Download or read book Robust Inference for the Cox s Proportional Hazards Model with Frailties written by Muhammad Jalaluddin and published by . This book was released on 1999 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Frailty Model written by Luc Duchateau and published by Springer Science & Business Media. This book was released on 2007-10-23 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: Readers will find in the pages of this book a treatment of the statistical analysis of clustered survival data. Such data are encountered in many scientific disciplines including human and veterinary medicine, biology, epidemiology, public health and demography. A typical example is the time to death in cancer patients, with patients clustered in hospitals. Frailty models provide a powerful tool to analyze clustered survival data. In this book different methods based on the frailty model are described and it is demonstrated how they can be used to analyze clustered survival data. All programs used for these examples are available on the Springer website.
Download or read book Robust Inference and Group Sequential Methods in Discrete Hazard Models written by Vinh Quang Nguyen and published by . This book was released on 2011 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: The current research focuses on the analysis of discrete-time data arising from periodic follow-up using discrete-time hazard models (analogs to the Cox proportional hazards model) when the model is misspecified. We begin by providing scientific examples that motivate the present research and provide some background and notation that lays the foundation for the remainder of the dissertation. We then describe methods for analyzing grouped proportional hazards data, and present simulation results to convey their relative performances. Focusing on discrete hazard models for analyzing grouped survival data, we then explore the impact of model misspecification, namely a time-varying treatment effect, on the maximum likelihood (ML) estimator of commonly used discrete-time models in the two-sample setting (e.g., clinical trials). We show that the ML estimator is consistent to a quantity that depends on the censoring pattern of the observations and the maximum follow-up time of the study. We propose a censoring-robust estimator that removes the influence of censoring by re-weighing observations based on the inverse of the Kaplan-Meier estimator of the censoring times for each group and derive its asymptotic distribution. Simulation is used to compare the two estimators in different scenarios and the proposed estimator is applied to data from clinical trial in HIV/AIDS. Next, we describe how robust inference can be extended to the observational study setting where multiple (possibly continuous) covariates are involved. In this setting, we rely on survival trees to identify group-specific censoring to aid in the estimation of the censoring distribution. Finally, we explore the use of the censoring-robust estimator in an interim testing context that is typical of late stage clinical trials. To that end, we derive the joint asymptotic distribution of the censoring-robust estimator calculated over time. We note that the estimating equation of the censoring-robust estimator lacks an independent increments structure, rendering standard group sequential methods inapplicable. We then propose a strategy for designing and evaluating group sequential trials based on the censoring-robust estimator using existing pilot data.
Download or read book Modeling Survival Data Extending the Cox Model written by Terry M. Therneau and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is for statistical practitioners, particularly those who design and analyze studies for survival and event history data. Building on recent developments motivated by counting process and martingale theory, it shows the reader how to extend the Cox model to analyze multiple/correlated event data using marginal and random effects. The focus is on actual data examples, the analysis and interpretation of results, and computation. The book shows how these new methods can be implemented in SAS and S-Plus, including computer code, worked examples, and data sets.
Download or read book GOODNESS OF FIT TESTS AND ROBUST STATISTICAL INFERENCE FOR THE COX PROPORTIONAL HAZARDS MODEL written by DANYU LIN and published by . This book was released on 1989 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: However, the current statistical literature lacks convenient goodness-of-fit tests and robust methods for the general Cox method.
Download or read book Proportional Hazards Regression written by John O'Quigley and published by Springer Science & Business Media. This book was released on 2008-01-25 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: The place in survival analysis now occupied by proportional hazards models and their generalizations is so large that it is no longer conceivable to offer a course on the subject without devoting at least half of the content to this topic alone. This book focuses on the theory and applications of a very broad class of models – proportional hazards and non-proportional hazards models, the former being viewed as a special case of the latter – which underlie modern survival analysis. Researchers and students alike will find that this text differs from most recent works in that it is mostly concerned with methodological issues rather than the analysis itself.
