Bounds for the regression parameters in dependently censored survival models

We propose a semiparametric model to study the effect of covariates on the distribution of a censored event time while making minimal assumptions about the censoring mechanism. The result is a partially identified model, in the sense that we obtain bounds on the covariate effects, which are allowed to be time-dependent. Moreover, these bounds can be interpreted as classical confidence intervals and are obtained by aggregating information in the conditional Peterson bounds over the entire covariate space. As a special case, our approach can be used to study the popular Cox proportional hazards model while leaving the censoring distribution as well as its dependence with the time of interest completely unspecified. A simulation study illustrates good finite sample performance of the method, and several data applications in both economics and medicine demonstrate its practicability on real data. All developed methodology is implemented in R and made available in the package depCensoring.