Statistical Analysis Skill

Generate reproducible code (Python preferred, R when necessary) for medical research analyses, run it, and produce publication-ready tables and figures from its output.

Data Privacy Check

Before reading any data file, check whether it might contain Protected Health Information (PHI):

1. If *_deidentified.* files exist in the working directory, use those.
2. If only raw CSV/Excel files exist, ask the user whether the data contain patient identifiers

(names, national ID / RRN, contact details); if so, have them de-identify it first with /deidentify.

1. Proceed once the user confirms the data are de-identified or contain no PHI.
2. NEVER display raw PHI values (names, phone numbers, RRN) in your output, because console

output is copied into transcripts and drafts. If you encounter them, warn the user and suggest /deidentify.

Reference Files

• ${CLAUDE_SKILL_DIR}/references/templates/ — reusable analysis scripts; read the matching one

before generating code.

• ${CLAUDE_SKILL_DIR}/references/analysis_guides/ — methodology guides; the Phase 2 table says

which to read.

• ${CLAUDE_SKILL_DIR}/references/table-standards/ — table-standards.md (universal and AMA

rules, footnote order, gtsummary pipeline), journal-profiles/ (YAML per journal: radiology, jama, nejm, lancet, european_radiology, ajr), table-types/ (one template per table type), tool-comparison.md (R/Python table tools).

• ${CLAUDE_SKILL_DIR}/references/style/figure_style.mplstyle — figure style.

Workflow

Phase 1: Data Assessment

1. Read the data file (CSV, Excel, TSV, or other tabular format).
2. Report to the user: shape (rows x columns); column names and inferred types (continuous,

categorical, ordinal, binary, datetime); missing values per column (count and percentage); first 5 rows; unique value counts for categorical columns.

1. Identify the analysis unit: patient, exam, lesion, image, rater, study, etc.
2. If a variable name or coding is uncertain, write [VERIFY: variable_name] and ask the user to

confirm it against the data dictionary; never guess a column name or coding.

Phase 2: Analysis Plan

Observational designs (cohort, case-control, cross-sectional, registry, survey): before planning, look for a variable_operationalization.md from /define-variables (or an equivalent codebook-backed definition table). If none exists, warn the user and recommend running /define-variables first, because exposure/outcome/covariate definitions and cutoffs invented ad hoc from the data dictionary are a common reason reviewers reject observational work. This is a warning, not a block: proceed on explicit user confirmation and record that the artifact was not available.

Propose an analysis plan; the user decides the research question and endpoints. Mark any clinical definition, cutoff, diagnostic criterion or guideline claim you could not confirm [VERIFY].

1. Detect the analysis type from the table in Analysis-Specific Guidelines, or accept the

user's specification.

1. List the specific tests to be performed.
2. Identify primary and secondary endpoints.
3. State the assumptions that will be checked (normality, homogeneity, independence).
4. Note data cleaning needed (recoding, outlier handling, missing-data strategy).
5. Anchor the estimand to the research question.

• Interaction, synergy or effect modification: the primary estimand is the **interaction

parameter itself (a likelihood-ratio test of the interaction term, or the interaction OR/HR on one stated scale) — not a main-effect OR whose CI is then read as "no synergy". A public-health or biological synergy claim is additive-scale: report RERI, AP or S**, each with a CI (R interactionR / epiR; Knol & VanderWeele reporting), not only a multiplicative product term, because a non-significant multiplicative interaction is compatible with a large additive one (and vice versa). Joint categories (high/high vs low/low) show joint association, not interaction; "stronger in A than in B" from separate stratum estimates is the difference-in-significance fallacy — report the formal interaction term.

• Equivalence or non-inferiority: declare the margin up front (a TOST procedure, or the CI

compared against a pre-stated MCID); a non-significant difference is not equivalence without a margin.

