Multiple imputation
What question does this help answer?
“How can we use partially observed data without pretending the missing values are known or automatically discarding every incomplete record?”
When to use it
Multiple imputation is often useful when important covariates or outcomes are missing and the missing-data assumptions are more plausible after conditioning on observed information.
When not to use it
Do not treat multiple imputation as a universal fix. The imputation model must match the data structure and scientific analysis, and missing-not-at-random mechanisms may require sensitivity analyses.
How it works in plain language
Instead of filling in one “best guess,” multiple imputation creates several plausible completed datasets. The substantive analysis is performed in each one, and estimates are combined so between-imputation uncertainty contributes to the final standard error.
What the imputation flow looks like
Why Mallard may recommend it
Mallard may recommend multiple imputation when complete-case analysis would discard substantial information or plausibly introduce selection bias.
Key assumptions and requirements
- The imputation model includes variables that predict missingness and the incomplete values.
- The imputation model is compatible enough with the substantive analysis.
- The number of imputations is sufficient.
- Complex structures such as clustering, interactions, nonlinear terms, and longitudinal data are handled appropriately.
- Missing-data assumptions are made explicit.
Combining the results: Rubin's rules
The estimates from the imputed datasets are combined by Rubin's rules. The combined estimate is the average of the estimates. Its variance adds two parts: the average of the variances within each dataset, and the variance of the estimates between datasets, inflated slightly for the finite number of imputations. The between-imputation part is what carries the uncertainty about the missing values, and it is why analysing a single imputed dataset gives standard errors that are too small. Pool on a scale where the estimate is roughly normal, such as log odds ratios or log hazard ratios, then transform back. Tests and intervals use degrees of freedom that reflect how much information is missing, with the Barnard-Rubin correction when the complete-data sample is small. The rules only pool; whether the result is valid depends on the imputation model being compatible with the analysis model. That means it contains every variable the analysis uses, the outcome included: an imputation model that leaves the outcome out imputes covariate values unrelated to it, which tends to bias their associations with the outcome toward no effect.
What to watch out for
Single mean imputation generally understates uncertainty. Multiple imputation does not make missing data harmless, and its validity depends on modeling and assumptions.
Clinical example
Impute missing baseline laboratory values before estimating an adjusted treatment-outcome association, then pool estimates across imputed datasets.
- Multiple imputation for missing data in epidemiological and clinical research: potential and pitfalls (opens in a new tab) · BMJ · doi 10.1136/bmj.b2393
- Missing Data in Clinical Research: A Tutorial on Multiple Imputation (opens in a new tab) · Can J Cardiol · doi 10.1016/j.cjca.2020.11.010
- Multiple imputation using chained equations: Issues and guidance for practice (opens in a new tab) · Stat Med · doi 10.1002/sim.4067