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

Abstract

The occurrence of events over time is analyzed by means of survival and event history models, and time is a key component of these models. Time can often be recorded over more than one time scale.

For example, in a clinical follow-up of cancer patients, the occurrence of the event death can be analyzed over time since diagnosis of the cancer, over time since treatment, or over age. Processes that involve multiple time scales are commonly found in medical and epidemiological studies but also in socio-demographic studies of the life course. Classical statistical models for the analysis of time-to-event data are limited in the way the effect of more than one time scale is investigated.

In this thesis, a statistical model that incorporates simultaneously multiple time scales in the analysis of time-to-event data is proposed. The model is also complemented by a statistical software, that promotes its use in applied research.

The proposed model is used to analyze mortality data of cancer patients, as well as transitions from non-marital cohabitation to marriage or separation. The results show how the proposed approach can identify diverse interplays between the time scales.