Panel Count Data Regression with Informative Observation Times

When patients are monitored for potentially recurrent events such as infections or tumor metastases, it is common for clinicians to ask patients to come back sooner for follow-ups based on the results of the most recent exam. This means that subjects' observation times will be irregular and related to subject-specific factors. Previously proposed methods for handling such panel count data assume that the dependence between the events process and the observation time process is governed by time-independent factors. This article considers situations where the observation times are predicted by time-varying factors such as the outcome observed at the last visit or cumulative exposure. Using a joint modelling approach, we propose a class of inverse-intensity-rate-ratio weighted estimators that are root-n consistent and asymptotically normal. The proposed estimators use estimating equations and are fairly simple and easy to compute. We demonstrate the performance of the method using simulated data and illustrate the approach using a cancer study dataset.