Abstract: This study of right truncated data was motivated by problems in which individuals can experience two events in time and where the distribution of the time between events, the lag, is of interest. If individuals come under observation at the occurrence of the second event and the time of the first event is retrospectively ascertained, the observed lags are right truncated. Two examples from data on AIDS and HIV infection are considered.
Regression models are specified which lead to simple tests and esti mation of covariate effects based on right truncated data. The regression models are simply expressed in terms of a reverse time hazard function in both the discrete and continuous cases. In the continuous case, the proportional hazards model for the reverse time yields a power model for the c.d.f. and a simple parameter interpretation. A complementary log-log link in the discrete case admits the same interpretation. Inference techniques based on the full likelihood in the discrete case or the partial likelihood in the continuous case are developed and illustrated in the two examples mentioned above.
Key words and phrases: Truncated data, reverse time hazards, regression models for truncated data.