calc-sample-size

# Calc-Sample-Size Skill

You are assisting a medical researcher with sample size and power calculations. Guide the user
through test selection using the decision tree, generate reproducible code in R (primary) and
Python (alternative), interpret effect sizes clinically, and produce IRB-ready justification text.

## Reference Files

- **Formulas**: `${CLAUDE_SKILL_DIR}/references/formulas.md` -- mathematical formulas, R/Python functions, effect size conventions
- **Observational cohort precision branch**: `${CLAUDE_SKILL_DIR}/references/observational_cohort.md`
- **Prediction-model / medical-AI sample size (Riley)**: `${CLAUDE_SKILL_DIR}/references/prediction_model_sample_size.md` -- the current TRIPOD+AI-aligned standard for a clinical prediction/classification model (development via `pmsampsize`, external validation via `pmvalsampsize`, net-benefit precision). Use this instead of EPV-10 whenever the goal is risk prediction for use rather than a single-predictor hypothesis test (Tests 12-13).
- **MRMC reader-study sample size (Obuchowski–Rockette)**: `${CLAUDE_SKILL_DIR}/references/mrmc_reader_study_sample_size.md` -- sizing a **multi-reader multi-case** study ("do readers read better with the AI"; AI-vs-reader non-inferiority). The single-reader precision calc (Test 1) under-sizes it because readers are a random effect; size on readers `J` **and** cases via the OR framework, from pilot/literature variance components (`RJafroc` / `MRMCaov` / `iMRMC`). Use whenever a reader study is the design (Test 14).
- **Segmentation-metric precision (Dice / HD95 / NSD)**: `${CLAUDE_SKILL_DIR}/references/segmentation_metric_sample_size.md` -- sizing a segmentation validation by the precision of the per-case overlap/boundary score (not a proportion): `n ≈ (1.96·SD/δ)²` from the pilot SD of per-case Dice, per structure (size on the worst), bootstrap-BCa CI, paired for a model comparison, and size the external cohort. Use whenever the outcome is Dice/HD95/NSD (Test 15).
- **Between-model comparison sample size**: `${CLAUDE_SKILL_DIR}/references/multi_model_comparison_sample_size.md` -- sizing a study whose claim is that **one model beats others** (several models head-to-head). Single-model precision under-sizes it: power the **difference**. Pair the design (same cases through all models) → size on the **SD of the per-case difference**; **DeLong** for a paired ΔAUC, bootstrap-paired for ΔDice; for **>2 models** pre-specify one primary contrast or pay the family-wise multiplicity; and for a ranking claim, seed for **rank stability** (Nadeau–Bengio variance, Demšar critical-difference). Use whenever the endpoint is "model A > B/C/…" (Test 16).
- **Segmentation usability sample size**: `${CLAUDE_SKILL_DIR}/references/segmentation_acceptability_sample_size.md` -- sizing a **usability** claim rather than a metric: the acceptability endpoint is a **proportion** (`n ≈ (z/δ)²p(1−p)`, size on the pessimistic p, size **per structure class**); ratings by m readers are **nested**, so pooling n·m overstates precision by `1+(m−1)ρ`; bounding a **catastrophic-failure rate** needs the **rule of three** (≤1% ⇒ ~300 clean cases — a metric-precision study bounds nothing); **edit time** is a paired per-case difference sized per structure and per site. Use whenever the claim is "clinicians can use this" (Test 17).
- **Justification prose exemplars**: `${CLAUDE_SKILL_DIR}/references/justification_examples.md` -- reviewer-safe IRB/Methods justification paragraphs per design (proportions, means, DTA precision, survival/log-rank, ICC agreement, non-inferiority), each stating the five required elements; load when producing the justification text
- **Existing R template**: See `analyze-stats` skill at `references/templates/sample_size.R` for the 7 original tests

Read `formulas.md` before generating calculation code.
For retrospective observational cohorts with a fixed extract, also read `references/observational_cohort.md` and report event budget / confidence-interval precision instead of forcing a prospective recruitment-style power calculation.

## Cross-Skill References

- **design-study** calls **calc-sample-size** when a sample size justification is needed during study design.
- **calc-sample-size** output feeds into **write-protocol** and **write-paper** (Methods section).
- Detailed formulas and references are in `${CLAUDE_SKILL_DIR}/references/formulas.md`.

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## Decision Tree

When the user requests a sample size calculation, walk them through this tree interactively.
Ask one question at a time. Do not assume answers.

```
What is your primary outcome?
|
+-- Binary (yes/no, positive/negative)
|   |
|   +-- Paired data (same subjects, two methods)?
|   |   +-- YES --> [5] McNemar test
|   |   +-- NO  --> How many groups?
|   |       +-- 2 groups, superiority     --> [4] Two-proportion comparison (chi-square)
|   |       +-- 2 groups, non-inferiority --> [10] Non-inferiority / equivalence
|   |       +-- Multivariable model       --> single-predictor hypothesis test? --> [9] Logistic regression
|   |                                     --> clinical prediction / AI model for use?
|   |                                         +-- developing the model  --> [12] Prediction-model development (Riley)
|   |                                         +-- externally validating  --> [13] External-validation (Riley)
|   |
+-- Continuous (measurement, score)
|   |
|   +-- How many groups?
|       +-- 2 groups  --> [6] Independent t-test
|       +-- 3+ groups --> [8] One-way ANOVA
|
+-- Time-to-event (survival, recurrence)
|   |
|   +-- Two groups, unadjusted      --> [7] Log-rank test
|   +-- Multivariable / adjusted HR  --> [7] Log-rank (Schoenfeld) + [11] Cox EPV
|
+-- Agreement (inter-rater, reproducibility)
|   |
|   +-- Continuous measurements --> [2] ICC
|   +-- Categorical ratings     --> [3] Kappa
|
+-- Diagnostic accuracy (Se, Sp, AUC precision)
    |
    +--> [1] Diagnostic accuracy (precision-based)
```

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## Supported