1. Screen every categorical/binary predictor for separation before fitting anything. A

predictor that perfectly predicts the outcome has no finite MLE, and the failure is silent: glm returns an odds ratio near 0 (or enormous), p ≈ 0.99, and an AUC that ends up in a table. Pathognomonic imaging signs (T2-FLAIR mismatch, the string sign, a halo sign) cause it routinely: 100% specificity means an empty cell by construction.

   python3 "${CLAUDE_SKILL_DIR}/scripts/check_separation.py" \
     --data cohort.csv --outcome idh_mutant --auto --strict

COMPLETE_SEPARATION (an empty cell) and QUASI_SEPARATION (a cell below the sparsity floor) both halt the plan. With two or more predictors the script also tests them jointly (a linear combination can separate the outcome when no single predictor does); that test needs scipy, and without it the report says the joint check was not run. The remedy is a design decision, made in the plan: Firth's penalised likelihood keeps one model, while a two-stage rule — classify the sign-positive cases directly, model only the sign-negative remainder — is usually the clinically meaningful choice for a pathognomonic sign, because a sign-positive patient is already diagnosed.

Present the plan and wait for user approval before executing.

Phase 3: Execute

Generate and run a Python (preferred) or R script. Every number you report MUST come from its executed output, never estimated or hand-typed, because a number no script reproduces cannot be verified.

#### Script Structure

Start every script with a reproducibility header:

"""
Analysis: {description}
Date: {YYYY-MM-DD}
Random seed: 42
Python: {version}
Key packages: {package==version, ...}
"""
import numpy as np
import pandas as pd
np.random.seed(42)

#### Execution Rules

1. Random seed: always np.random.seed(42) or set.seed(42).
2. Figure style: always load the matplotlib style file:

   import matplotlib.pyplot as plt
   style_path = os.path.join(os.environ.get('CLAUDE_SKILL_DIR', '.'), 'references/style/figure_style.mplstyle')
   if os.path.exists(style_path):
       plt.style.use(style_path)

1. Output files: save next to the input data, or in a user-specified output directory.
2. Tables as CSV plus a printed markdown version (see Output Conventions); figures as

PDF (vector) and PNG (300 DPI).

1. Console output: a summary with every number that would appear in the text, formatted for

direct copy-paste into the Results section.

#### Assumption Checking

Choose the summary and test from the design and the distribution, not a preliminary test:

• Shape: QQ plot / histogram and skewness; for Table 1, |skewness| > 1 → median (IQR) with a

rank test, else mean (SD) (table-types/table1_demographics.md). Never gate on a Shapiro-Wilk or KS P value: it flags trivial departures at large n, misses real ones at small n, and test-then-test inflates the type I error (Rochon et al. 2012).

• Unequal variances: default to Welch's t / Welch ANOVA, not a Levene gate; Mann-Whitney

tests a different hypothesis and does not fix them. State the choice and reason in Methods.

#### Stratified & Ordinal-Trend Reporting

• Strata disjointness gate (before any ordinal trend test). Before a Cochran-Armitage trend

test (or any analysis that treats tiers as an ordered partition), assert that the strata are mutually exclusive and exhaustive: sum(n per stratum) == unique N and sum(events per stratum) == total events. A trend test on overlapping or non-exhaustive strata is invalid. Print the per-stratum N/event table and the reconciliation (the analysis-side mirror of /self-review check_cohort_arithmetic.py PARTITION_OVERLAP).

• Secondary stratum HR/OR: report each with (a) its reference contrast (the referent

category), (b) the event count in each stratum, and (c) a sparse-stratum caveat when any stratum has few events (< 10 is unstable). "HR 1.55 in lean participants" without the referent and the events is uninterpretable.

• Proportion CI lower-bound clamp: clamp every lower bound to max(0, lower). A zero-event

Wilson/score interval can print a negative or tiny-exponent bound (e.g. 3.47e-16) that is a display artifact; report 0 (or 0.0%), and prefer an exact (Clopper-Pearson) interval for zero/near-zero cells.

#### Output Manifest

After all analyses complete, save _analysis_outputs.md in the output directory, in the format given in references/analysis_run_workflow.md, so /make-figures and /write-paper can find the outputs without asking.

For prespecified binary predictions on independent units, use the bundled scripts/run_analysis.py run workflow in that file: it embeds data/configuration/code/output hashes, exact counts, metric-specific denominators and the reproduction command in the same manifest (audit checks recorded versions without rewriting them; compare separates declared context and numeric equality from byte drift). It does not select thresholds or establish study validity, privacy clearance or reuse rights. Synthetic example: python3 ${CLAUDE_SKILL_DIR}/scripts/demo_analysis_run.py --out demo-project.

