🧩MNAR

NEW

Also known as: Missing Not At Random

A missing-data mechanism where missingness depends on the unobserved values themselves.

DESCRIPTION

MNAR describes a situation where the probability of missing data depends on the missing values, even after accounting for observed information. Analyses assuming MAR or MCAR can be biased under MNAR. Handling MNAR often involves modeling the missingness process, using selection or pattern-mixture models, or conducting sensitivity analyses. Multiple imputation may require explicit assumptions for MNAR. Recognizing MNAR is crucial for robust inference, especially in clinical, survey, and operational datasets. MNAR can be mitigated by improved data collection and careful study design. Documentation and governance help track missingness mechanisms. Model diagnostics and domain expertise are essential to assess plausibility. MNAR is central in statistical theory of missing data and remains widely relevant.

ALTERNATIVE DEFINITIONS

Penn State Eberly College of Science

Missing not at random (MNAR) means that the probability an observation is missing depends on the value itself which is missing.

Emphasizes dependence on the unobserved value itself.

Source

UCLA Institute for Digital Research and Education

When data are missing not at random (MNAR), the probability that data are missing depends on the unobserved data even after controlling for observed data.

Explicitly notes dependence after controlling for observed covariates.

Source

European Medicines Agency

Under MNAR, the propensity for missingness is related to unobserved outcomes, so the missingness cannot be fully explained by observed data.

Regulatory framing highlighting implications for confirmatory trials.

Source

RELATED TERMS

Missing Data Multiple Imputation Rubin’s Rules Complete Case Analysis Inverse Probability Weighting Sensitivity Analysis Selection Bias Data Quality

COMPETING TERMS

MCAR MAR

KNOWLEDGE AREAS

Data Science Mathematics Data Quality Data Management

TARGET AUDIENCE

Data Scientist Data Analyst Data Steward Data Management Consultant

EXTERNAL SOURCES

• Wikipedia - Missing data
• Wiley - Classic text on missing data mechanisms
• The Turing Way - Practical guidance for handling missing data
• scikit-learn - Documentation on imputation strategies

TOP QUESTIONS

What makes MNAR different from MAR and MCAR in missing data analysis?

MNAR means missingness depends on unobserved values themselves, while MAR depends only on observed variables and MCAR is entirely random. This difference critically affects bias and model assumptions.

Category: Requirements

How do analysts detect MNAR in practice?

You cannot definitively test MNAR from observed data alone; use study design knowledge, missingness patterns, and sensitivity analyses to assess plausibility of MNAR mechanisms.

Category: Misunderstanding

What are common mistakes when handling MNAR?

Assuming MAR without justification, using complete-case analysis, or applying naive imputation can bias results under MNAR. Always document assumptions and perform sensitivity checks.

Category: Mistakes

What are recommended approaches to handle MNAR?

Consider selection models, pattern-mixture models, or targeted multiple imputation with sensitivity parameters. Combine statistical modeling with domain expertise.

Category: Management

Why is MNAR relevant in healthcare and survey data?

Nonresponse often relates to unobserved outcomes (e.g., severity), making MNAR plausible. Ignoring MNAR risks biased efficacy estimates and flawed population inference.

Category: Relevancy

What risks arise if MNAR is ignored?

Estimates may be severely biased and confidence intervals misleading. Policy or clinical decisions based on such results can be harmful.

Category: Risks

Is multiple imputation valid under MNAR?

Standard multiple imputation assumes MAR; under MNAR, imputation requires explicit modeling of missingness or sensitivity parameters to remain credible.

Category: Opinion

How should MNAR be documented in data governance?

Record missingness drivers, collection processes, and assumptions. Include mechanisms in metadata and analytical readme, and require sensitivity analyses for critical metrics.

Category: Management

What is a practical example illustrating MNAR?

Patients with severe symptoms may skip follow-up surveys, and severity is unobserved, making missingness depend on the missing outcome itself.

Category: Example