Pattern-Mixture Sensitivity Model¶

Method — instantiates Missingness-Aware Estimator Selection

Models outcomes by missingness pattern and varies unobserved departures to explore MNAR-sensitive conclusions.

Version: v1 · 2026-08-24 · History
Mechanism #: 6089
Type: Method
Form family: Analysis, Modeling & Optimization
Solution family: Evidence, Inference & Validation
Problem family: Uncertainty, Evidence & Inference Failure
Problem subfamily: Sampling, Selection, Missingness & Generalization
Origin domain: Statistics & Experimental Design
Instantiates: Missingness-Aware Estimator Selection

The Pattern-Mixture Sensitivity Model stratifies the sample by its missingness pattern, models the outcome separately within each stratum, and then mixes the strata back together to recover the overall estimand. The completers have their outcome distribution estimated directly; the incompleters' unobserved outcome distribution is set by assumption — typically as the completers' distribution shifted by an explicit delta — and the analyst sweeps that delta across a defensible range to see how the pooled answer moves. Its defining move is factoring the joint distribution of outcome and missingness as outcome-conditional-on-pattern, so the untestable assumption lives in one transparent, tunable place: a per-pattern shift you set by hand rather than a mechanism you fit. That factorization is what distinguishes it from any model that instead writes an equation for how the outcome drives the chance of being missing.

Example¶

A psychiatry trial tracks a continuous depression-symptom score weekly over eight weeks; many patients drop out, and the worry is that they leave because they are not improving. The pattern-mixture model groups patients by their dropout pattern — completed all visits, dropped at week 6, dropped at week 4, and so on — and estimates the symptom trajectory within each group from the visits it does have. For each dropout group, the missing later weeks are then imputed as that group's own extrapolated trajectory plus a delta that assumes dropouts fared, say, 2, 4, or 6 points worse than a like-for-like completer would have. Pooling the strata under each delta yields a curve of the treatment effect against the assumed penalty. The report says: the drug's advantage persists under mild-to-moderate departures but disappears once dropouts are assumed to have deteriorated by more than a clinically large margin — and the delta at which that happens is stated in the score's own units, for a clinician to weigh.

How it works¶

Inventory and stratify. Identify the distinct missingness patterns and split the sample by them.
Model within pattern. Estimate the outcome distribution for each pattern from its observed data.
Impose a departure on the unobserved. Set the missing strata's outcomes as a shifted version of an observed reference — the delta encodes the MNAR assumption.
Mix and sweep. Recombine the strata into the overall estimand, and repeat across a range of deltas to trace the conclusion's sensitivity.

Tuning parameters¶

Delta range and spacing — how far and how finely the unobserved shift is swept; a wider range is more honest about MNAR, a narrower one more decisive.
Reference for the shift — whether missing cases are anchored to their own pattern, to completers, or to a control-arm reference (a "reference-based" choice), which changes the default conservatism.
Pattern granularity — many fine patterns capture structure but leave sparse strata; coarse patterns are stable but blur distinctions.
Mixing weights — how strata are weighted when pooled, which must match the target population to keep the estimand intact.

When it helps, and when it misleads¶

Its strength is transparency about the untestable: the MNAR assumption is a number a domain expert can argue about, and because the model conditions on the actually-observed pattern, completers are never distorted to accommodate dropouts.^[n1]

Its failure mode is that fine stratification starves the strata — a pattern with six patients yields a noisy within-group model, and the pooled estimate inherits that noise. The results are also only as meaningful as the delta range: too timid a sweep manufactures false robustness. The classic misuse is to run it under a single convenient delta (often zero, i.e. missing-at-random-in-disguise) and present it as an MNAR analysis. The guarding discipline is to justify the delta range from domain knowledge and to report the whole sensitivity curve, not the one point that flatters the conclusion.

How it implements the components¶

missingness_pattern_inventory — stratification requires the full inventory of patterns; the model is literally organized around which units are missing which values in which combination.
estimand_preservation_statement — by mixing the pattern-specific models back with population-matched weights, it keeps the pooled target the intended overall estimand rather than a completers-only quantity.
sensitivity_and_tipping_point_plan — the delta sweep is its sensitivity plan: a structured exploration of how conclusions shift as the unobserved departure grows.

It does not write an explicit equation for how the outcome drives the probability of being observed — missingness_mechanism_assumption_frame in that joint-response-modeling sense is Selection-Model Sensitivity Analysis's; pattern-mixture instead reads the pattern off the data and shifts the outcome within it, never modeling the response process directly.

Instantiates: Missingness-Aware Estimator Selection — the pattern-stratified route to MNAR sensitivity.
Consumes: Missingness Indicator Matrix supplies the pattern strata the model is built on.
Sibling mechanisms: Doubly Robust Missingness Adjustment · Full-Information Maximum Likelihood Path · Inverse-Probability Weighting Model · MCAR Diagnostic Test and Balance Review · Missingness Indicator Matrix · Multiple Imputation Workflow · Process-Based Missingness Audit · Selection-Model Sensitivity Analysis · Tipping-Point Analysis

Editorial Notes¶

Form Classification¶

Form family: Analysis, Modeling & Optimization

Rationale: Pattern-Mixture Sensitivity Model operates as an analytical, modeling, inference, comparison, or optimization procedure that derives insight or a solution because it models outcomes by missingness pattern and varies unobserved departures to explore MNAR-sensitive conclusions.

Independent corroboration: The frozen evidence defines Pattern-Mixture Sensitivity Model as 'Models outcomes by missingness pattern and varies unobserved departures to explore MNAR-sensitive conclusions', so its operative form is Analysis, Modeling & Optimization.

Review outcome: Independent reviewer agreement; high confidence.

Origin Attribution¶

Primary origin: Statistics & Experimental Design

Origin pattern: Single lineage

Present-day reach: Specialized

Rationale: Pattern-Mixture Sensitivity Model is rooted in experimental design and statistics: Pattern-mixture models are a formal statistical treatment of outcomes conditional on missingness patterns.