Missing Data in Statistical Analysis: Delete, Impute, or Model?
Missing data can reduce precision and bias estimates. The correct response depends on the reason values are missing, the information observed about that reason, and the model used to answer the research question.
Start with the missingness process
Three labels organize assumptions:
- Missing completely at random, or MCAR: missingness does not depend on observed or unobserved data in the analysis context.
- Missing at random, or MAR: after conditioning on observed information, missingness does not depend on the missing value itself.
- Missing not at random, or MNAR: missingness still depends on unobserved information after conditioning on observed data.
These mechanisms are assumptions about a process, not properties proven by one significance test.
Describe the pattern before choosing a method
Report missing counts and percentages by variable, important groups, site, and time. Examine whether variables are missing together and whether observed characteristics predict missingness. Distinguish not applicable, skipped, refused, lost to follow-up, and technical failure.
Your data-cleaning checklist should preserve these categories rather than collapsing every code into a generic blank.
Complete-case analysis
Complete-case analysis uses observations with all variables required by the model. It is transparent and may be appropriate under defensible conditions, but it can discard substantial information and may be biased when inclusion in the complete sample is related to the outcome.
Always report how many observations entered each analysis. Compare included and excluded records on relevant observed variables.
Single imputation
Replacing a missing value with a mean, median, last observation, or one predicted value is simple but often understates uncertainty and distorts relationships. It may be useful for limited operational preprocessing or specific validated algorithms, but it is generally not a default inferential solution.
Multiple imputation
Multiple imputation creates several completed datasets, analyzes each using the planned model, and pools estimates and uncertainty. A defensible imputation model should include variables in the analysis, predictors of missingness, and useful predictors of the incomplete values.
Compatibility matters. Respect variable types, bounds, interactions, nonlinearities, clustering, repeated measures, and the analysis model. More imputations do not repair a poorly specified model.
Model-based approaches
Likelihood-based mixed models, survival models, and other methods may use partially observed records under specific assumptions. These approaches do not make missingness irrelevant. The analyst still must state the assumptions and investigate departures from them.
Sensitivity analysis for MNAR concerns
When the conclusion could change under plausible departures from MAR, use a sensitivity analysis. Examples include delta adjustments, pattern-mixture models, selection models, tipping-point analyses, or clearly defined best and worst cases.
The goal is not to prove the assumption. It is to show how much the conclusion depends on it.
A practical decision sequence
- Define the estimand and primary model.
- Describe missingness and reasons.
- Identify variables related to missingness and incomplete values.
- Evaluate complete-case consequences.
- Select an imputation or model-based approach compatible with the design.
- Validate distributions and relationships after processing.
- Run sensitivity analyses.
- Report the number analyzed, assumptions, software, settings, and pooled results.
What to report
Include missing amounts and patterns, reasons when known, assumptions, method, variables in the imputation model, number of imputations, diagnostics, pooling rules, complete-case comparison, sensitivity analyses, and any difference in conclusions.
Use the DataStatPro analysis index to match the completed dataset with the planned statistical procedure. Do not let a software default silently define the missing-data strategy.
Frequently asked questions
How much missing data is acceptable?
There is no universal percentage. Impact depends on the mechanism, pattern, variables affected, model, sample size, and information available to address missingness.
Is mean imputation acceptable?
It is usually unsuitable as a default inferential method because it can reduce variability and distort associations while ignoring imputation uncertainty.
Does multiple imputation require MAR?
Standard multiple-imputation analyses commonly rely on an MAR assumption conditional on included information. Sensitivity analysis can examine plausible departures.
Should I impute the outcome variable?
The answer depends on the estimand, design, imputation model, analysis method, and missingness process. Do not apply a universal rule without methodological justification.