Calc-Sample-Size Skill

Decision Tree

Walk the user through this tree one question at a time; do not assume answers. Reader studies, segmentation and model-comparison designs sit outside the tree: see Tests 14–17.

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)

Tests 1–11

Once the test is chosen, read ${CLAUDE_SKILL_DIR}/references/formulas.md § Test N — the parameter table with defaults, the effect-size interpretation, the formula, R/Python code and the methodological reference.

#	Test	Use when
1	Diagnostic accuracy — Se/Sp precision	desired 95% CI half-width for sensitivity or specificity
2	ICC agreement (Walter 1998 test; Bonett 2002 CI width)	inter-/intra-rater agreement on continuous measurements (tumor size, angle)
3	Kappa agreement (Donner & Eliasziw 1992; needs the trait prevalence)	agreement on categorical ratings (BI-RADS category, lesion present/absent)
4	Two-proportion comparison (chi-square)	two independent groups (AI vs conventional detection rate)
5	McNemar (paired proportions)	paired binary outcomes (two readers on the same cases, before/after)
6	Independent t-test	means in two independent groups (lesion size, malignant vs benign)
7	Survival / log-rank (Schoenfeld events, then patients)	time-to-event between two groups
8	One-way ANOVA	means across 3+ independent groups
9	Logistic regression (Peduzzi EPV + Hsieh 1998, continuous or binary predictor)	multivariable binary outcome, single-predictor hypothesis test
10	Non-inferiority / equivalence	new method not worse than standard by more than a pre-specified margin, or equivalent within it
11	Cox regression EPV	multivariable Cox model — enough events for stable estimates

• Test 9: Peduzzi EPV ≥ 10 is a minimum baseline for a single-predictor hypothesis test only. For a clinical prediction / medical-AI model intended for use, EPV-10 is outdated and reviewer-vulnerable — use Test 12 (development) / Test 13 (validation). Always report both Peduzzi and Hsieh and recommend the larger N.
• Test 10: NI alpha is one-sided (typically 0.025); orient the difference so > 0 favours the new method. Equivalence is TOST, powered jointly. The margin must be clinically justified (see formulas.md § Margin selection).
• Test 11: EPV ensures model stability, not power for a specific HR. If an HR is available, also run Test 7 (Schoenfeld) and recommend the larger N.

Tests 12–17 (specialised designs)

Each has its own reference file (parameters, method, reporting); read it once the test is chosen.

• Test 12 — Prediction-model development (Riley). Developing a clinical prediction / classification model (including a medical-AI model evaluated as one) for use. EPV-10 does not apply: N is the largest satisfying all Riley criteria — three for a binary or time-to-event outcome, four for a continuous one (R pmsampsize).
• Test 13 — External validation (Riley). Validating an existing prediction/AI model: size for the CI width of the C-statistic, calibration slope, O:E and (if claimed) net benefit (R pmvalsampsize); ≥ 100 events and ≥ 100 non-events is only a floor. For Tests 12–13 read ${CLAUDE_SKILL_DIR}/references/prediction_model_sample_size.md.
• Test 14 — MRMC reader study (Obuchowski–Rockette). Readers with vs without the AI, or AI non-inferior to readers. Test 1 under-sizes it because readers are a random effect: size readers J × cases from pilot/literature variance components with RJafroc / MRMCaov / iMRMC (do not hand-roll the OR algebra) and report the J × N power grid. Read ${CLAUDE_SKILL_DIR}/references/mrmc_reader_study_sample_size.md.
• Test 15 — Segmentation-metric precision (Dice / HD95 / NSD). The outcome is a per-case score, not a proportion: n ≈ (1.96·SD/δ)² from the pilot SD of per-case Dice, sized on the worst structure; CI by patient-level bootstrap (BCa). This is precision; a comparison is Test 16. Read ${CLAUDE_SKILL_DIR}/references/segmentation_metric_sample_size.md.
• Test 16 — Between-model comparison. Model A beats B, C, …: power the paired per-case difference, n = ((z₁₋α/₂ + z₁₋β)·SD_Δ/Δ)² (a CI sized to just exclude zero has ~50% power), not each model's precision; for > 2 models pre-specify one primary contrast or pay the family-wise correction; a ranking claim needs multiple seeds. Read ${CLAUDE_SKILL_DIR}/references/multi_model_comparison_sample_size.md.
• Test 17 — Segmentation usability. Clinicians can use it (acceptability rate, catastrophic-failure bound, edit time): acceptability is a proportion sized per structure class; DE ≈ 1 + (m−1)ρ holds only when each case has its own readers — the same readers on every case (crossed) add a reader term more cases cannot shrink; bounding failures at ≤ 1% needs ~300 clean cases (rule of three). Read ${CLAUDE_SKILL_DIR}/references/segmentation_acceptability_sample_size.md.

