Local likelihood analysis of survival data with censored intermediate events

AIDS Clinical Trials Group protocol 193A was a randomized trial designed to compare survival and progression-free survival among patients on different treatment regimens. A complicating feature of the analysis of progression-free survival is that different censoring mechanisms operated on progression and survival, which resulted in more complete information on survival. A simple analysis that uses the minimum of the times to progression and survival and the minimum of the corresponding censoring times may sacrifice the extra information available on survival. To address this problem, we have developed a method that exploits the bivariate nature of these data and thereby uses all of the available information. We obtain smooth, nonparametric estimates of the hazard functions for a terminal event, before and after the occurrence of an intermediate event. These hazards can be used to estimate the distribution of progression-free survival. Our method uses local likelihood estimation, which assumes that the underlying true hazard functions can be approximated locally by polynomials. We use an iterative imputation algorithm to perform the estimation when the intermediate events are right censored.