Inference based on imputed failure times for the proportional hazards model with interval-censored data

We propose an approach to the proportional hazards model for interval-censored data in which parameter estimates are obtained by solving estimating equations that are the partial likelihood score equations for the full-data proportional hazards model, averaged over all rankings of imputed failure times consistent with the observed censoring intervals. Imputed failure times are generated using a parametric estimate of the baseline distribution; the parameters of the baseline distribution are estimated simultaneously with the proportional hazards regression parameters. Although a parametric form for the baseline distribution must be specified, simulation studies show that the method performs well even when the baseline distribution is misspecified. The estimating equations are solved using Monte Carlo techniques. We present a recursive stochastic approximation scheme that converges to the zero of the estimating equations; the solution has a random error that is asymptotically normally distributed with a variance-covariance matrix that can itself be estimated recursively.