Download or read book Frailty Models in Survival Analysis written by Andreas Wienke and published by CRC Press. This book was released on 2010-07-26 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of frailty offers a convenient way to introduce unobserved heterogeneity and associations into models for survival data. In its simplest form, frailty is an unobserved random proportionality factor that modifies the hazard function of an individual or a group of related individuals. Frailty Models in Survival Analysis presents a comprehensive overview of the fundamental approaches in the area of frailty models. The book extensively explores how univariate frailty models can represent unobserved heterogeneity. It also emphasizes correlated frailty models as extensions of univariate and shared frailty models. The author analyzes similarities and differences between frailty and copula models; discusses problems related to frailty models, such as tests for homogeneity; and describes parametric and semiparametric models using both frequentist and Bayesian approaches. He also shows how to apply the models to real data using the statistical packages of R, SAS, and Stata. The appendix provides the technical mathematical results used throughout. Written in nontechnical terms accessible to nonspecialists, this book explains the basic ideas in frailty modeling and statistical techniques, with a focus on real-world data application and interpretation of the results. By applying several models to the same data, it allows for the comparison of their advantages and limitations under varying model assumptions. The book also employs simulations to analyze the finite sample size performance of the models.
Download or read book The Cox Model and Its Applications written by Mikhail Nikulin and published by Springer. This book was released on 2016-04-11 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book will be of interest to readers active in the fields of survival analysis, genetics, ecology, biology, demography, reliability and quality control. Since Sir David Cox’s pioneering work in 1972, the proportional hazards model has become the most important model in survival analysis. The success of the Cox model stimulated further studies in semiparametric and nonparametric theories, counting process models, study designs in epidemiology, and the development of many other regression models that could offer more flexible or more suitable approaches in data analysis. Flexible semiparametric regression models are increasingly being used to relate lifetime distributions to time-dependent explanatory variables. Throughout the book, various recent statistical models are developed in close connection with specific data from experimental studies in clinical trials or from observational studies.
Download or read book R for Health Data Science written by Ewen Harrison and published by CRC Press. This book was released on 2020-12-31 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this age of information, the manipulation, analysis, and interpretation of data have become a fundamental part of professional life; nowhere more so than in the delivery of healthcare. From the understanding of disease and the development of new treatments, to the diagnosis and management of individual patients, the use of data and technology is now an integral part of the business of healthcare. Those working in healthcare interact daily with data, often without realising it. The conversion of this avalanche of information to useful knowledge is essential for high-quality patient care. R for Health Data Science includes everything a healthcare professional needs to go from R novice to R guru. By the end of this book, you will be taking a sophisticated approach to health data science with beautiful visualisations, elegant tables, and nuanced analyses. Features Provides an introduction to the fundamentals of R for healthcare professionals Highlights the most popular statistical approaches to health data science Written to be as accessible as possible with minimal mathematics Emphasises the importance of truly understanding the underlying data through the use of plots Includes numerous examples that can be adapted for your own data Helps you create publishable documents and collaborate across teams With this book, you are in safe hands – Prof. Harrison is a clinician and Dr. Pius is a data scientist, bringing 25 years’ combined experience of using R at the coal face. This content has been taught to hundreds of individuals from a variety of backgrounds, from rank beginners to experts moving to R from other platforms.
Download or read book Inference for the Proportional Hazards Model written by Ronghui Xu and published by . This book was released on 1996 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Cox Proportional Hazards Models for Modeling the Time to Onset of Decompression Sickness in Hypobaric Environments written by Laura A. Thompson and published by . This book was released on 2003 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Survival Analysis State of the Art written by John P. Klein and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Survival analysis is a highly active area of research with applications spanning the physical, engineering, biological, and social sciences. In addition to statisticians and biostatisticians, researchers in this area include epidemiologists, reliability engineers, demographers and economists. The economists survival analysis by the name of duration analysis and the analysis of transition data. We attempted to bring together leading researchers, with a common interest in developing methodology in survival analysis, at the NATO Advanced Research Workshop. The research works collected in this volume are based on the presentations at the Workshop. Analysis of survival experiments is complicated by issues of censoring, where only partial observation of an individual's life length is available and left truncation, where individuals enter the study group if their life lengths exceed a given threshold time. Application of the theory of counting processes to survival analysis, as developed by the Scandinavian School, has allowed for substantial advances in the procedures for analyzing such experiments. The increased use of computer intensive solutions to inference problems in survival analysis~ in both the classical and Bayesian settings, is also evident throughout the volume. Several areas of research have received special attention in the volume.