Out of Scope

Do not compute adaptive trials (group-sequential, sample size re-estimation), cluster-randomized trials (design effect, ICC-based inflation), Bayesian sample size determination, crossover designs, or multi-endpoint correction (mention Bonferroni if asked, but do not compute corrected sample sizes). Say the design is beyond this skill and point to G*Power (free, https://www.psychologie.hhu.de/gpower), PASS, or a biostatistician.

Workflow

Phase 1: Understand the Study

1. Ask the user to describe the study briefly (design, primary outcome, groups).
2. Walk the decision tree to a test, and confirm it with the user before proceeding.

Phase 2: Collect Parameters

1. Present the selected test's parameter table.
2. For each parameter without a user-provided value, explain it and offer the default.
3. Estimate effect sizes from prior literature (ask for the references) or pilot data; use Cohen's conventions only as a last resort, noting that convention-based estimates are less precise.

Phase 2b: Retrospective Studies

When the dataset already exists, formal power analysis is often impractical. Offer:

• Fixed extract: read ${CLAUDE_SKILL_DIR}/references/observational_cohort.md and report event budget / confidence-interval precision instead of forcing a prospective recruitment-style power calculation.
• Experience-based justification (acceptable for IRB and many journals):
  • Institution volume: total exams in period × prevalence × (1 − exclusion rate) = expected N. Ask for the annual exam volume for the modality, study period, prevalence and exclusion rate. This gives a realistic upper bound for N.
  • Prior studies: report the N of 3–5 comparable published studies and cite them; the user's N should be in the same range or larger.
  • IRB templates for both: ${CLAUDE_SKILL_DIR}/references/justification_examples.md § Retrospective.

Use a formal calculation (Phase 3) even for a retrospective study when a subset is enrolled prospectively, the primary analysis tests a hypothesis (not just estimation), the journal's Instructions for Authors require a power analysis, or the IRB requires it.

Phase 3: Calculate and Report

1. Generate R code (primary) and Python code (alternative) from the reference formula.
2. Run the R code via Bash; the reported N is the number it prints, not a hand calculation.
3. Present the result in the Output Format below. Cite methodological sources only from formulas.md or the test's reference file; any other reference needs a DOI/PMID confirmed via /search-lit, otherwise mark it [UNVERIFIED - NEEDS MANUAL CHECK]. Mark an effect size, clinical definition or threshold you could not confirm [VERIFY].
4. In a project, save the IRB text as protocol/sample_size_justification.md and the scripts as protocol/sample_size_calc.R / .py: /write-protocol and /write-paper embed that text verbatim, so the numbers are never retyped.

Phase 4: Sensitivity Analysis (Optional)

If a parameter is uncertain or the effect-size estimate is vague, flag it and offer a table of N across plausible values (e.g., varying effect size, or power from 0.80 to 0.90).

Output Format

Always structure the final output as follows:

## Sample Size Calculation Report

### Study Design
[1-2 sentence summary of the design and test selected]

### Parameters
| Parameter | Value | Source |
|-----------|-------|--------|
| ... | ... | user / literature / convention |

### Result
- **Required sample size**: N = [value]
- **With [X]% attrition adjustment**: N_adj = [value]

### R Code (Reproducible)
```r
# [complete, self-contained R script]
# Dependencies: [list packages]
# Run: Rscript sample_size_calc.R

Python Code (Alternative)

# [complete, self-contained Python script]
# Dependencies: [list packages]
# Run: python sample_size_calc.py

IRB Justification Text

A sample of [N] participants is required to detect [effect description] with [power]% power at a [one/two]-sided significance level of [alpha], assuming [key assumptions]. Accounting for an estimated [X]% attrition rate, we plan to enroll [N_adj] participants. This calculation is based on [formula/method reference].

Effect Size Interpretation

[Cohen's benchmark classification + clinical meaning in the context of this study]

The IRB text must state N; name the test and its formula source; give every assumed parameter
(effect size, alpha, power); state the attrition adjustment and final enrollment target; cite the
methodological reference (e.g., "Schoenfeld, 1981"); and use formal, third-person language. Read
`${CLAUDE_SKILL_DIR}/references/justification_examples.md` for per-design exemplars when writing it.