git:20260725.67fd47f to git:20260930.69d672e

- 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`.

-

- ---

-

- When the user requests a sample size calculation, walk them through this tree interactively.

- Ask one question at a time. Do not assume answers.

- ---

-

- ## Supported Tests

-

- ### Test 1: Diagnostic Accuracy (Sensitivity/Specificity Precision)

-

- **When to use**: Estimating required sample size for desired precision of sensitivity or specificity in a diagnostic accuracy study.

-

- **Required parameters** (ask the user):

- | Parameter | Description | Default |

- |-----------|-------------|---------|

- | `sensitivity_expected` | Expected sensitivity | 0.85 |

- | `ci_half_width` | Desired half-width of 95% CI | 0.05 |

- | `prevalence` | Disease prevalence in study population | 0.30 |

- | `alpha` | Significance level | 0.05 |

- | `attrition_rate` | Expected dropout/exclusion rate | 0.15 |

-

- **Effect size interpretation**: The CI half-width determines precision. A half-width of 0.05 means the 95% CI for sensitivity will be within +/-5 percentage points. Narrower CIs require larger samples.

-

- ---

-

- ### Test 2: ICC Agreement (Bonett 2002)

-

- **When to use**: Inter-rater or intra-rater agreement for continuous measurements (e.g., tumor size, angle measurement).

-

- **Required parameters**:

- | Parameter | Description | Default |

- |-----------|-------------|---------|

- | `icc_expected` | Expected ICC value | 0.75 |

- | `icc_null` | Null hypothesis ICC (lower bound) | 0.50 |

- | `n_raters` | Number of raters | 2 |

- | `alpha` | Significance level | 0.05 |

- | `power` | Desired power | 0.80 |

- | `attrition_rate` | Expected dropout rate | 0.10 |

-

- **Effect size interpretation**: ICC < 0.50 = poor, 0.50-0.75 = moderate, 0.75-0.90 = good, > 0.90 = excellent (Koo & Li, 2016).

-

- ---

-

- ### Test 3: Kappa Agreement (Donner & Eliasziw 1992)

-

- **When to use**: Inter-rater agreement for categorical ratings (e.g., BI-RADS category, lesion present/absent).

-

- **Required parameters**:

- | Parameter | Description | Default |

- |-----------|-------------|---------|

- | `kappa_expected` | Expected kappa value | 0.70 |

- | `kappa_null` | Null hypothesis kappa | 0.40 |

- | `po_expected` | Expected proportion of agreement | 0.75 |

- | `alpha` | Significance level | 0.05 |

- | `power` | Desired power | 0.80 |

- | `attrition_rate` | Expected dropout rate | 0.10 |

-

- **Effect size interpretation**: Kappa < 0.20 = slight, 0.21-0.40 = fair, 0.41-0.60 = moderate, 0.61-0.80 = substantial, 0.81-1.00 = almost perfect (Landis & Koch, 1977).

-

- ---

-

- ### Test 4: Two-Proportion Comparison (Chi-Square)

-

- **When to use**: Comparing proportions between two independent groups (e.g., AI detection rate vs. conventional detection rate).

-

- **Required parameters**:

- | Parameter | Description | Default |

- |-----------|-------------|---------|

- | `p1` | Proportion in group 1 | -- |

- | `p2` | Proportion in group 2 | -- |

- | `alpha` | Significance level | 0.05 |

- | `power` | Desired power | 0.80 |

- | `attrition_rate` | Expected dropout rate | 0.15 |

-

- **Effect size interpretation**: Cohen's h = 2 * arcsin(sqrt(p1)) - 2 * arcsin(sqrt(p2)). Small = 0.20, medium = 0.50, large = 0.80.

-

- ---

-

- ### Test 5: McNemar Test (Paired Proportions)

-

- **When to use**: Paired binary outcomes (e.g., two readers reading same cases, before/after on same patients).

-

- **Required parameters**:

- | Parameter | Description | Default |

- |-----------|-------------|---------|

- | `p01` | P(Method A negative, Method B positive) | -- |

- | `p10` | P(Method A positive, Method B negative) | -- |

- | `alpha` | Significance level | 0.05 |

- | `power` | Desired power | 0.80 |

- | `attrition_rate` | Expected dropout rate | 0.10 |

-

- **Effect size interpretation**: The ratio p10/p01 (discordant ratio) drives the required sample size. Larger asymmetry in discordant pairs means fewer subjects needed. Only discordant pairs contribute information.

-

- ---

-

- ### Test 6: Independent t-Test

-

- **When to use**: Comparing means between two independent groups (e.g., lesion size in malignant vs. benign).

-

- **Required parameters**:

- | Parameter | Description | Default |

- |-----------|-------------|---------|

- | `mean_diff` | Expected mean difference | -- |

- | `pooled_sd` | Pooled standard deviation (from literature/pilot) | -- |

- | `alpha` | Significance level | 0.05 |

- | `power` | Desired power | 0.80 |

- | `attrition_rate` | Expected dropout rate | 0.15 |

-

- **Effect size interpretation**: Cohen's d = mean_diff / pooled_sd. Small = 0.20, medium = 0.50, large = 0.80. In clinical terms, d = 0.50 means the groups differ by half a standard deviation.

