Recurrent Events with Competing Risks

Specialeforsvar ved Sofie Korn

Titel: Recurrent Events with Competing Risks

Abstract: In this thesis, we study methods for modelling recurrent events when a competing risk is present. It is often seen that the occurrence of the event, being for instance cancer tumours or heart attacks, involves an elevated risk of experiencing a competing event, such as death, which excludes further events from happening. We, therefore, study methods which allow for dependence between the recurrent events and the competing event.
We have focused on marginal models for the mean recurrence frequency, which is defined as the mean of the cumulative number of recurrent events over time. Both a non-parametric estimator (Cook & Lawless 1997) and a regression model (Ghosh & Lin 2002) are discussed. These two models make no assumptions on the dependence structure among the recurrent events or between the recurrent and the competing events.
They are thus applicable in situations where the recurrent events and the competing event are dependent. Furthermore, a regression model via pseudo-observations computed from the non-parametric estimator is proposed.
We implement the models in R and show that both the multiplicative means model and the model based on pseudo-observations are able to provide unbiased estimates of a covariate effect on the mean frequency function. We find, that the two models show similar performance when the sample sizes are not too small. Moreover, by investigating the asymptotic distribution of pseudo-obser-vations, we are able to suggest a method for performing joint inference. This is of interest when a covariate effects both the recurrent event and the competing event processes.
We found that the proposed methods are useful for analysing data of recurrent events with competing risks and we used the models to analyse a clinical trial of stage I bladder cancer tumours. Applying the models to the data enables us to analyse the effect of thiotepa treatment on the recurrence rate of the bladder tumours. We found, that patients receiving thiotepa treatment experience fewer tumour recurrences on average and that the treatment does not have a significant effect on the survival of the patients.
More generally, this study suggests that the proposed methods may have a wide range of applicability, as it enables us to analyse the direct effect on the event recurrence frequency, even if the recurrent event and a competing event are dependent.

Vejledere: Susanne Ditlevsen,
                   Per Kragh Andersen, Institut for Folkesundhed
Censor:     Søren Andersen, Novo