Modeling Discrete Time-to-Event Data by Gerhard Tutz and Matthias Schmid (review)

This work deals primarily with analysis of survival data when a discrete-time scale is used. Books on this type of data usually draw on a more general continuous data framework and tested and confirmed models (for example, Cox’s proportional hazard model). However, in many cases, particularly in the social sciences, data are collected and observed discretely.

The authors review the main types of processing classically used in survival analysis (exploratory data analysis, regression models), providing a broad panorama of conceptual schemata, including multiple outcomes models (analyses of different exits from unemployment, for example) and repeated events models (the birth of a new child in fertility histories, for example). They also mention methodologies seldom presented in connection with this type of data: algorithmic segmentation techniques (CART models) and variable selection machine learning techniques (boosting).

Chapter 1 presents the main concepts and several data sets that use the discrete framework and lists the advantages of methodologies developed for it: the tied events problem that arises with several proportional hazards models, use of the general linear model, simplified interpretation of the hazard ratio (instantaneous risk).

Chapter 2 discusses widely used nonparametric types of analysis, length-of-stay tables and Kaplan-Meier analyses. The mathematic formulas are clearly explained, as are the indicators selected from demographic length-of-stay tables. Bibliographical references, functions, and packages to use with R programs are included after each section, together with exercises that apply the chapter’s main concepts.

Chapter 3 reviews the different types of regression models, each applied to an example, and discusses them critically. It includes a comparison with the continuous framework, together with discussions on using the Cox model. The case of time-varying covariates is also discussed in detail. But it is surprising to see no reference here to Paul D. Allison’s work.

Chapter 4, a comprehensive continuation of Chapter 3, presents various tools for testing predictor significance or a model’s predictive performance. Chapter 5 further extends this presentation, applying more complex models whose effect on risk predictors may not be linear.

Chapter 6 raises the question of possible interactions between predictor variables and introduces segmentation techniques (regression trees, CART method) for processing survival data collected in discrete time. Various result stabilization techniques (bagging, random forests) are explained and adapted to survival data. Chapter 7 discusses the question of variable selection (lasso method, boosting).

Competing risks models are analyzed in Chapter 8 (for example, analysis of unemployment periods that end with a full- or part-time job), as well as the use of multinomial logit models. This important chapter could have been more fully developed, given how often the questions it addresses arise in the analyses.

The last chapter takes up the question of unobserved heterogeneity and extends fragility models to discrete cases. The book concludes with a presentation of mixed effects and Cure models. The latter are used in situations where a part of the population will never undergo the event; they therefore account more effectively for asymptotes in survival functions curves.

The book seems to me quite complete, though some sections could have been developed in greater depth. It is a precious resource for all social science practitioners who need to process censored, retrospective or prospective longitudinal data for which only measurements in discrete time are available. And the included discSurv R-package, which uses the book’s functions and practice data sets, is very useful.