Abstract
The accelerated failure time model presents a way to easily describe and interpret survival regression data. We assume, that each observed unit ages internally faster or slower, depending on the covariate values.
It is desirable to check if observed data fit the model assumptions, therefore we present a goodness-of-fit testing procedure based on modern martingale theory. We work with the generalized model introduced in Cox & Oakes (1984) and studied in Lin & Ying (1995), which allows for covariates that change through time.
We focus on particular important situations where time-varying covariates are used, such as when an additional factor is added during the observation or when the influence of one covariate gradually increases. On simulated data we estimate the empirical properties of the test.