Phase 3.5: Generated-Code Quality Gate

Before reporting any script as final, lint every emitted .py/.R file:

python3 ${CLAUDE_SKILL_DIR}/scripts/check_generated_code.py {script.py} --strict
# or scan a whole output directory:
python3 ${CLAUDE_SKILL_DIR}/scripts/check_generated_code.py --code-dir {analysis_dir} --strict

Fix every Major before reporting the script: MISSING_SEED (randomness with no seed), HARDCODED_DATA_LITERAL (hand-typed, table-shaped data instead of read_csv()/read.csv() + subset), HARDCODED_ABS_PATH (non-portable and a PII risk), and INPLACE_SOURCE_OVERWRITE (writing to the path read as input — never modify raw data; write derived outputs to a new path). Fix the flags DEBUG_LEFTOVER and UNUSED_IMPORT when tidying. Minor, Python only: API_DEFAULT_STUDENT_T (scipy's ttest_ind without equal_var is Student's t; state Welch or the reason for Student) and API_DEFAULT_PENALIZED_OR (LogisticRegression with none of penalty, C, l1_ratio, in a file that exponentiates a coef_). R's t.test() is Welch by default.

Phase 4: Report

After execution, generate manuscript-ready text from the script's output:

1. Results paragraph: 3-8 sentences with specific numbers, formatted as:

• Continuous: "mean +/- SD" or "median (IQR)"
• Proportions: "n/N (XX.X%)"
• Test results: "statistic = X.XX, p = 0.XXX"
• Effect sizes: "Cohen's d = X.XX (95% CI: X.XX-X.XX)"
• AUC: "AUC = 0.XXX (95% CI: 0.XXX-0.XXX)"

1. Table/figure captions: draft captions referencing table/figure numbers.
2. Methods snippet: 2-3 sentences describing the statistical methods, for the Methods

section. Cite only references whose DOI/PMID /search-lit confirmed; mark any other [UNVERIFIED - NEEDS MANUAL CHECK].

Report statistical results; leave judgments of clinical significance to the user. For designs this skill does not cover (adaptive or Bayesian trials, complex multilevel or causal-mediation models), say so and recommend biostatistician review before the results are reported.

Statistical Reporting Rules (Always Enforced)

1. Exact p-values: report exact values (e.g., p = 0.034), not inequalities; below 0.001,

report p < 0.001.

1. Confidence intervals: always report 95% CIs for primary endpoints.
2. Effect sizes: report one alongside every p-value (Cohen's d, eta-squared, odds ratio,

risk ratio, etc., as appropriate).

1. Multiple comparisons: for 3+ tests on the same dataset, apply Bonferroni or

Benjamini-Hochberg correction, state the method, and report both uncorrected and corrected p-values.

1. Sample size: state n for each group/analysis.
2. Missing data: report how many cases were excluded and why.
3. Decimal places: p-values to 3 decimals, proportions to 1 decimal, means/SDs to the

precision of the measurement.

1. Design/power statistics are code outputs, never hand-computed. Any minimum detectable

effect (MDE), a-priori power, or required sample size that will appear in the manuscript MUST be printed by the committed script with its method and inputs (n per arm, alpha, power, allocation ratio, one/two-sided), not computed in a side tool (GPower, an online calculator) and pasted in, because a manuscript value no script reproduces cannot be checked. Use one method family throughout (e.g. the exact noncentral-t via `statsmodels` `TTestIndPower` or `scipy`'s `nct`); do not mix a normal approximation for some values with exact-t for others. Do not report post-hoc (observed) power*: it is a function of the P value and adds nothing (Hoenig & Heisey 2001); report the CI of the effect instead.

1. Estimand & CI output contract. Every primary point estimate — including quantile

estimands (T25, median time-to-event), pooled proportions and subdistribution HRs, not just ORs/HRs/AUCs — MUST be emitted with its 95% CI, because /self-review treats a primary metric without one as a defect. In the output CSV carry the interval as explicit columns (estimate, ci_lower, ci_upper) or as one text column in est (lo–hi) form; never a point estimate with no interval beside it. Round ORs/HRs/sHRs to 2 decimals and AUC/C-statistic to 3.

