Precision of estimators in interval censored parametric survival models

Recently, several advances have been made in the analysis of interval censored (IC) data mainly in relation to semi-parametric proportional hazard (PH) models (Gómez et al., 2009, Lesaffre et al., 2005). It is arguable, however, that the parametric case has been somewhat neglected, overall, and that more can be learned, especially in relation to non-PH models. Accordingly, we focus on simple parametric models for interval censored survival data arising in longitudinal RCTs. For the exponential regression model we compare the performance of a general likelihood with commonly used proxy likelihoods, which ignore the interval censoring by treating the interval censored times to events as if they were exact. We show analytically that use of proxy likelihoods leads to estimators which are artificially precise and we quantify the extent of the resulting biases in a simulation study and by analyzing real data. We also compare the likelihoods using non-PH models and obtain different findings.