Statistical modelling of biomarkers incorporating non-proportional effects for survival data: with illustration by application to two residual risk models for predicting risk in early breast cancer

Abstract

Personalised medicine is replacing the one-drug-fits-all approach with many prognostic models incorporating biomarkers available for risk stratifying patients. Evidence has been emerging that the effects of biomarkers change over time and therefore violate the assumption of proportional hazards when performing Cox regression. Analysis using the Cox model when the assumptions are invalid can result in misleading conclusions. This thesis reviews existing approaches for the analysis of non-proportional effects with respect to survival data. A number of well-developed approaches were identified but to date their uptake in practice has been limited. There is a need for more widespread use of flexible modelling to move away from standard analysis using a Cox model when the assumption of proportional hazards is violated. Two novel approaches were applied to investigate the impact of follow-up duration on two residual risk models, IHC4 and Mammostrat, for predicting risk in early breast cancers using two studies with different lengths of follow up; the Edinburgh Breast Conservation Series (BCS) and the Tamoxifen versus Exemestane Adjuvant Multinational (TEAM) trial. Similar results were observed between the two approaches that were considered, the multivariable fractional polynomial time (MFPT) approach and Royston-Parmer flexible parametric models, with their respective advantages and disadvantages being discussed. The analyses identified a strong time-varying effect of IHC4 score with the prognostic effect of IHC4 score on time-to distant recurrence decreasing with increasing follow-up time. Mammostrat score identified a group of patients with an increased risk of distant recurrence over full follow-up in the TEAM and Edinburgh BCS cohorts. The results suggest a combined IHC4 and Mammostrat risk score could provide information on the risk of recurrence and warrants further study.