Effect-Size Real-World Translation

Whenever a primary result is a correlation, a standardized coefficient, a regression slope, an OR/HR/RR or a Cohen's d, also report it as a plain-language unit shift a non-statistician can act on — in addition to the effect size (rule 3), not instead of it. This applies to continuous exposure–outcome associations (Spearman's rho, Pearson's r, standardized slopes), to relative measures where the audience needs an absolute-risk feel, and to reader or expert-elicitation studies, clinical-utility framing, abstracts and figure captions.

1. Pick an anchored contrast on the exposure, not a 1-unit step. Default: 25th to 75th

percentile (IQR), both endpoints in native units.

1. Translate to the outcome scale.

• Regression slope b in native units: delta_outcome = b * (x_p75 - x_p25). Keep the sign:

a negative b is a decrease.

• Per-SD slope (exposure standardized): delta_outcome = beta * (x_p75 - x_p25) / SD_x; a

fully standardized beta is also multiplied by SD_outcome.

• A correlation is not a slope. Pearson r converts to the simple regression slope of the same

data (b = r * SD_outcome / SD_x), which is the mean change per unit only if the relation is linear; Spearman's rho converts to no change in outcome units. Fit the outcome on the exposure and translate that slope (Theil-Sen if outliers are why Spearman was used); for a monotonic but curved association, report the fitted outcome at x_p25 and at x_p75 instead.

• Report as: "going from {x_p25} to {x_p75} {units} is associated with about {delta_outcome}

{outcome units} on average", and state the linearity assumption behind it.

1. Bound the claim: report the contrast, the assumption and a CI on the coefficient; do not

imply causation from a crude or unadjusted estimate.

Output contract (clinical utility is a default, not an optional add-on):

• OR/HR/RR primary outcomes → the relative measure and the absolute risk at a stated

baseline, the absolute risk difference, and NNT = 1/ARR (or NNH = 1/ARI), with the baseline risk explicit. A relative-only headline is incomplete.

• Continuous outcomes → the IQR/clinically anchored "Real-world translation" line beneath

the effect size.

• Prediction / classification (incl. medical-AI) models → calibration (Brier score,

calibration plot, or calibration slope/intercept) alongside discrimination, because AUC alone is insufficient; a decision-curve / net-benefit pass at the relevant threshold is standard output. An incremental claim reports the added-value test on the new term (likelihood ratio / Wald in the nested model), ΔC-statistic with its CI and Δnet benefit over the established clinical model, not the new model's AUC alone; NRI only as the categorical, event/non-event-split version, and IDI with caution. See references/table-standards/table-types/incremental_value.md and the make-figures decision_curve exemplar (and render_core_figures.py for the rendered curve).

Error Handling

• If a script fails, diagnose the likely cause (missing package, data format mismatch, wrong

column name) and present a fix. Do not rerun the same script more than once without modifying it or asking the user.

• If an R package is unavailable, suggest install.packages() and wait for user confirmation.

Output Conventions

Code, tables, figures and console output are in English.

Tables

Before generating any publication table, load:

1. ${CLAUDE_SKILL_DIR}/references/table-standards/journal-profiles/{journal}.yaml if a target

journal is known (it sets footnote markers, P and CI format, title and abbreviation order)

1. ${CLAUDE_SKILL_DIR}/references/table-standards/table-types/{type}.md for the table type
2. If no journal is specified, default to AMA style (Radiology profile)

Output formats (always generate all three): a CSV file (downstream use and archival), a console markdown rendering (user review), and R gtsummary code (Word/LaTeX export). Read ${CLAUDE_SKILL_DIR}/references/table-standards/table-standards.md for the gtsummary pipeline and the footnote placement order (general note, abbreviations, specific notes, probability notes).

Validation checklist (run before finalizing any table):

• [ ] No vertical lines — horizontal rules only (top, below header, bottom)
• [ ] Binary variables show only one level (e.g., Male only)
• [ ] Units in headers, not cells; consistent decimal places per column
• [ ] Variability measure stated: mean (SD) or median (IQR)
• [ ] Statistical test named (footnote or general note); exact P values, never "NS"
• [ ] Effect sizes per clinically meaningful unit (per 10 years, not per 1 year)
• [ ] Reference category stated for categorical predictors
• [ ] Abbreviations defined in footnotes, self-contained per table

Figures

PDF (vector) + PNG (300 DPI), styled with figure_style.mplstyle (Arial, colorblind-safe palette); width 3.5 inches (single column) or 7.0 inches (double column); axis labels with units.

