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Multiple imputation
Understand the model, recognise it in a stem, separate the look-alikes, then apply it.
Start with the mental model
If a fifth of a trial's participants have a missing follow-up score, what should the analysis do with the gap? Simply dropping them loses information and can biasA systematic error that skews a study's results away from the truth in a particular direction.Read more → the result; filling each gap with a single guessed value (such as the group's average) pretends the analysis knows the true value exactly, which understates how uncertain the result really is. Multiple imputation (MI) is a statistical technique that fills each missing value not once but many times, with a different plausible value each time, so the final result honestly reflects the real uncertainty created by the missing data. For example, imagine a depression trial where several participants dropped out before their final rating scale was recorded. In practice, this means multiple imputation produces several complete versions of the dataset, each with slightly different plausible values standing in for the missing scores, rather than one single 'best guess' dataset.
01Core model
Multiple imputation works in three steps. First, the imputation step generates several (commonly at least five, often more) complete datasets, each filling in the missing values with plausible values drawn from a statistical model built on the relationships between the observed variables, most commonly using an approach called multiple imputation by chained equations (MICE), which imputes each variable in turn conditional on the others. Second, the analysis step runs the planned statistical analysis separately on each of these completed datasets, producing a slightly different estimate and standard error from each one, because each dataset filled the gaps with different plausible values. Third, the pooling step combines the separate estimates into one overall result using Rubin's rules, which average the point estimates and combine two sources of variance: the average within-imputation variance (the usual sampling uncertainty) and the between-imputation variance (how much the estimate itself changed depending on which plausible values were imputed). This second, between-imputation term is exactly the extra uncertainty that a single-imputation method discards, which is why multiple imputation produces a wider, more honest confidence interval than filling the gap once. The approach's standard justification depends on the missing data being missing at random (MAR): that the probability of a value being missing depends only on other observed variables in the dataset, not on the unobserved value itself.