Proportional hazards model for interval-censored failure times and time-dependent covariates: application to hazard of HIV infection of injecting drug users in prison

Interval-censored survival data are data in which the failure times are not known precisely, but are known to lie within an interval. Such data can be analysed using a proportional hazards model with piecewise exponential baseline hazard, a model which can be fitted by an EM algorithm easily programmed in standard statistical software. In this paper we extend the model to allow for time-dependent covariates and left-truncation, and demonstrate its use by assessing the effect of imprisonment on hazard of HIV infection in a cohort of injecting drug users from Edinburgh. No conclusive effect of incarceration on hazard of HIV infection was found, but there was a suggestion that imprisonment might have been a significant relative risk factor for infection in the later period, when risk behaviour among drug users in the community was reduced. Copyright (C) 2001 John Wiley & Sons, Ltd.