= Solution
Ordinary <multiple imputation by chained equations> relies on <missing at random>, conditional on the variables included in its models, together with adequate model specification and suitable <conditional distributions>. For <Bayesian inference> that ignores the response mechanism, the usual sufficient condition also includes <distinct parameters> for data and missingness models, with an appropriately separate prior.
\b[The suspected dependence on withheld responses makes the usual missing-at-random assumption doubtful.] An accurately fitted observed-data model cannot, on its own, establish what the nonresponders would have reported. Use substantive judgement and <sensitivity analysis> under plausible <missing not at random> departures, for example a <pattern-mixture sensitivity analysis> shifting the imputed condom <log odds> or partner-count distribution relative to the observed-data prediction. Report how the final association changes. Additional informative measurements may make <missing at random> more credible, but cannot verify it.
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