Missing data are a commonly occurring threat to the validity and efficiency of epidemiologic studies. Perhaps the most common approach to handling missing data is to simply drop those records with 1 or more missing values, in so-called "complete records" or "complete case" analysis. In this paper, we bring together earlier-derived yet perhaps now somewhat neglected results which show that a logistic regression complete records analysis can provide asymptotically unbiased estimates of the association of an exposure of interest with an outcome, adjusted for a number of confounders, under a surprisingly wide range of missing-data assumptions. We give detailed guidance describing how the observed data can be used to judge the plausibility of these assumptions. The results mean that in large epidemiologic studies which are affected by missing data and analyzed by logistic regression, exposure associations may be estimated without bias in a number of settings where researchers might otherwise assume that bias would occur.