bio-clinical-biostatistics-categorical-tests

What it does

Tests associations between categorical variables in clinical data using chi-square, Fisher's exact, Boschloo, Cochran-Mantel-Haenzel, and modern McNemar variants with calibrated confidence intervals (Wilson, Newcombe, Miettinen-Nurminen). Use when analyzing categorical outcomes, paired binary endpoints, or testing treatment-outcome independence in confirmatory or exploratory clinical trials.

How it works

The skill prescribes a taxonomy of tests with design and operating characteristics, and includes executable code patterns (Python) for:

• Pearson chi-square (no continuity correction) with contingency table construction and an explicit check on expected counts; switch to Boschloo or permutation chi-square for sparse data.
• Fisher's exact test for 2x2 with an alternative Boschloo example, noting Boschloo computes an unconditional p-value and conditions on one margin.
• CMH (Mantel-Haenszel) analysis across strata, producing pooled odds ratio, CMH test, and Breslow-Day test; includes per-method failure modes and guidance on interpretation.
• McNemar tests for paired binary data: asymptotic (no continuity correction) when b+c >= 25, mid-p when b+c < 25, and exact conditional when mandated; includes examples of matrix inputs and function calls.
• Effect sizes: Phi for 2x2 and Cramer's V for RxC, with guidance on bias-corrected variants and usage with pingouin.

Code samples reference functions and objects like chi2_contingency, from scipy.stats import fisher_exact, boschloo_exact, pd.crosstab, StratifiedTable, mcnemar, and pingouin; the workflow emphasizes checking expected counts, choosing tests by scenario, and reporting stratum-specific results where appropriate.

When to use it

Use in scenarios described in the decision tree for experimental design: independent 2x2 with adequate counts; independent 2x2 with small counts; independent RxC; stratified designs; paired binary data; matched-pair non-inferiority; and when selecting effect-size measures for categorical data. Also when regulatory considerations or SAPs prefer certain tests (e.g., Boschloo over Fisher) and when interpreting potential Simpson's paradox or heterogeneity across strata.

What it can touch

The skill uses Python and scipy-based tools as primary interfaces. It references scipy.stats.chi2_contingency, scipy.stats.fisher_exact, boschloo_exact, statsmodels.stats.contingency_tables.StratifiedTable, mcnemar, and pingouin for effect sizes. It assumes access to data arranged in contingency tables or data frames suitable for pd.crosstab.

Caveats

Compatibility notes specify SciPy 1.12+ (Boschloo and Barnard added in 1.7), StatsModels 0.14+, pingouin 0.5+, exact2x2 (R) 1.6+, pandas 2.1+, numpy 1.26+. It warns that exact conditional tests can be conservative, and that CMH requires attention to stratification to avoid inflated Type-I error; it advises supplementing with stratum-specific ORs or logistic regression with interaction. It notes potential limitations in per-method power under sparse data, and emphasizes verifying versions and API parameters when code throws ImportError, AttributeError, or TypeError.