Analysis-Specific Guidelines

Before generating code for any row, read the files listed for it (paths relative to ${CLAUDE_SKILL_DIR}); they carry the method rules this file does not repeat.

Comparing models: use a paired DeLong test for two separate scores on the same patients. For a nested "baseline + new term" model fitted and evaluated on the same data, DeLong is not the added-value test — test the term (likelihood ratio) and report ΔAUC with its CI.

The rules below have no separate guide.

Survey/Likert

• Descriptives per item: median, IQR, frequency distribution. Group comparisons: Mann-Whitney

or Kruskal-Wallis (ordinal data). Visualization: diverging stacked bar chart.

• Internal consistency: Cronbach's alpha with item-total correlations.
• Reverse-coding guard (run before reliability): recode every negatively worded item

(min+max) - x before computing the scale total or Cronbach's alpha. An un-recoded reverse item produces a negative item-rest correlation and can make alpha negative — a coding bug, not evidence of a multidimensional construct; do not defend it as one. likert_summary.py prints per-item item-rest correlations, flags negative ones as reverse-code suspects, warns on a negative alpha, and applies the recode with --reverse-items E3 .... To screen at cleaning time, run python3 "${CLAUDE_SKILL_DIR}/../clean-data/scripts/check_reverse_coding.py".

Covariate Pitfalls: Structural Zeros & Dose/Duration Variables

Applies to any multivariable adjustment (logistic / linear / Cox / propensity score / survey- weighted) with a dose/duration variable anchored to a categorical exposure (pack-years under smoking status, grams/week under alcohol use, cessation duration under former smoker):

• Structural-zero guard (do not impute): a never-smoker's pack_years is a *structural

zero* — known to be 0 by definition of the category, not missing. Imputing it (MICE/MNAR) fabricates a dose for unexposed subjects and corrupts the exposure contrast. Before imputing a dose/duration column, set the implied zero explicitly (IF status == 'never' THEN dose = 0) and impute only the genuinely missing residual among the exposed. /clean-data flags never rows with a NULL dose (scripts/check_structural_zero.py).

• Complete-case collapse (adjust for status, not dose): a dose variable in a complete-case

model drops the unexposed stratum wholesale when its zeros are stored as NULL, collapsing n (commonly 40–60%) and distorting subgroup estimates. Adjust for the categorical status (never/former/current); reserve the continuous dose for an exposed-only secondary analysis. Report n before and after model fitting and confirm the denominator did not silently collapse.

Covariate Selection: Over-adjustment in a Cross-Sectional Outcome Model

Applies to any cross-sectional / single-visit outcome regression (temporal order is not observed). Select covariates causally, not statistically:

• Do not adjust for a consequence or mediator of the outcome — that is over-adjustment /

collider bias and removes part of the effect under study. Signature case: with eGFR as the outcome, serum uric acid is renally excreted (a lower eGFR raises urate), so it is an outcome-consequence, not a confounder; blood pressure and HbA1c are often similarly downstream. Classify each candidate covariate against a DAG as confounder / mediator / outcome-consequence / collider, and keep only confounders in the primary model.

• "It differs in Table 1" is not a confounder-selection criterion. Imbalance justifies

considering a variable; a mediator or outcome-consequence stays out however imbalanced it is.

• Report the suspect-covariate sensitivity + VIF. Make a parsimonious, history-/design-based

model primary; report the fuller model as a sensitivity analysis that drops (or adds) the suspect covariate and show whether the headline estimate moves. Print VIF and the n actually fitted. If dropping the covariate materially changes the estimate, carry that to the abstract and conclusion.

• Compare adjusted vs unadjusted on the SAME frame. When extended adjustment adds covariates

with missingness, the analytic n shrinks (e.g. 84 → 49 events), and comparing that estimate with the full-frame unadjusted one confounds adjustment with who was dropped. Refit the unadjusted model on the reduced complete-case frame and report unadjusted and adjusted on that frame beside the full-frame estimate; never describe "adjustment changed the estimate" from a comparison across different frames (or use multiple imputation so all models share one frame).