The Book

Likelihood Methods in Survival Analysis

With R Examples

Jun Ma, Annabel Webb and Harold Malcolm Hudson

Chapman & Hall/CRC Biostatistics Series, 1st edition, 2024. Boca Raton: Chapman and Hall/CRC.

• DOI: 10.1201/9781351109710
• ISBN (ebook): 9781351109710
• Publisher page: taylorfrancis.com

survivalMPL is the reference implementation of the maximum penalised likelihood (MPL) methods developed in this book. Where the book explains why the baseline hazard can be estimated jointly with the regression coefficients, and how the non-negativity constraints and the smoothing parameter are handled, the package provides the fitting machinery: coxph_mpl(), the basis functions for $h_0$, and the inference built on top of them.

What the book covers

The book develops likelihood-based survival analysis from first principles and then works through the penalised likelihood approach that this package implements:

• likelihoods for right-, left- and interval-censored data, and for left truncation;
• the Cox model estimated by penalised full likelihood rather than partial likelihood, with the baseline hazard expanded in non-negative basis functions;
• constrained optimisation under $\boldsymbol{\theta} \geq \mathbf{0}$, and automatic selection of the smoothing parameter;
• asymptotic results and variance estimators for the constrained estimates;
• stratified Cox models, checking the proportional hazards assumption, and extensions including time-varying covariates and competing risks;
• worked R examples throughout, several of which appear in these articles.

Where the articles follow the book

Article	Book material
Interval Censoring	Chapter 2 examples on partly interval-censored data, including the pseudo-melanoma recurrence study
Right Censoring	The residual and proportional hazards diagnostics of Section 5.2.1
Basis Functions for the Baseline Hazard	The definitions of the uniform, Gaussian, M-spline and Epanechnikov bases and their roughness penalties
Comparing coxph() and coxph_mpl()	The comparison between partial and penalised full likelihood estimation

Citing the book

@book{MaWebbHudson2024,
  author    = {Ma, Jun and Webb, Annabel and Hudson, Harold Malcolm},
  title     = {Likelihood Methods in Survival Analysis: With {R} Examples},
  year      = {2024},
  publisher = {Chapman and Hall/{CRC}},
  address   = {Boca Raton},
  edition   = {1st},
  isbn      = {9781351109710},
  doi       = {10.1201/9781351109710}
}

The underlying paper

The right-censored case, including the sandwich variance estimator reported by summary() as M2HM2, is developed in:

Ma, J., Heritier, S. and Lo, S. N. (2014). On the maximum penalised likelihood approach for proportional hazard models with right censored survival data. Computational Statistics & Data Analysis 74, 142-156. DOI: 10.1016/j.csda.2014.01.005