### Department of Biostatistics Seminar/Workshop Series

# Survival Estimation for a Composite Outcome When Ascertainment of Events Is Delayed

## T. Charles Casper

### PhD Candidate, Department of Statistics

University of Wisconsin

### Wednesday, February 13, 1:30-2:30pm, MRBIII Conference Room 1220

### Intended Audience: Persons interested in applied statistics, statistical theory, epidemiology, health services research, clinical trials methodology, statistical computing, statistical graphics, R users or potential users

In many large clinical trials there are delays between the time at which events occur and the time at which they are reported. The Kaplan--Meier estimator is inconsistent in these circumstances. We will briefly discuss existing methods for estimating survival in the single-event setting with reporting delays. When events of interest are of multiple types or recurrent in nature, the data structure is fundamentally different from that assumed by existing methods. Survival analysis for the composite outcome of time to first event is particularly difficult. This is due the fact that events may not be reported in the order in which they occur. I propose several new estimators that can be used in this setting. The approach taken is to consider first the entire recurrent-event process and then assume a relationship between this process and the first-event process. We will examine the results of a series of simulations comparing the new estimators to each other, to existing estimators for delay data, and to the Kaplan-Meier estimator. We will also calculate some of these quantities using data from TNT, a clinical trial in which there were delays and the data structure violated the assumptions of existing methods.