Competing Risks Models with Two Time Scales

Angela Carollo , Max Planck Institute for Demographic Research
Hein Putter, Leiden University Medical Center
Paul Eilers, Erasmus Medical Centre, Rotterdam
Jutta Gampe, Max Planck Institute for Demographic Research

Competing risks models can involve more than one time scale. A relevant example is the study of mortality after a cancer diagnosis, where time since diagnosis but also age may jointly determine the cause-specific hazards of death. Here death due to cancer and other causes of death are the competing risks. Another example is transition out of non-marital cohabitation where age of the individual and duration of cohabitation both are relevant time scales. Here the competing risk are transition to marriage or separation. Multiple time scales have rarely been explored in the context of competing events. Here, we propose a model in which the cause-specific hazards vary smoothly over two times scales. It is estimated by two-dimensional P-splines, exploiting the equivalence between hazard smoothing and Poisson regression. The data are arranged on a grid so that we can make use of generalized linear array models for efficient computations. As a motivating example we analyse mortality after a breast cancer diagnosis and we distinguish between death due to breast cancer and all other causes of death. The time scales are age and time since diagnosis. We use data from the Surveillance, Epidemiology and End Results (SEER) program. In the SEER data, age at diagnosis is provided with a last open-ended category, leading to coarsly grouped data. We use the two-dimensional penalised composite link model to ungroup the data before applying the competing risks model with two time scales.

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 Presented in Session 96. Modelling and Forecasting Mortality