title: Inconsistent treatment estimates from mis-specified logistic regression analyses of randomized trials.
abstract: When the difference between treatments in a clinical trial is estimated by a difference in means, then it is well known that randomization ensures unbiassed estimation, even if no account is taken of important baseline covariates. However, when the treatment effect is assessed by other summaries, for example by an odds ratio if the outcome is binary, then bias can arise if some covariates are omitted, regardless of the use of randomization for treatment allocation or the size of the trial. We present accurate closed-form approximations for this asymptotic bias when important normally distributed covariates are omitted from a logistic regression. We compare this approximation with ones in the literature and derive more convenient forms for some of these existing results. The expressions give insight into the form of the bias, which simulations show is usable for distributions other than the normal. The key result applies even when there are additional binary covariates in the model.
authors: School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne, U.K.
authors: J N S
authors: JN
authors: Matthews
authors: Statistics Department, Benghazi University, Benghazi, Libya.
authors: N H
authors: NH
authors: Badi
mesh_terms: D000704:Analysis of Variance; D015982:Bias; D006801:Humans; D016015:Logistic Models; D016032:Randomized Controlled Trials as Topic / Q000379:methods / Q000706:statistics & numerical data*; D012107:Research Design / Q000706:statistics & numerical data*; D016008:Statistical Distributions
keywords: asymptotic bias; baseline values; logistic regression; probit regression; randomized clinical trial