Survival Analysis

Survival analysis is crucial in many fields, including biomedical research, actuarial science, reliability analysis, business and customer analytics, econometrics, and social science. It has witnessed significant advancements in recent decades. However, most of this progress remains in scattered theoretical and applied publications, often focusing on exploratory analysis rather than the design and analysis of clinical trials. Non-proportional hazards are less well addressed. Competing risks are frequently overlooked, and the counting process approach often remains a mystery to many practitioners. Consequently, these critical topics are often not well understood or thoroughly analyzed.

Survival Analysis: Principles and Applications in Clinical Trials and Beyond aims to address these gaps. It provides an up-to-date and reader-friendly account of topics, progressing from the log-rank test, stratified analysis, and Cox regression to more advanced analyses. Heuristic arguments are used, leaving rigorous results to the appendices. The book dedicates separate chapters to topics such as clinical trials basics, modeling and analysis for non-proportional hazards, testing and summarizing treatment effects, trial design and interim monitoring, and the analysis of terminal and non-terminal events. A separate chapter is also devoted to detailed martingale heuristics beyond what is typically offered in other texts. Furthermore, a new contribution to recurrent event analysis is the rigorous formulations of marginal models and an exploration of related properties for statistical applications. The often overlooked one- and two-sample cases are also discussed.

This book provides an exposition of both the theory and practical applications of survival analysis, covering traditional topics and more recent advancements. It illustrates the methods with real world data, discussing the strengths and limitations of various approaches, and emphasizing modeling assumptions and interpretations. The three appendices offer overviews of modern analytic frameworks pivotal for understanding and developing challenging yet vital statistical solutions. R packages are also available for newer methods. It is an up-to-date, critical and accessible textbook for graduate students and researchers across industry, government, or academia that will enhance their understanding of complex topics, boosting their confidence in exploring different methods and interpreting the findings. It also encourages a critical evaluation of current literature and motivates the readers to develop new research ideas.

Key Features: Emphasis on model interpretations and comparison of different methods Intuitive explanations and heuristic derivation of the methods Real large trial data applications and R packages for newer methodologies Inclusion of more recently researched topics Modern analytical methods applied to rigorous asymptotics for key problems (in appendices)