Goodness-of-Fit Testing for a Regression Model With a Doubly Truncated Response

In survival analysis and epidemiology, among other fields, interval sampling is often employed. With interval sampling, the individuals undergoing the event of interest within a calendar time interval are recruited. This results in doubly truncated event times. Double truncation, which may appear with other sampling designs too, induces a selection bias, so ordinary statistical methods are generally inconsistent. In this paper, we introduce goodness-of-fit procedures for a regression model when the response variable is doubly truncated. With this purpose, a marked empirical process based on weighted residuals is constructed and its weak convergence is established. Kolmogorov-Smirnov- and Cramér-von Mises-type tests are consequently derived from such core process, and a bootstrap approximation for their practical implementation is given. The performance of the proposed tests is investigated through simulations. An application to model selection for AIDS incubation time as depending on age at infection is provided.