Joint modelling of pre-randomisation event counts and multiple post-randomisation survival times with cure rates: application to data for early epilepsy and single seizures

Abstract

In this paper, we consider the analysis of recurrent event data that examines the differences between two treatments. The outcomes that are considered in the analysis are the pre-randomisation event count and post-randomisation times to first and second events with associated cure fractions. We develop methods that allow pre-randomisation counts and two post-randomisation survival times to be jointly modelled under a Poisson process framework, assuming that outcomes are predicted by (unobserved) event rates. We apply these methods to data that examine the difference between immediate and deferred treatment policies in patients presenting with single seizures or early epilepsy. We find evidence to suggest that post-randomisation seizure rates change at randomisation and following a first seizure after randomisation. We also find that there are cure rates associated with the post-randomisation times to first and second seizures. The increase in power over standard survival techniques, offered by the joint models that we propose, resulted in more precise estimates of the treatment effect and the ability to detect interactions with covariate effects.

Keywords:

• epilepsy
• Poisson process
• proportion cured
• recurrent events
• survival analysis

Acknowledgements

The authors thank Tony Marson and David Chadwick for providing the MRC Multicentre Trial in Early Epilepsy and Single Seizures. The authors thank these investigators further for their additional advice. The authors also thank Karla Hemming for her statistical input in the early stages of the methodological development. J.K. Rogers would like to thank the Engineering and Physical Sciences Research Council for funding her PhD, which allowed this work to be carried out.