ABSTRACT
The setting for this chapter is time-to-event data in clinical studies, with discrete categorical responses and covariates observed for individual subjects at fixed or grouped discrete times. The topics covered in the chapter fall under the heading of longitudinal data, but that term covers a much broader array of data structures, including data observed irregularly at different times for different individuals, where responses may themselves be repeated quantitative measurements not restricted to occurrence times for clinical endpoints. For broader coverage of repeated measurements over time, we refer the reader elsewhere: for categorical regression models
(both generalized-linear and loglinear) to Refs. [1,2]; for longitudinal-linear and generalized-linear models (GLMs) to Refs. [3,4]; for repeated measures and panel data models to Refs. [5]; for ordinal and nominal data regression topics to Ref. [6]; and for categorical-response models with specifically time series flavor to Ref. [7]. The literature on each of these topics is large, with extensive ramifications in the social sciences. The restrictions of scope in this chapter-to discrete times, categorical responses mostly from GLMs and possibly with random effects-are imposed in the interest of manageable length and a unified parametric theoretical framework in a biostatistical context. The focus on explanatory and likelihood-based models enables us also to treat goodness-of-fit topics and model criticism. Covariate measurements within this framework may be discrete or continuous, and the data structures are allowed to have possibly time-dependent covariates, multiple responses per subject, and general patterns of censoring. Texts and monographs which can serve as general references for the topics
covered here include Refs. [3,4,8]. There seems to be no text which has drawn together the longitudinal-data methods specifically applicable to time-to-event modeling, although perhaps Ref. [8] is closest to having done so.
