We present an excess risk regression model for matched cohort data, where the occurrence of some events for individuals with a disease is compared to that of healthy controls that are matched at the onset-of-disease by various factors. By using the matched structure, we show how to estimate the excess risk and its dependence on covariates on both proportional and additive form. We remove the individual effects on background mortality related to matching factors by considering differences. The model handles two different time scales, namely attained age and follow-up time. First, we solve estimating equations for the non-parametric and parametric components of the excess risk model, providing large sample properties for the suggested estimators. Next, we report results from a simulation study. Lastly, we describe an application of the method on childhood cancer data, to study the excess risk of cardiovascular events in adults' life among childhood cancer survivors.
Keywords: Aalen's model; Cox's model; counting process; excess risk model; matched cohort data; multiple time scales.