bio-clinical-biostatistics-subgroup-analysis

What this skill does

## Version Compatibility

Reference examples tested with: statsmodels 0.14+, scipy 1.12+, numpy 1.26+, pandas 2.1+, matplotlib 3.8+, scikit-learn 1.4+. R packages cited: grf, policytree, causalToolbox, personalized, SIDES, stepp, gMCP, partykit, RBesT, brms.

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

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

# Subgroup Analysis and Heterogeneous Treatment Effects

**"Analyze treatment effects across subgroups"** -> Test whether treatment effects differ across pre-specified or data-discovered subgroups using interaction tests, stratified estimators, modern data-adaptive HTE methods, or Bayesian shrinkage -- with explicit declaration of confirmatory vs exploratory intent and credibility assessment.

## The Senn Foundation -- Why Most Subgroup Claims Are Wrong

**Senn 2018 *Nature* 563:619-621 (and *Statistical Issues in Drug Development* Ch. 9, 14):** observed between-patient response variation is NOT evidence of patient-level HTE. It conflates within-patient noise, period effects, regression-to-the-mean, and measurement error with true individual heterogeneity. Senn-Rolfe-Julious 2011 *SMMR* 20:657 documents that variance-component decomposition of replicate-crossover trials repeatedly fails to find subject-by-treatment interaction even where reviewers were certain one must exist.

**Brookes et al 2004 *J Clin Epidemiol* 57:229 — the 4x penalty:** detecting a treatment-by-subgroup interaction requires approximately 4x the sample size needed to detect the main treatment effect of similar magnitude. A trial powered to detect OR=0.6 overall cannot reliably detect subgroup differences of similar magnitude. Non-significant interaction tests are usually underpowered, not null.

**Senn's aphorism (paraphrased from SIDD):** "a trial can have subgroup analyses or proper power, not both." A single trial cannot simultaneously be powered for a primary effect AND for credible subgroup discovery; pretending otherwise misrepresents posterior uncertainty.

## Algorithmic Taxonomy

| Method | What it answers | Inference | Strength | Fails when |
|--------|-----------------|-----------|----------|------------|
| Mantel-Haenszel / CMH | Common OR across pre-defined strata | Asymptotic | Preserves stratification factor from randomisation | Stratum ORs reverse direction (Simpson) |
| Breslow-Day | Homogeneity of stratum ORs | Asymptotic chi-square | Test of effect modification | Underpowered with few/sparse strata; non-significance NOT proof of homogeneity |
| Gail-Simon 1985 | **Qualitative** interaction (sign reversal) | Likelihood ratio | Distinguishes quantitative from qualitative | Original LR is liberal at small n; use exact critical values (Pan-Wolfe 1997) |
| Logistic regression interaction | Per-subgroup conditional OR | Wald, LR | Most efficient single-model approach | Conditional ORs subject to non-collapsibility; over-fits in multi-way |
| RERI | Additive interaction on multiplicative scale | Delta-method or bootstrap CI | Captures public-health-relevant scale | Delta-method poor near boundary; nonlinear function of three ORs |
| STEPP (Bonetti-Gelber 2000) | Continuous covariate subgroups via overlapping windows | Permutation supremum test | Avoids dichotomisation of biomarkers | Window-size choice affects results; correlated estimates require permutation inference |
| SIDES / SIDEScreen (Lipkovich 2011) | Data-discovered subgroups via recursive partitioning | Resampling-adjusted base-vs-complement p | Multiplicity correctly absorbed | Tuning skeleton parameters affects FWER calibration |
| QUINT (Dusseldorp 2014) | Qualitative-interaction trees | Bootstrap stability | Directly tests crossover (A-better, B-better, equal) | Only two-arm continuous/binary; survival extensions ad hoc |
| Virtual Twins (Foster 2011) | Per-subject CATE via twin RF predictions | Bootstrap | Decouples nuisance from interpretable subgroup | Biased when RF underestimates effect heterogeneity in either arm |
| Causal forests (Athey-Wager 2019) | Pointwise CATE with honest splits | Influence-function CI | Asymptotic Gaussianity; doubly robust via AIPW | Finite-sample CI validity at trial-scale n debated (Rehill 2025) |
| Meta-learners X/R-learner (Künzel 2019) | Marginal/conditional CATE | Cross-fit influence function | X-learner dominates T-learner when arms unbalanced | Needs propensity for X-learner; R-learner requires nuisance n^(1/4) rate |
| MOB (Zeileis 2008) | Parameter-instability trees | M-fluctuation test | Theoretically clean; invariant to monotone transforms | Worse out-of-sample CATE than causal forest at large p |
| Bayesian shrinkage (Dixon-Simon 1991) | Posterior subgroup effects shrunken to overall | Posterior intervals from MCMC | Honest about prior expectation of no qualitative interaction | Prior choice on tau drives results; Dane et al 2019 white paper warns against for signal generation |
| EXNEX (Neuenschwander 2016) | Mixture of exchangeable + per-basket non-exchangeable | Posterior | Avoids HM "catastrophic borrowing" when one basket truly different | Weight choice (often 0.5/0.5 default) affects borrowing strength |

