Effect of an event occurring over time and confounded by health status: estimation and interpretation. A study based on survival data simulations with application on breast cancer

Abstract

Estimating the prognostic effect of a time-dependent covariate could be tricky using a classical Cox model, despite adjustment on other known prognostic factors. This study evaluated and compared the performance of a Cox model including the covariate occurring over time as a time-dependent covariate and the so-called 'illness-death' multistate model, which is usually used to describe event-history data. We assess breast cancer prognosis related to a subsequent pregnancy occurring over time after cancer treatment in young women. We generated simulations. We considered constant and time-varying prognostic hazard ratios ( HR(t)) between patients undergoing the intermediate event and those who did not. We used both the classical Cox model and the multistate model to estimate the prognostic effect of the intermediate event HR(t). We also used the latter to estimate the covariate effect on each transition (exp(β(ij) )), thus helping to interpret HR(t) by taking into account the disease history. We applied these approaches to a female cohort treated and followed up in eight French Hospitals since 1990.