To choose a missing data method, judge why the values are missing: every method assumes a reason. Complete-case analysis and multiple imputation are defensible when their assumptions are plausible; last observation carried forward, mean imputation and missing indicators are not valid in general. Justify your assumption, then use a sensitivity analysis to test whether the conclusion survives a different one.
CONSORT 2025 item 21c asks how missing data were handled in a trial, and STROBE item 12(c) asks the same of observational studies. Counting missing values in each group, with reasons, is covered in how to write the Results section of a clinical paper.
Missing data mechanisms: MCAR, MAR and MNAR in plain words
The classification goes back to Rubin (1976). It describes how missing values relate to observed ones, not how many are missing.
| Mechanism | What it means | Invented example |
|---|---|---|
| Missing completely at random (MCAR) | No systematic difference between the missing values and the observed ones | A freezer fault destroys a random batch of samples |
| Missing at random (MAR) | Any systematic difference is explained by observed data; it does not mean "random" | Older patients miss more visits, age is recorded, and within each age group the missing scores resemble the observed ones |
| Missing not at random (MNAR) | Systematic differences remain after the observed data are taken into account | Patients whose pain worsens stop returning questionnaires, and nothing recorded predicts it |
No test can show that data are MAR, because the values that would settle it are the ones you lack. Sterne and colleagues' 2009 paper calls missing at random "an assumption that justifies the analysis, not a property of the data". Record why each value is missing: the evidence is indirect. An administrative reason, such as a cancelled clinic, makes MAR more plausible; an unrecorded reason linked to worsening disease makes it less plausible.
When complete-case analysis is defensible, and what it costs
Complete-case analysis uses only the participants with every analysis variable recorded. It can be biased, and discarding incomplete records costs precision whenever they carry information about the question.
Complete-case analysis can be unbiased even when data are not MCAR (Hughes and colleagues, 2019). For most regression models, it is unbiased when the chance of being a complete case does not depend on the outcome once the model's covariates are taken into account. If only a once-measured outcome is missing and no auxiliary variables exist, imputation adds no information, and complete-case analysis is the better choice. For a small chart review, stating Hughes and colleagues' condition in the Methods, with the reason it is plausible, is what can justify the complete-case reply in ten statistical reviewer comments, decoded.
In a randomised trial, excluding any randomised participant means the analysis is no longer strictly intention-to-treat, as the CONSORT 2025 flow diagram guide explains.
Why last observation carried forward, mean imputation and missing indicators are not valid in general
Single imputation fills each gap with one value and analyses it as if measured, so standard errors are usually too small. Sterne and colleagues conclude that mean imputation, a missing-category indicator and carrying the last value forward are not statistically valid in general.
Last observation carried forward (LOCF) assumes the outcome stops changing when a participant leaves, which the CONSORT 2025 explanation and elaboration says "will rarely be valid". Nor is LOCF reliably conservative: depending on the disease course and the timing of dropout, it can bias a result either way, including in favour of a new treatment. A US National Research Council panel advised against single imputation as the primary approach unless its assumptions are scientifically justified.
A missing indicator, a "missing" category added to a variable, is valid for missing baseline covariates in a randomised trial but typically biased in non-randomised studies. Used as a confounder in an adjusted model, a "Not recorded" category becomes the missing-indicator method. Keeping "not documented" apart from "not present" is covered in writing the Methods for a retrospective chart review.
What a multiple imputation model must contain
Multiple imputation fills each gap with several plausible values drawn from a model of the observed data, analyses each completed dataset, and pools the results with Rubin's rules, whose standard error combines the uncertainty within each dataset with the variation between datasets. It is valid under MAR only if the imputation model is right, so check four things.
- The outcome, even when only covariates are imputed. Leaving it out can weaken the associations you estimate.
- Every analysis variable and interaction.
- Auxiliary variables: variables outside the analysis model that predict the missing values or who is missing, such as an earlier outcome measurement. They can reduce bias and improve precision.
- Suitable forms. Transform skewed variables or use predictive mean matching, and say how categorical variables were imputed.
