Estimating correlation between time-to-event outcomes using counting process martingales

Music City Center 

In the setting where individual subjects have time-to-event data for multiple events, estimating the correlation between the times to these events can be challenging in the presence of right censoring. Standard association measures such as linear correlation cannot be estimated when not all failure times are observed. In order to allow for the estimation of correlation between event times we propose the use of counting process martingales indexed by time. This method can be used even in the presence of right censoring. In order to highlight the utility of this method we use data from hospitalized patients who are determined to be at risk for deterioration. In this case researchers are interested in the correlation between the time to certain actions such as the ordering of labs or giving medication. However, because not all actions are taken for every patient standard techniques are not possible. We highlight how using counting process martingales can be useful in this scenario, and discuss the different ways that this method can be used depending on the type of censoring.

Survival analysis

Correlation

Martingales

Censoring

Cumulative hazard

Counting process 

Biometrics Section