The abcs of nest survival : Theory and application from a biostatistical perspective

We consider how nest-survival studies fit into the theory and methods that have been developed for the biostatistical analysis of survival data. In this framework, the appropriate view of nest failure is that of a continuous time process which may be observed only periodically. The timing of study entry and subsequent observations, as well as assumptions about the underlying continuous time process, uniquely determines the appropriate analysis via the data likelihood. We describe how continuous-time hazard-function models form a natural basis for this approach. Nonparametric and parametric approaches are presented, but we focus primarily on the middle ground of weakly structured approaches and how they can be performed with software such as SAS PROC NLMIXED. The hazard function approach leads to complementary log-log (cloglog) link survival models, also known as discrete proportional-hazards models. We show that cloglog models have a close connection to the logistic-exposure and related models, and hence these models share similar desirable properties. We raise some cautions about the application of random effects, or frailty, models to nest-survival studies, and suggest directions that software development might take.