Dissertation

Statistical analysis of time-to-event data with multiple time scales

Abstract

The occurrence of events over time can often be recorded over more than one time scale. Processes that involve multiple time scales are commonly found in medical and epidemiological studies but also in socio-demographic studies of the life course. For example, in a clinical follow-up of cancer patients, the occurrence of the event death can be analysed over time since diagnosis of the cancer, over time since treatment, or over age. As time scales serve as proxies for underlying mechanisms causing the events of interest, each of these time scales represents a different pathway to the event, for example the cumulative negative effect of the cancer on the body, or the changing capacity of the body to withstand disease load. Classical statistical models for the analysis of time-to-event data require the selection of one time scale over which the occurrence of events can be described. Whenever researchers are confronted with problems involving more than one time scale, they often opt for solutions that either require selection of one main time scale for the analysis, or account for the effects of multiple time scales in non-flexible ways. This thesis offers an approach to incorporate multiple time scales in the analysis of time-to-event data. Specifically, hazard surfaces can be modeled over two time scales simultaneously by using two-dimensional P -splines. The approach is extended to allow for covariates’ effects on the baseline hazard in a proportional hazards model, and to analyse time-to-event data with competing risks. Finally, a statistical software program is provided that implements the described approach.