Dynamic inference in general nested case-control designs

Nested case-control designs are attractive in studies with a time-to-event endpoint if the outcome is rare or if interest lies in evaluating expensive covariates. The appeal is that these designs restrict to small subsets of all patients at risk just prior to the observed event times. Only these small subsets need to be evaluated. Typically, the controls are selected at random and methods for time-simultaneous inference have been proposed in the literature. However, the martingale structure behind nested case-control designs allows for more powerful and flexible non-standard sampling designs. We exploit that structure to find simultaneous confidence bands based on wild bootstrap resampling procedures within this general class of designs. We show in a simulation study that the intended coverage probability is obtained for confidence bands for cumulative baseline hazard functions. We apply our methods to observational data about hospital-acquired infections.