Missing Data Mechanisms: MCAR, MAR, and MNAR
How to classify missingness under Rubin's taxonomy, why mean imputation distorts variance, and when Multiple Imputation (MICE) is appropriate.
In this lesson you will learn
- 1Distinguish Missing Completely at Random (MCAR), Missing at Random (MAR), and Missing Not at Random (MNAR) in clinical cohorts.
- 2Explain why simple Mean Imputation artificially shrinks standard deviations and inflates Type I error rates.
- 3Evaluate how Attrition Bias arises when non-responding or toxic patients drop out and are excluded via complete-case deletion.
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Donald Rubin's Missingness Framework (1976)
This section explains Rubin's three missingness mechanisms (MCAR, MAR, MNAR) and compares Listwise Deletion, Mean Imputation, and Multiple Imputation (MICE).
Deleting patients who dropped out due to worsening symptoms (MNAR) biases your trial towards making an ineffective or toxic treatment look beneficial.
When evaluating a clinical manuscript, peer reviewers examine how missing observations were handled. Simply dropping incomplete rows (Complete Case Analysis) or plugging in the column average (Mean Imputation) can severely distort conclusions:
- MCAR (Missing Completely at Random): A blood tube is accidentally dropped in the lab. Missingness is independent of patient health. Complete-case analysis remains unbiased, though it loses sample power.
- MAR (Missing at Random): Older participants are less likely to attend a non-mandatory follow-up clinic, and
Ageis recorded for everyone. Because observed covariates explain the missingness pattern, Multiple Imputation by Chained Equations (MICE) produces unbiased estimates and preserves standard errors. - MNAR (Missing Not at Random): Participants experiencing severe drug toxicity or lack of efficacy withdraw from the trial. Deleting their rows causes Attrition Bias.
Missing Data Mechanism & Attrition Bias Simulator
True treatment effect across all 10 enrolled patients is an 18.0 mmHg drop in systolic BP
Under MNAR, the 4 non-responding patients dropped out, inflating the apparent BP reduction from 18.0 to 24.0 mmHg (+6.0 mmHg false benefit). Intention-to-Treat (ITT) and sensitivity models are required.
Clinical Example
An antihypertensive trial enrols 100 patients (true mean SBP drop = 18.0 mmHg). Twenty non-responding patients drop out before Week 12.
Interpretation: Analysing only the 80 completers inflates the apparent blood-pressure reduction by 5.0 mmHg. CONSORT guidelines require reporting all 20 dropouts and performing Intention-to-Treat sensitivity analyses.
Common Pitfall
Replacing missing biomarker cells with the column mean (Single Mean Imputation), which artificially collapses variance and produces falsely small p-values.
Key takeaways
- 1Missing Completely at Random (MCAR) means missingness is unrelated to any observed or unobserved variable (Little's MCAR test p > .05).
- 2Missing at Random (MAR) means missingness depends only on observed variables recorded in the dataset—making Multiple Imputation (MICE) valid.
- 3Missing Not at Random (MNAR) occurs when missingness depends on the unseen outcome itself (e.g. patients drop out because of severe side effects), requiring sensitivity models and CONSORT flow reporting.
Check your understanding
One question per screen with immediate methodological rationale after each answer
In a 100-patient trial, 18 participants withdraw because their symptoms worsened on the experimental drug. If the analyst simply deletes those 18 rows, which bias occurs?
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