Regression Model Fitting for the Interval Censored 1 Responses

In the interval censored case 1 data, an event occurrence time is unobservable, but one observes an inspection time and whether the event has occurred prior to this time or not. Such data is also known as the interval censored case 1 data. It is of interest to assess the effect of a covariate on the event occurrence time variable. This note constructs tests for fitting a class of parametric regression models to the regression function of the log of the event occurrence time variable when the data are interval censored case 1 and when the error distribution is known. These tests are based on a certain martingale transform of a marked empirical process. They are asymptotically distribution free in the sense that their asymptotic null distributions neither depends on the null model nor on any of the distributions of the covariate, the inspection time or error variables. However, the test statistic itself depends on the error distribution. Some simulation studies assessing some finite sample level and power behavior of some of the proposed tests are also given.