Complete case logistic regression with a dichotomised continuous outcome led to biased estimates

Objectives: To investigate whether a complete case logistic regression gives a biased estimate of the exposure odds ratio (OR) if miss-ingness depends on a continuous outcome, but a binary version is used for analysis; to examine whether any bias could be reduced by including a misclassified form of the incomplete outcome as an auxiliary variable in multiple imputation (MI).Study Design and Setting: Analytical investigation, simulation study, and data from a UK cohort.Results: There was bias in the exposure OR when the probability of being a complete case was independently associated with the expo-sure and (continuous) outcome but this was generally small unless the association with the outcome was strong. Where exposure and (continuous) outcome interacted in their effect on this probability, the bias was large, particularly at high levels of missing data. Inclusion of the auxiliary variable resulted in important bias reductions when this had high sensitivity and specificity.Conclusion: The robustness of logistic regression to missing data is not maintained when the outcome is a binary version of an underlying contin-uous measure, but the bias will be small unless the association between the continuous outcome and missingness is strong. (c) 2022 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

This study investigated the bias in exposure odds ratio (OR) estimation when using complete case logistic regression with a binary outcome that depends on a continuous outcome. The inclusion of a misclassified form of the incomplete outcome as an auxiliary variable in multiple imputation was also examined for bias reduction. The results showed that there was bias in the exposure OR, especially when the association between the continuous outcome and missingness was strong. The inclusion of the auxiliary variable helped reduce bias, particularly when it had high sensitivity and specificity.