Frailty and Bias Under Cox’s Model

Oregon Convention Center 

Nonproportionality can come from various sources under the Cox's model, and it is well known that omission of a balancing yet unobservable covariate could be one such cause. The nonproportionality could introduce a substantial bias in the main effect estimate in the model. The unobservable nonproportionality-inducing covariate could be a biomarker positivity, an overlooked binary stratification factor, or a continuous covariate as a strong prognostic factor whose distributions are also unbalanced between treatment groups. Frailty models have been utilized to derive the optimal weights for the weighted log-rank tests and also to quantify the bias in the estimators under Cox's model. We revisit the relevant literature on the topic of the frailty model and bias in the hazard ratio, extend the existing results, and propose a remedy to correct the bias partially.

Bias

Proportional hazards model

Gamma frailty

Hazard ratio

Two-point frailty 

Lifetime Data Science Section