The number of imputations is guidance, not a rule. Sterne and colleagues say at least 20 "may be preferable"; White, Royston and Wood (2011) proposed at least as many imputations as the percentage of incomplete cases. Under MNAR, multiple imputation can be as biased as a complete-case analysis, or more. Involve a statistician where you can, and report the complete-case result beside the imputed one.
Test the conclusion with a delta-adjusted or tipping-point analysis
Every analysis of incomplete data rests on assumptions the data cannot verify, so test the primary analysis with one that changes the assumption. A second method that also assumes MAR, such as a mixed model beside multiple imputation, does not count.
In a delta-adjusted analysis, you impute under MAR, then shift the imputed values by an amount, δ, so participants with missing data do worse, or better, than similar observed ones. δ = 0 is the MAR analysis. A tipping-point analysis increases δ until the conclusion changes, then asks whether that δ is clinically plausible. Cro and colleagues' practical guide cautions against tipping-point analyses when no careful thought has been given to which values of δ are plausible. Best-case and worst-case imputation suits a few missing binary outcomes, as in reporting a diagnostic accuracy study with STARD 2015.
Pre-specify the primary and sensitivity analyses, ideally in a registered protocol and certainly before unblinded data are seen. Agreement between them is reassuring, not proof. Box 8 of the CONSORT 2025 explanation and elaboration asks for at least a summary of the sensitivity analyses in the main paper, with full results in the supplement.
A decision table: situation, defensible method, what to write
Match your situation to a row; the last column is what your Methods should state. Repeated measures, clustering and complex imputation models still need a statistician.
| Situation | Defensible primary method | What to write |
|---|---|---|
| Values lost for a reason unrelated to any variable | Complete-case analysis | The reason, and that the loss costs precision but is not expected to cause bias |
| Only a once-measured outcome missing; no auxiliary variables | Complete-case analysis, adjusting for predictors of missingness | That being a complete case does not depend on the outcome given the covariates, and why that is plausible |
| Covariates missing, or auxiliary variables available | Multiple imputation under MAR | Model contents, number of imputations, complete-case comparison |
| Repeated outcome measurements with dropout | Multiple imputation or a likelihood-based mixed model; LOCF only if its assumption is justified | The MAR assumption and why it is plausible |
| Missing baseline covariates in a randomised trial | Missing-indicator method or multiple imputation | That they are baseline covariates in a randomised comparison |
| Missing confounders in an observational study | Multiple imputation, or complete-case analysis if its condition holds; not a missing category | Which confounders had gaps, and why the assumption is plausible |
| Recorded reasons suggest MNAR, such as dropout after worsening symptoms | The most plausible stated assumption, plus delta-adjusted or tipping-point analyses | The δ range agreed in advance, and the tipping point |
| Treatment stopped, but the outcome can still be measured | Not missing data: keep measuring | Discontinuation and withdrawal reported separately, as the International Council for Harmonisation (ICH) E9(R1) addendum distinguishes them |
| The value cannot exist, such as quality of life after death | Not missing data: define its handling in advance | How data truncated by death were handled |
Template Methods sentences for a missing data paragraph
These sentences expand the single missing-data slot in the statistical analysis template of how to write the Methods section; keep the ones that match your method. The last one belongs in the Discussion.
Assumption. [variable] was missing for [n] of [N] participants ([%]), mainly because [reasons]. We assumed the data were missing at random given [observed variables], because [evidence].
Complete-case analysis. The primary analysis included the [n] participants with complete data. This is unbiased if being a complete case does not depend on [outcome] once [covariates] are accounted for, which we considered plausible because [reason].
Multiple imputation. [variables] were imputed by [method] in [software and version], using every analysis variable, the outcome, [interactions] and the auxiliary variables [list]. Estimates from [m] imputed datasets were pooled with Rubin's rules; complete-case results are reported for comparison.
Sensitivity analysis. Imputed values of [outcome] in [group] were shifted by δ from 0 to [value] [units] to find where [the conclusion] changed. Values up to [value] were judged plausible in [the statistical analysis plan, version and date].
Limitation (Discussion). Our estimates assume that missing [outcome] values were missing at random given [observed variables], which [recorded reasons or auxiliary variables] make [more or less] plausible. If participants with missing data in [group] had [worse or better] outcomes than similar observed participants, the [effect] would be [overestimated or underestimated].
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