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When the difference between treatments in a clinical trial is estimated by adifference in means, then it is well known that randomization ensures unbiassedestimation, even if no account is taken of important baseline covariates.However, when the treatment effect is assessed by other summaries, e.g. by anodds ratio if the outcome is binary, then bias can arise if some covariates areomitted, regardless of the use of randomization for treatment allocation or thesize of the trial. We present accurate closed-form approximations for thisasymptotic bias when important Normally distributed covariates are omitted froma logistic regression. We compare this approximation with ones in theliterature and derive more convenient forms for some of these existing results.The expressions give insight into the form of the bias, which simulations showis usable for distributions other than the Normal. The key result applies evenwhen there are additional binary covariates in the model.

Inconsistent treatment estimates from mis-specified logistic regression analyses of randomized trials