  Interval censoring arises frequently in clinical, epidemiological, financial,
and sociological studies, where the event or failure of interest is known only
to occur within an interval induced by periodic monitoring. We formulate the
effects of potentially time-dependent covariates on the interval-censored
failure time through a broad class of semiparametric transformation models that
encompasses proportional hazards and proportional odds models. We consider
nonparametric maximum likelihood estimation for this class of models with an
arbitrary number of monitoring times for each subject. We devise an EM-type
algorithm that converges stably, even in the presence of time-dependent
covariates, and show that the estimators for the regression parameters are
consistent, asymptotically normal, and asymptotically efficient with an easily
estimated covariance matrix. Finally, we demonstrate the performance of our
procedures through extensive simulation studies and application to an HIV/AIDS
study conducted in Thailand.
