bio-clinical-biostatistics-missing-data

What this skill does

## Version Compatibility

Reference examples tested with: R `mmrm` 0.3+ (Roche/openpharma), R `rbmi` 1.5+ (Roche/Bayer via insightsengineering), R `mice` 3.16+, R `mitools` 2.4+, Python `sklearn` 1.4+, `statsmodels` 0.14+.

Before using code patterns, verify installed versions match. If versions differ:
- R: `packageVersion('<pkg>')` then `?function_name`
- Python: `pip show <package>` then `help(module.function)`

If code throws ImportError, AttributeError, or TypeError, introspect the installed package and adapt the example to match the actual API rather than retrying.

# Missing Data Sensitivity for Confirmatory Trials

**"Handle missing data in a confirmatory clinical trial"** -> Pre-specify the missing-data assumption per ICH E9(R1); execute the primary analysis under the chosen assumption (typically MAR via MMRM or MI); run clinically-articulable MNAR sensitivity analyses (reference-based MI per Carpenter-Roger 2013); report the tipping delta that would overturn the conclusion (Permutt 2016).

## The Foundation -- NRC 2010 and ICH E9(R1)

**The U.S. National Research Council Panel** ("The Prevention and Treatment of Missing Data in Clinical Trials," 2010; chaired by Roderick Little; Little, D'Agostino, Cohen et al 2012 *NEJM* 367:1355): 18 recommendations grouped as prevention (Recs 1-7), analysis (Recs 8-14), sensitivity (Recs 15-18).

Key recommendations:

- **Rec 10/11:** explicitly REJECT LOCF and BOCF as default; they are biased even under MCAR
- **Rec 13:** endorses WGEE (weighted GEE) for marginal estimands
- **Rec 15:** "examining sensitivity to assumptions about the missing-data mechanism should be a mandatory component of reporting"

**ICH E9(R1) (2019)** forces the ordering: define the estimand (5 attributes including ICE strategy) BEFORE choosing the analysis. The missing-data strategy maps to the ICE handling strategy:

- **Treatment policy** ICE strategy + missing post-ICE data -> reference-based MI (J2R typical)
- **Hypothetical** ICE strategy -> MMRM under MAR; g-computation
- **Composite** ICE strategy -> ICE becomes part of endpoint; no missing-data problem for that subject
- **While-on-treatment** ICE strategy -> pre-ICE values only; censored at ICE
- **Principal stratum** -> latent stratum, requires Bayesian or sensitivity over unverifiable assumptions

## Missing-Data Mechanisms

| Mechanism | Definition | Testable? | Valid method |
|-----------|------------|-----------|--------------|
| MCAR | Independent of all data | Partially (Little's 1988 test) | Complete-case unbiased but loses power |
| MAR | Depends on observed data only | NOT testable | MMRM under MAR; MI under MAR |
| MNAR | Depends on unobserved values | NOT testable | Sensitivity analysis (J2R, CR, CIR, tipping point, pattern-mixture, selection model) |

**Critical philosophical point: MAR vs MNAR cannot be distinguished from observed data alone.** This is fundamental. Pre-specify the assumed mechanism in the SAP based on clinical reasoning, not the data.

