= Solution
Treat the extra measurements as <auxiliary variables for multiple imputation>. Include alcohol consumption and disease history as predictors in both the $C$ and $P$ <conditional distributions>, together with age, sex and the other incomplete response. If these auxiliary variables themselves have missing entries, give them appropriate models and update them within the same <multiple imputation by chained equations> sweeps. Preserve observed entries throughout.
\b[Useful auxiliary measurements can improve predictions, precision and the plausibility of missing at random.] Their association with the missing responses reduces uncertainty in the imputed values; association with nonresponse may explain some selection that otherwise depends on unobserved values. This can reduce <selection bias> under the enlarged <missing at random> model and reduce between-imputation <variance>. It does not guarantee elimination of <missing not at random> dependence. They need not be added to the final substantive <logistic regression> merely because they help imputation: the final analysis should still estimate its intended association.
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