Missing Data

Missing Data

Missing data are values needed for an analysis that were not observed or are unavailable in the dataset being used. They can affect a clinical outcome, cost, covariate, date or even whether a person enters the recorded population. This page identifies what is missing, explains assumptions about why, and shows how the assumptions change an estimate and its uncertainty.

Find the missingness before choosing a method

Begin with a clear analysis population and a variable-by-time inventory. A blank value may mean a test was not ordered, a participant stopped answering, care occurred elsewhere, a code was not captured or the value genuinely does not apply. Those possibilities have different meanings and should not all be recoded as zero.

Pattern	Example	Why it matters
Missing outcome	A participant's follow-up quality-of-life score is unavailable.	The treatment effect may differ among people without follow-up.
Missing covariate	Disease severity was not recorded for some people.	Adjustment and eligibility definitions may change.
Intermittent missingness	A middle visit is absent but later visits exist.	Longitudinal methods can use observed neighbouring information under assumptions.
Dropout	Measurements cease after a particular visit.	Reasons for stopping may predict later outcomes.
Unobserved care	A patient attends another provider outside the dataset.	An apparent absence of treatment or events may be incomplete coverage.

Report counts and percentages by treatment group, variable and time, along with known reasons and the characteristics of people with and without data. Prevent avoidable losses through careful collection and follow-up before relying on statistical repair. Define the intended treatment effect or other estimand, including how events such as treatment discontinuation are handled, before calling a value “missing.”

What MCAR, MAR and MNAR actually assume

The mechanism concerns the probability that a value is missing, conditional on information available in the study. Missing completely at random (MCAR) means missingness is unrelated to observed and unobserved values relevant to the analysis. Missing at random (MAR) permits dependence on observed information, but after conditioning on suitable observed variables, missingness does not additionally depend on the missing value itself. Missing not at random (MNAR) describes remaining dependence on the unobserved value or another inadequately accounted-for factor.

Assumption	Illustrative story	Implication
MCAR	A random equipment failure deletes some measurements independently of patient status.	Complete cases may be unbiased for certain estimands but lose precision.
MAR, conditional on observed data	Follow-up is less likely among people with a recorded prior poor score, and that prior score adequately explains the dependence.	A correctly specified method can use observed predictors to account for missingness.
MNAR relative to available data	People with an unobserved worsening outcome are less likely to return even after accounting for recorded history.	The missing values cannot be identified from observed data alone without extra assumptions or evidence.

These labels are relative to which variables are actually observed and included in an analysis. They cannot generally be established by a simple test of the recorded values, because the missing outcomes themselves are unseen. MCAR is a strong assumption; MAR is not the same as random dropout, and MNAR sensitivity analysis asks what follows if MAR is wrong.

See how the observed denominator can mislead

Consider a fictional trial with 100 participants assigned to each of two groups. In the intervention group, outcomes are observed for 80 people, of whom 40 succeed; in control, outcomes are observed for 90 people, of whom 36 succeed. The complete-case success rates are $40/80=0.50$ and $36/90=0.40$, an observed-data difference of 10 percentage points.

There are 20 missing intervention outcomes and 10 missing control outcomes. If every missing intervention outcome were a failure and every missing control outcome a success, the full-group difference would be $40/100-46/100=-0.06$. Under the opposite extreme, it would be $60/100-36/100=0.24$. These extreme assignments are transparent bounds for this binary outcome, not plausible estimates of what actually happened.

Calculation	Intervention	Control	Difference, intervention minus control
Observed cases only	40/80 = 50%	36/90 = 40%	+10 percentage points.
Adverse extreme for intervention	40/100 = 40%	46/100 = 46%	-6 percentage points.
Favourable extreme for intervention	60/100 = 60%	36/100 = 36%	+24 percentage points.

The wide range exposes how much the unobserved outcomes could matter without assigning a mechanism. It does not imply that all missing patients would succeed or fail. If the analysis target is a different estimand, such as success while remaining on treatment, define it carefully rather than silently changing denominators.

Select an analysis tied to defensible assumptions

Complete-case analysis discards incomplete records and can lose precision or introduce bias when missingness relates to outcomes or predictors. Multiple imputation draws several plausible replacements conditional on an imputation model, analyses each completed dataset and combines estimates with uncertainty from missingness. A single filled-in value or mean replacement generally understates uncertainty and may distort associations.

Likelihood-based longitudinal models and inverse-probability weighting may be useful under their respective modelling and positivity assumptions. Include variables predictive of missingness and the missing value, preserve the substantive model's structure, and avoid using information unavailable at the decision point if that would contaminate an applied prediction. The correct method depends on the estimand, data structure and plausible mechanism; no method can recover information that was never collected without assumptions.

Sensitivity analysis should vary assumptions not identified by the observed data. A pattern-mixture approach might lower imputed outcomes for participants who dropped out by a clinically meaningful amount; a tipping-point analysis finds how large a departure would change the conclusion. State the size and direction of the departure, its clinical rationale and the effect on both point estimates and uncertainty.

Consequences for health-economic models

Missing costs and health outcomes may be correlated, and complete cases can exclude people with complex, high-cost care. Imputation or joint modelling should respect skewed costs, bounded utilities, structural zero costs and longitudinal timing where relevant. A model built from observed data should carry uncertainty and plausible missingness-related bias through to incremental costs and effects rather than treating an imputed spreadsheet as fully observed truth.

If people leave an electronic record system, the absence of a later admission may mean no admission or care outside the system. Linkage, follow-up checks and alternative data sources can reduce that ambiguity. Explicitly examine how the economic conclusion changes under plausible missing cost, quality-of-life and event scenarios.

• Define the estimand: Identify which outcomes and post-treatment events the analysis intends to represent.
• Describe the pattern: Report missingness by group, variable, time and known reason.
• Avoid automatic zeros: An unrecorded cost or event is not necessarily zero.
• Preserve uncertainty: Multiple imputation requires repeated datasets and appropriate combining rules.
• Test departures: A MAR-based primary analysis should be accompanied by relevant MNAR sensitivity analyses when missingness could change the decision.
• State limits: No statistical procedure alone proves the missing-data mechanism or restores inaccessible care.

Sources and further reading

The Sterne and colleagues paper on multiple imputation explains assumptions, bias and practical pitfalls, while CONSORT reporting guidance specifies transparent reporting of missing trial data. A methodological paper on missing outcome data in trials connects the analysis to the target treatment effect, and a controlled multiple-imputation tutorial illustrates sensitivity analysis. The trial numbers and extreme assignments above are original teaching examples.