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

Area of Science:

• Biostatistics
• Epidemiology
• Statistical Modeling

Background:

• Logistic regression is widely used for binary outcomes.
• Missing data can introduce bias in statistical analyses.
• The impact of outcome-dependent missingness on logistic regression requires careful consideration.

Purpose of the Study:

• To assess bias in exposure odds ratios (OR) from complete case logistic regression when missingness depends on a continuous outcome, analyzed as binary.
• To evaluate the effectiveness of using a misclassified auxiliary outcome variable in multiple imputation (MI) for bias reduction.

Main Methods:

• Analytical investigation of bias mechanisms.
• Simulation studies to quantify bias under various missingness scenarios.
• Analysis of data from a UK cohort study.

Main Results:

• Bias in exposure OR was observed when missingness depended on exposure and the continuous outcome, generally small unless the outcome association was strong.
• Significant bias occurred when exposure and continuous outcome interacted in influencing missingness, especially with high missing data.
• Incorporating an auxiliary variable in MI substantially reduced bias when it possessed high sensitivity and specificity.

Conclusions:

• The robustness of logistic regression to missing data is compromised when a binary outcome represents an underlying continuous measure.
• Bias is typically small unless the association between the continuous outcome and missingness is strong.
• Multiple imputation with a well-chosen auxiliary variable can mitigate bias in such scenarios.