**Postdoc reading list:**

- Wang et al 2007 *NEJM* 357:2189 ("Reporting of subgroup analyses in clinical trials") — the canonical NEJM-mandated practice
- Sun et al 2010/2012 *BMJ* 340:c117 and 344:e1553 — 11 credibility criteria
- Dane, Spencer, Rosenkranz, Lipkovich, Parke 2019 *Pharm Stat* 18:126 with Hemmings-Koch commentary at 18:140 — EFSPI white paper + critique
- EMA 2019 Guideline on subgroups (CHMP/EWP/117211/2010 effective Aug 2019) — distinguishes "assessment subgroups" (regulatory, pre-specified) from "discovery subgroups" (exploratory)
- Athey & Wager 2019 *Observational Studies* 5:37; Athey, Tibshirani, Wager 2019 *Ann Stat* 47:1148 — causal forests
- Rehill 2025 *Int Stat Rev* — applied causal forest audit; ~70% of papers misreport tuning and skip honest-splitting validation

## Decision Tree by Scenario

| Scenario | Recommended approach | Why |
|----------|----------------------|-----|
| Pre-specified subgroup in confirmatory trial | Interaction term in single model + graphical-procedure multiplicity (gMCP) | EMA 2019 "assessment subgroup"; interaction test + Bonferroni-graph alpha control |
| Stratified randomisation by site/region | CMH or logistic with strata as covariates; stratum-specific OR reported in forest plot | Kahan-Morris 2012; ignoring strata inflates Type-I; strata-specific ORs for transparency |
| 5-15 pre-specified subgroups, regulatory submission | Forest plot + interaction tests + Holm/graphical FWER correction | Default regulatory presentation; multiplicity adjustment expected |
| Continuous biomarker subgroup (e.g., HbA1c, biomarker score) | STEPP (sliding-window plot + permutation supremum test) | Avoids arbitrary dichotomisation; cite Bonetti-Gelber 2004 |
| Suspected qualitative interaction (treatment helps some, harms others) | Gail-Simon 1985 LR test with Pan-Wolfe 1997 exact critical values | Distinguishes quantitative from qualitative; critical for label restriction |
| Data-discovery of HTE subgroup | SIDES/SIDEScreen with permutation FWER + replication mandate | Lipkovich 2011; signal-discovery not signal-confirmation |
| Continuous CATE estimation with many covariates | Causal forest (R `grf::causal_forest`) + RATE test (Yadlowsky 2025) | Modern HTE; honest splitting; influence-function CIs; RATE tests whether ranking is predictive vs prognostic |
| Basket trial across rare-disease strata | EXNEX or robust MAP with `RBesT` | Borrows across strata while permitting one to detach if truly different |
| Subgroup signal needing replication planning | Bayesian shrinkage for adjusted