Random-effects regression analysis of correlated grouped-time survival data

Random-effects regression modelling is proposed for analysis of correlated grouped-time survival data. Two analysis approaches are considered. The first treats survival time as an ordinal outcome, which is either right-censored or not. The second approach treats survival time as a set of dichotomous indicators of whether the event occurred for time periods up to the period of the event or censor. For either approach both proportional hazards and proportional odds versions of the random-effects model are developed, while partial proportional hazards and odds generalizations are described for the latter approach. For estimation, a full-information maximum marginal likelihood solution is implemented using numerical quadrature to integrate over the distribution of multiple random effects. The quadrature solution allows some flexibility in the choice of distributions for the random effects; both normal and rectangular distributions are considered in this article. An analysis of a dataset where students are clustered within schools is used to illustrate features of random-effects analysis of clustered grouped-time survival data.