A quantitative study of the bias in estimating the treatment effect caused by omitting a balanced covariate in survival models

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Abstract
This paper discusses the quantitative aspects of bias in estimates of treatment effect in survival models when there is failure to adjust on balanced prognostic variables. A simple numerical example of this bias is given along with approximate formulae for its calculation in the multiplicative exponential survival model. The accuracy of the formulae is checked by simulation. In addition, approximate calculations and simulations of power loss and the effects of omitting more than one prognostic covariate are presented. The Weibull and Cox models are also examined using simulation. Study of this bias is pertinent to much applied work, and shows that the effect of omitting balanced covariates can be modest unless the variables are strongly prognostic or many in number. This work emphasizes the need for thorough comparisons of adjusted and unadjusted analyses for sensible interpretation of treatment effects.