## Algorithmic Taxonomy

| Method | Estimand strategy | Identification | Variance | Strength | Fails when |
|--------|-------------------|----------------|----------|----------|------------|
| Complete-case analysis | MAR or MCAR | MAR | Standard | Simple; valid under MCAR | Loses power; biased under MAR with informative covariates |
| LOCF | Implicit MNAR | Assumes flat post-ICE trajectory | Standard | Historically used | Biased even under MCAR (Mallinckrodt 2008); NRC 2010 rejects |
| MMRM with UN+KR | Hypothetical via MAR | MAR | Kenward-Roger SE | FDA-favoured continuous longitudinal | High differential dropout makes MAR implausible |
| Multiple imputation (MAR) | Hypothetical via MAR | MAR | Rubin's rules | Flexible; handles arbitrary patterns | sample_posterior must be enabled; only works with default estimator in sklearn |
| Reference-based MI (J2R, CR, CIR, LMCF) | Treatment policy / MNAR sensitivity | Clinical narrative (e.g., "after withdrawal patient resembles placebo") | Cro 2019 information-anchored vs Wolbers 2022 frequentist (active debate) | FDA-acceptable; clinician-interpretable | Variance choice contested; Rubin over-conservative, jackknife may inflate Type-I |
| Tipping-point delta-adjustment | MNAR sensitivity | Pre-specified delta function | Standard | Direct regulatory question: "how bad would missing data have to be?" | Delta interpretation depends on scale |
| Pattern-mixture with CCMV | Pattern-mixture MNAR | "Missing pattern resembles completer pattern" | Multiple imputation | Identifies missing cells via restriction | CCMV may be implausible if completers are atypical |
| Pattern-mixture with NCMV | Pattern-mixture MNAR | "Missing pattern resembles neighbouring pattern" | MI | Less extreme assumption than CCMV | Choice of "neighbouring" is ambiguous |
| Pattern-mixture with ACMV | Pattern-mixture MNAR (equivalent to MAR) | "Missing pattern resembles available cases" | MI | Equivalent to MAR (Molenberghs 1998) | Reduces to standard MAR analysis |
| Selection model (Diggle-Kenward 1994) | MNAR | Joint normal outcome + logistic dropout | Likelihood | Theoretically elegant | Conclusions driven by untestable parametric assumptions; FDA discouraged |
| Retrieved-dropout MI | Treatment policy | Sampling from observed post-discontinuation data | MI variance | Empirically grounded (no model assumption for missing) | Requires actual post-ICE data collection |

**Postdoc reading list:**

- NRC 2010 *Prevention and Treatment of Missing Data in Clinical Trials* (National Academies)
- Little RJA, D'Agostino R, Cohen ML et al 2012 *NEJM* 367:1355 (NRC summary)
- Mallinckrodt CH 2008/2014 Drug Information Journal / TIRS (MMRM case)
- Carpenter JR, Roger JH, Kenward MG 2013 *J Biopharm Stat* 23:1352 (reference-based MI)
- Cro S, Carpenter JR, Kenward MG 2019 *JRSS-A* 182:623 (information-anchored variance)
- Bartlett JW 2021 *Stat Biopharm Res* 15(1):178 (frequentist variance counter)
- Wolbers M, Noci A, Delmar P et al 2022 *Pharm Stat* 21(6):1246-1257 (CMI+jackknife)
- Permutt T 2016 *Stat Med* 35:2876 (analyst as adversary; tipping point)
- Diggle PJ, Kenward MG 1994 *JRSS-C* 43:49 (selection model + canonical critique)
- Molenberghs G, Michiels B, Kenward MG, Diggle PJ 1998 *Stat Neerl* 52:153 (pattern-mixture identifying restrictions; ACMV = MAR under monotone)
- Olarte Parra C, Bartlett JW, Daniel RM 2022 *Stat Biopharm Res* (MMRM-MAR IS a hypothetical estimator)

## Decision Tree by Scenario

| Scenario | Recommended approach | Why |
|----------|---------------------|-----|
| Continuous endpoint, monotone missingness, MAR plausible | MMRM with UN + Kenward-Roger via R `mmrm` | FDA-favoured Mallinckrodt 2008/2014 default |
| Continuous endpoint, ICE = treatment discontinuation, treatment policy estimand | Hybrid: J2R for discontinuation ICEs, MMRM-MAR for other (Aprocitentan 2024 precedent) | De facto FDA standard 2024-2025 |
| Continuous endpoint, treatment policy + post-ICE data collected | Retrieved-dropout MI (Wegovy STEP precedent) | Empirically grounded; FDA 2025 obesity guidance endorses |
| Continuous endpoint, MNAR sensitivity required | J2R via `rbmi` with both Rubin's variance AND frequentist (CMI+jackknife) | Cro vs Bartlett debate; report both for safety |
| Continuous endpoint, tipping-point analysis | Permutt 2016 delta-adjustment in active arm only | Direct regulatory question; pre-specify delta range |
| Binary endpoint with missing primary | MI with logistic imputation; modified Poisson for marginal RR | Per FDA 2023 covariate adjustment |
| Time-to-event with informative censoring | IPCW (Robins) or sensitivity under composite | Censoring-as-event composite; cite Lewis 2023 |
| Very high missingness (>40%) | Report as hypothesis-generating; multiple sensitivity analyses | NRC 2010 caveat |
| Aducanumab-style differential dropout pattern | MAR primary is questionable; treatment-policy with reference-based MI primary | Lessons from FDA 6-1 AdCom decision (2021) |
| Pediatr