazards Model with Extreme Gradient Boosting Regression." Journal of Alzheimer's Disease 85, no. 2 (January 18, 2022): 837–50. http://dx.doi.org/10.3233/jad-215266.
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Background: Evaluating the risk of Alzheimer’s disease (AD) in cognitively normal (CN) and patients with mild cognitive impairment (MCI) is extremely important. While MCI-to-AD progression risk has been studied extensively, few studies estimate CN-to-MCI conversion risk. The Cox proportional hazards (PH), a widely used survival analysis model, assumes a linear predictor-risk relationship. Generalizing the PH model to more complex predictor-risk relationships may increase risk estimation accuracy. Objective: The aim of this study was to develop a PH model using an Xgboost regressor, based on demographic, genetic, neuropsychiatric, and neuroimaging predictors to estimate risk of AD in patients with MCI, and the risk of MCI in CN subjects. Methods: We replaced the Cox PH linear model with an Xgboost regressor to capture complex interactions between predictors, and non-linear predictor-risk associations. We endeavored to limit model inputs to noninvasive and more widely available predictors in order to facilitate future applicability in a wider setting. Results: In MCI-to-AD (n = 882), the Xgboost model achieved a concordance index (C-index) of 84.5%. When the model was used for MCI risk prediction in CN (n = 100) individuals, the C-index was 73.3%. In both applications, the C-index was statistically significantly higher in the Xgboost in comparison to the Cox PH model. Conclusion: Using non-linear regressors such as Xgboost improves AD dementia risk assessment in CN and MCI. It is possible to achieve reasonable risk stratification using predictors that are relatively low-cost in terms of time, invasiveness, and availability. Future strategies for improving AD dementia risk estimation are discussed.
Dissertations / Theses on the topic "Proportional hazards (PH)"
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Fei, Mingwei. "A study of the robustness of Cox's proportional hazards model used in testing for covariate effects." Kansas State University, 2012. http://hdl.handle.net/2097/13528.
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Master of ArtsDepartment of Statistics
Paul Nelson
There are two important statistical models for multivariate survival analysis, proportional hazards(PH) models and accelerated failure time(AFT) model. PH analysis is most commonly used multivariate approach for analysing survival time data. For example, in clinical investigations where several (known) quantities or covariates, potentially affect patient prognosis, it is often desirable to investigate one factor effect adjust for the impact of others. This report offered a solution to choose appropriate model in testing covariate effects under different situations. In real life, we are very likely to just have limited sample size and censoring rates(people dropping off), which cause difficulty in statistical analysis. In this report, each dataset is randomly repeated 1000 times from three different distributions (Weibull, Lognormal and Loglogistc) with combination of sample sizes and censoring rates. Then both models are evaluated by hypothesis testing of covariate effect using the simulated data using the derived statistics, power, type I error rate and covergence rate for each situation. We would recommend PH method when sample size is small(n<20) and censoring rate is high(p>0.8). In this case, both PH and AFT analyses may not be suitable for hypothesis testing, but PH analysis is more robust and consistent than AFT analysis. And when sample size is 20 or above and censoring rate is 0.8 or below, AFT analysis will have slight higher convergence rate and power than PH, but not much improvement in Type I error rates when sample size is big(n>50) and censoring rate is low(p<0.3). Considering the privilege of not requiring knowledge of distribution for PH analysis, we concluded that PH analysis is robust in hypothesis testing for covariate effects using data generated from an AFT model.
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Pelagia, Ioanna. "Variable selection of fixed effects and frailties for Cox Proportional Hazard frailty models and competing risks frailty models." Thesis, University of Manchester, 2016. https://www.research.manchester.ac.uk/portal/en/theses/variable-selection-of-fixed-effects-and-frailties-for-cox-proportional-hazard-frailty-models-and-competing-risks-frailty-models(c75c6314-f43e-4d69-a2de-942bece6a404).html.
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This thesis focuses on two fundamental topics, specifically in medical statistics: the modelling of correlated survival datasets and the variable selection of the significant covariates and random effects. In particular, two types of survival data are considered: the classical survival datasets, where subjects are likely to experience only one type of event and the competing risks datasets, where subjects are likely to experience one of several types of event. In Chapter 2, among other topics, we highlight the importance of adding frailty terms on the proposed models in order to account for the association between the survival time and characteristics of subjects/groups. The main novelty of this thesis is to simultaneously select fixed effects and frailty terms through the proposed statistical models for each survival dataset. Chapter 3 covers the analysis of the classical survival dataset through the proposed Cox Proportional Hazard (PH) model. Utilizing a Cox PH frailty model, may increase the dimension of variable components and estimation of the unknown coefficients becomes very challenging. The method proposed for the analysis of classical survival datasets involves simultaneous variable selection on both fixed effects and frailty terms through penalty functions. The benefit of penalty functions is that they identify the non-significant parameters and set them to have a zero effect in the model. Hence, the idea is to 'doubly-penalize' the partial likelihood of the Cox PH frailty model; one penalty for each term. Estimation and selection implemented through Newton-Raphson algorithms, whereas closed iterative forms for the estimation and selection of fixed effects and prediction of frailty terms were obtained. For the selection of frailty terms, penalties imposed on their variances since frailties are random effects. Based on the same idea, we further extend the simultaneous variable selection in the competing risks datasets in Chapter 4, using extended cause-specific frailty models. Two different scenarios are considered for frailty terms; in the first case we consider that frailty terms vary among different types of events (similar to the fixed effects) whereas in the second case we consider shared frailties over all the types of events. Moreover, our 'individual penalization' approach allows for one covariate to be significant for some types of events, in contrast to the frequently used 'group-penalization' where a covariate is entirely removed when it is not significant over all the events. For both proposed methods, simulation studies were conduced and showed that the proposed procedure followed for each analysis works well in simultaneously selecting and estimating significant fixed effects and frailty terms. The proposed methods are also applied to real datasets analysis; Kidney catheter infections, Diabetes Type 2 and Breast Cancer datasets. Association of the survival times and unmeasured characteristics of the subjects was studied as well as a variable selection for fixed effects and frailties implemented successfully.
Conference papers on the topic "Proportional hazards (PH)"
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Xing, Xiao, Mengshan Yu, Olayinka Tehinse, Weixing Chen, and Hao Zhang. "The Effects of Pressure Fluctuations on Hydrogen Embrittlement in Pipeline Steels." In 2016 11th International Pipeline Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/ipc2016-64478.
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Hydrogen embrittlement is one of the most severe steel degradation mechanisms. Using hydrogen enhanced decohesion (HEDE) and hydrogen enhanced local plasticity (HELP), we can predict if more hydrogen atoms will accumulate into the plastic zone, enhancing the hydrogen embrittlement and the crack growth rate. In the current study, a relationship has been proposed between operations of pipeline steels and hydrogen accumulation to quantify the effects of hydrogen embrittlement. The study find that hydrogen accumulation rate is proportional to stress intensity and inversely proportional to temperature; hence, higher stress intensity and lower temperature will enhance hydrogen accumulation and crack propagation. Hydrogen potential, diffusivity, hydrostatic stress near the crack tip, and the critical loading frequency have been considered in the new model to predict crack propagation rates in pipeline steels. The predicted values are compared with experimental results of X-65 steel in two near-neutral pH solutions to verify the model. This hydrogen diffusion model helps show former neglected hazard operations such as minor cycles, and offers an easier way to optimize operations that will prolong the life of pipeline steels.