Survival extrapolation in the presence of cause specific hazards

Health economic evaluations require estimates of expected survival from patients receiving different interventions, often over a lifetime. However, data on the patients of interest are typically only available for a much shorter follow‐up time, from randomised trials or cohorts. Previous work showed how to use general population mortality to improve extrapolations of the short‐term data, assuming a constant additive or multiplicative effect on the hazards for all‐cause mortality for study patients relative to the general population. A more plausible assumption may be a constant effect on the hazard for the specific cause of death targeted by the treatments. To address this problem, we use independent parametric survival models for cause‐specific mortality among the general population. Because causes of death are unobserved for the patients of interest, a polyhazard model is used to express their all‐cause mortality as a sum of latent cause‐specific hazards. Assuming proportional cause‐specific hazards between the general and study populations then allows us to extrapolate mortality of the patients of interest to the long term. A Bayesian framework is used to jointly model all sources of data. By simulation, we show that ignoring cause‐specific hazards leads to biased estimates of mean survival when the proportion of deaths due to the cause of interest changes through time. The methods are applied to an evaluation of implantable cardioverter defibrillators for the prevention of sudden cardiac death among patients with cardiac arrhythmia. After accounting for cause‐specific mortality, substantial differences are seen in estimates of life years gained from implantable cardioverter defibrillators. © 2014 The Authors Statistics in Medicine Published by John Wiley & Sons Ltd.