Calc Sample Size

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 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 For a clinical prediction / medical-AI model intended for use, EPV-10 is outdated and reviewer-vulnerable — use Test 12 (development) / Test 13 (validation).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.