Applying the Cox proportional hazards model for analysis of latency data with interval censoring

The latency time of an infectious disease is defined as the time from infection to disease onset. This paper applies the proportional hazards model to estimate the effect of covariates on latency when the time of disease onset is exact or right-censored but the time of infection is interval-censored. We use a Monte Carlo EM algorithm to estimate parameters of the joint distribution of infection times and latency times. At each EM iteration, exact infection times are multiply imputed from the density determined by the parameters of the infection and latency time distributions. The methodology is tested using a simulation study and is applied to data from a cohort of haemophiliacs with HIV disease.