Multiple imputation for simple estimation of the hazard function based on interval censored data

A data augmentation algorithm is presented for estimating the hazard function and pointwise variability intervals based on interval censored data. The algorithm extends that proposed by Tanner and Wong for grouped right censored data to interval censored data. It applies multiple imputation and local likelihood methods to obtain smooth non-parametric estimates for the hazard function. This approach considerably simplifies the problem of estimation for interval censored data as it transforms it into the more tractable problem of estimation for right censored data. The method is illustrated for two real data sets: times to breast cosmesis deterioration and times to HIV-1 infection for individuals with haemophilia. Simulations are presented to assess the effects of various parameters on the estimates and their variances.