ABSTRACT
This chapter discusses methods that aim to relax the assumptions in various ways, and to test the agreement between model assumptions and available data. Consider the same independent and identically distributed setup with generalizations to allow the second phase selection rates to be time-dependent during cohort follow-up, and to include a multivariate failure time outcome. The procedures just sketched would allow hazard ratio estimation for a broad class of univariate or multivariate sampling designs. One of the earliest cohort sampling designs, so-called nested case–control sampling, involves selecting a specified number of controls who were without prior failure or censoring, at each uncensored failure time in a study cohort, for a univariate failure time variable. The statistical literature on relaxing the assumptions is mostly restricted to univariate failure times. The chapter outlines extensions of the methods for the estimation of marginal single and double failure hazard rates.
