Handling survival bias in proportional hazards models: A frailty approach

Survival bias is a potential problem when subjects are lost to follow-up, and this selection issue may arise in a wide range of biomedical studies. Controlling for the bias is difficult because subjects may be lost due to unmeasured factors. This article presents a two-step method that adjusts for survival bias in the proportional hazards model, even when unmeasured factors influence survival. First, we fit a standard Cox proportional hazards model to estimate a naive marginal hazard ratio. Then, this estimate is adjusted to account for survival bias. The approach is based on frailty theory, and the unobserved risk factors are assumed to follow a parametric distribution in the population. Importantly, we are able to estimate the parameters of this distribution using published, real-life data on familial risks. An approach that is valid for instrumental variable analysis with proportional hazard models is also presented. Finally, these methods are applied to real data in a crude example, assessing the effect of alcohol on mortality. ∗Corresponding author. Email: [email protected] 1 ar X iv :1 70 1. 06 01 4v 4 [ st at .M E ] 1 A ug 2 01 7