A Tutorial on Statistical Models Based on Counting Processes

TL;DR

This paper provides a comprehensive tutorial on statistical models based on counting processes, covering foundational theories, key methods, and extensions in survival analysis relevant to epidemiology and clinical research.

Contribution

It offers an in-depth review of core results and methods in survival analysis, including extensions beyond classical frameworks, serving as a valuable educational resource.

Findings

Discusses consistency, asymptotic normality, bias, and variance estimation in survival models.

Explores semi-Markov models and Turnbull's estimator outside classical counting process frameworks.

Connects survival analysis techniques to practical epidemiological applications.

Abstract

Since the famous paper written by Kaplan and Meier in 1958, survival analysis has become one of the most important fields in statistics. Nowadays it is one of the most important statistical tools in analyzing epidemiological and clinical data including COVID-19 pandemic. This article reviews some of the most celebrated and important results and methods, including consistency, asymptotic normality, bias and variance estimation, in survival analysis and the treatment is parallel to the monograph Statistical Models Based on Counting Processes. Other models and results such as semi-Markov models and the Turnbull's estimator that jump out of the classical counting process martingale framework are also discussed.