Instrumental variable estimation for duration data

In this article we focus on time-to-event studies with a randomised treatment assignment that may be compromised by selective compliance. Contrary to most of the extensive literature on evaluation studies we do not consider the effect of the treatment on some average outcome but on the hazard rate. In time-to-event studies the treatment may vary over time. Another complication of duration data is that they are usually heavy censored. Censoring limits the observation period, but is not a feature of the treatment program. Therefore, a natural choice is to relate the treatment to the hazard rate. We show that even if the compliance is selective, we can still use the randomisation to estimate the impact of the program corrected for selective compliance on the hazard. The only requirement is that participation in the program is affected by a variable that is not correlated with the baseline duration. We develop an Instrumental Variable estimation procedure for the Generalized Accelerated Failure Time (GAFT) model. The GAFT model is a duration data model that encompasses two competing approaches to such data; the (Mixed) Proportional Hazard (MPH) model and the Accelerated Failure Time (AFT) model. We discuss the large sample properties of this Instrumental Linear Rank Estimation and show how we can improve its efficiency. The estimator is used to re-analyze the data from the Illinois unemployment bonus experiment.