1st Edition

Likelihood Methods in Survival Analysis With R Examples

By Jun Ma, Malcolm Hudson, Annabel Webb Copyright 2025
    404 Pages 38 B/W Illustrations
    by Chapman & Hall

    Many conventional survival analysis methods, such as the Kaplan-Meier method for survival function estimation and the partial likelihood method for Cox model regression coefficients estimation, were developed under the assumption that survival times are subject to right censoring only. However, in practice, survival time observations may include interval-censored data, especially when the exact time of the event of interest cannot be observed. When interval-censored observations are present in a survival dataset, one generally needs to consider likelihood-based methods for inference. If the survival model under consideration is fully parametric, then likelihood-based methods impose neither theoretical nor computational challenges. However, if the model is semi-parametric, there will be difficulties in both theoretical and computational aspects.

    Likelihood Methods in Survival Analysis: With R Examples explores these challenges and provides practical solutions. It not only covers conventional Cox models where survival times are subject to interval censoring, but also extends to more complicated models, such as stratified Cox models, extended Cox models where time-varying covariates are present, mixture cure Cox models, and Cox models with dependent right censoring. The book also discusses non-Cox models, particularly the additive hazards model and parametric log-linear models for bivariate survival times where there is dependence among competing outcomes.


    • Provides a broad and accessible overview of likelihood methods in survival analysis
    • Covers a wide range of data types and models, from the semi-parametric Cox model with interval censoring through to parametric survival models for competing risks
    • Includes many examples using real data to illustrate the methods
    • Includes integrated R code for implementation of the methods
    • Supplemented by a GitHub repository with datasets and R code

    The book will make an ideal reference for researchers and graduate students of biostatistics, statistics, and data science, whose interest in survival analysis extends beyond applications. It offers useful and solid training to those who wish to enhance their knowledge in the methodology and computational aspects of biostatistics.


    1. Introduction
    2. Semi-Parametric Cox Model with Interval Censoring
    3. Extension to Include Truncation
    4. Extension to Include a Cured Fraction
    5. Stratified Cox Models under Interval Censoring
    6. Cox Models with Time-Varying Covariates under Right Censoring
    7. Copula Cox Models for Dependent Right Censoring
    8. Additive Hazards Model
    9. Parametric Survival Models for Competing Risks Data


    Jun Ma, School of Mathematical and Physical Sciences, Macquarie University, North Ryde, Australia

    Annabel Webb, School of Mathematical and Physical Sciences, Macquarie University, North Ryde, Australia

    Malcolm Hudson, School of Mathematical and Physical Sciences, Macquarie University & NHMRC Clinical Trial Centre, University of Sydney, Sydney, Australia