Download or read book Modeling Survival Data Using Frailty Models written by David D. Hanagal and published by Springer Nature. This book was released on 2019-11-16 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the basic concepts of survival analysis and frailty models, covering both fundamental and advanced topics. It focuses on applications of statistical tools in biology and medicine, highlighting the latest frailty-model methodologies and applications in these areas. After explaining the basic concepts of survival analysis, the book goes on to discuss shared, bivariate, and correlated frailty models and their applications. It also features nine datasets that have been analyzed using the R statistical package. Covering recent topics, not addressed elsewhere in the literature, this book is of immense use to scientists, researchers, students and teachers.
Download or read book Inference in the Cox Proportional Hazards Model with Missing Covariate Data written by Marian Glynis Pugh and published by . This book was released on 1993 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Study of the Robustness of Cox s Proportional Hazards Model Used in Testing for Covariate Effects written by Mingwei Fei and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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[less than or equal to]20) and censoring rate is high(p[greater then or equal to]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[greater than or equal to]50) and censoring rate is low(p[less than or equal to]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.
Download or read book Post selection Inference in Cox Proportional Hazards Models written by Carla Louw and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Variable selection causes the distributions of parameter estimators to be unknown and difficult to determine. To do inference after selection, conditional distributions for parameter estimators given the selected model are needed. Taylor and Tibshirani (2018) call this post-selection inference and describe an estimator of regression parameters along with the corresponding conditional distribution, making post-selection inference possible. The Polyhedral Lemma (Lee et al., 2016) is used to determine the conditional distribution of this estimator given the model selected - a truncated normal distribution. We implement Taylor and Tibshirani's (2018) method in the Cox Proportional Hazards Regression setting and do a Monte Carlo study. The results are analyzed. The method controls the level of tests and coverage of confidence intervals well - much better than unadjusted Cox Proportional Hazards techniques. Numerical difficulties in the Cox Proportional Hazards software are identified and addressed in the post-selection inference context.
Download or read book Survival Analysis and Causal Inference written by Denise Rava and published by . This book was released on 2021 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: In chapter 1 we study explained variation under the additive hazards regression model for right-censored data. We consider different approaches for developing such a measure, and focus on one that estimates the proportion of variation in the failure time explained by the covariates. We study the properties of the measure both analytically, and through extensive simulations. We apply the measure to a well-known survival dataset as well as the linked surveillance, epidemiology, and end results-Medicare database for prediction of mortality in early stage prostate cancer patients using high-dimensional claims codes. In chapter 2 we propose a new flexible method for survival prediction: DeepHazard, a neural network for time-varying risks. Prognostic models in survival analysis are aimed at understanding the relationship between patients' covariates and the distribution of survival time. Traditionally, semiparametric models, such as the Cox model, have been assumed. These often rely on strong proportionality assumptions of the hazard that might be violated in practice. Moreover, they do not often include covariates' information updated over time. Our approach is tailored for a wide range of continuous hazards forms, with the only restriction of being additive in time. A flexible implementation, allowing different optimization methods, along with any norm penalty, is developed. Numerical examples illustrate that our approach outperforms existing state-of-the-art methodology in terms of predictive capability evaluated through the C-index metric. The same is revealed on the popular real datasets as METABRIC, GBSG, ACTG and PBC. In chapter 3 we consider the conditional treatment effect for competing risks data in observational studies. While it is described as a constant difference between the hazard functions given the covariates, we do not assume the additive hazards model in order to adjust for the covariates. We derive the efficient score for the treatment effect using modern semiparametric theory, as well as two doubly robust scores with respect to both the assumed propensity score for treatment and the censoring model, and the outcome models for the competing risks. We provide the asymptotic distributions of the estimators when the two sets of working models are both correct, or when only one of them is correct. We study the inference based on these estimators using simulation. The estimators are applied to the data from a cohort of Japanese men in Hawaii followed since 1960s in order to study the effect of midlife drinking behavior on late life cognitive outcomes. In chapter 4 we consider doubly robust estimation of the causal hazard ratio in observational studies. The treatment effect of interest, described as the constant ratio between the hazard functions of thetwo potential outcomes, is parametrized by the Marginal Structural Cox Model. Under the assumption of no unmeasured confounders, causal methods, as Cox-IPW, have been developed for estimation of the treatment effect of interest. However no doubly robust methods have been proposed under the Marginal Structural Cox model. We develop an AIPW estimator for this popular model that is both model and rate-doubly robust with respect to the treatment assignment model and the conditional outcome model. The proposed estimator is applied to the data from a cohort of Japanese men in Hawaii followed since 1960s in order to study the effect of mid-life alcohol exposure on overall death.