-

- ---

-

- ### Test 7: Survival / Log-Rank Test (Schoenfeld 1981)

-

- **When to use**: Comparing survival or time-to-event between two groups (e.g., treatment vs. control, RFA vs. surgery).

-

- **Required parameters**:

- | Parameter | Description | Default |

- |-----------|-------------|---------|

- | `hr` | Expected hazard ratio | -- |

- | `median_ctrl` | Median survival in control arm (months) | -- |

- | `accrual_time` | Accrual period (months) | 12 |

- | `follow_up` | Follow-up after accrual (months) | 24 |

- | `drop_rate` | Annual dropout rate | 0.05 |

- | `alpha` | Significance level | 0.05 |

- | `power` | Desired power | 0.80 |

-

- **Effect size interpretation**: HR < 1 favors treatment. HR = 0.50 means treatment halves the hazard (strong effect). HR = 0.80 is a modest 20% reduction. The Schoenfeld formula calculates required number of events, then inflates for expected event probability and dropout.

-

- ---

-

- ### Test 8: One-Way ANOVA (NEW)

-

- **When to use**: Comparing means across 3 or more independent groups (e.g., comparing AI model performance across 3 architectures, comparing measurement accuracy across multiple readers).

-

- **Required parameters**:

- | Parameter | Description | Default |

- |-----------|-------------|---------|

- | `k` | Number of groups | -- |

- | `f` | Cohen's f effect size | -- |

- | `alpha` | Significance level | 0.05 |

- | `power` | Desired power | 0.80 |

- | `attrition_rate` | Expected dropout rate | 0.15 |

-

- **Help user estimate Cohen's f**:

- - If the user knows group means and pooled SD: f = sigma_means / pooled_SD

- - If the user knows eta-squared: f = sqrt(eta_sq / (1 - eta_sq))

- - Benchmarks: small = 0.10, medium = 0.25, large = 0.40

-

- **R function**: `pwr::pwr.anova.test(k, f, sig.level, power)`

- **Python equivalent**: `statsmodels.stats.power.FTestAnovaPower().solve_power(effect_size, nobs, alpha, power, k_groups)`

-

- **Effect size interpretation**: Cohen's f = 0.25 (medium) means the group means span about half a pooled SD. In clinical terms, this is typically a meaningful difference across treatment arms or measurement methods.

-

- ---

-

- ### Test 9: Logistic Regression (NEW)

-

- **When to use**: Multivariable binary outcome models (e.g., predicting malignancy from multiple imaging features). Two approaches are provided.

-

- **Required parameters**:

- | Parameter | Description | Default |

- |-----------|-------------|---------|

- | `n_predictors` | Number of predictor variables | -- |

- | `event_rate` | Expected event rate (proportion with outcome) | -- |

- | `or_interest` | Odds ratio of interest (for Hsieh formula) | -- |

- | `r2_other` | R-squared of covariate with other predictors | 0.0 |

- | `alpha` | Significance level | 0.05 |

- | `power` | Desired power | 0.80 |

- | `attrition_rate` | Expected dropout rate | 0.10 |

-

- **Approach A: Peduzzi Rule of Thumb (EPV >= 10)**

- - N_events = 10 * n_predictors

- - N_total = N_events / event_rate

- - Simple, widely cited, conservative. Use as 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 the Riley criteria in Test 12

- (development) / Test 13 (validation) instead.

-

- **Approach B: Hsieh (1989) Formula**

- - Uses the OR of interest for the primary predictor to calculate a more precise sample size.

- - Accounts for correlation with other predictors via R-squared adjustment.

-

- **Always report both approaches** and recommend the larger N.

-

- **Effect size interpretation**: OR = 1.5 is a small-to-moderate effect; OR = 2.0 is moderate; OR = 3.0+ is large. The Peduzzi rule ensures model stability; the Hsieh formula targets power for the primary predictor.

-

- ---

-

- ### Test 10: Non-Inferiority / Equivalence (NEW)

-

- **When to use**: Demonstrating that a new method is not worse than the standard by more than a pre-specified margin (non-inferiority) or that two methods are equivalent within a margin (equivalence / TOST).

-

- **Required parameters**:

- | Parameter | Description | Default |

- |-----------|-------------|---------|

- | `design` | "non-inferiority" or "equivalence" | "non-inferiority" |

- | `outcome_type` | "proportion" or "continuous" | -- |

- | `p_reference` | Reference group proportion (if proportion) | -- |

- | `margin` | Non-inferiority or equivalence margin (delta) | -- |

- | `sd` | Standard deviation (if continuous) | -- |

- | `alpha` | One-sided alpha for NI; two one-sided for equivalence | 0.025 (NI) / 0.05 (equiv) |

- | `power` | Desired power | 0.80 |

- | `attrition_rate` | Expected dropout rate | 0.15 |

-

- **Key guidance for margin selection**:

- - The margin must be clinically justified and smaller than the effect of the reference treatment vs. placebo.

- - Common approach: margin = 50% of the established treatment effect (preservation of effect).

- - For proportions: absolute difference margin (e.g., delta = 0.10 means new method can be at most 10 percentage points worse).

- - For continuous: margin in the same unit as the outcome.

-

- **Non-inferiority (one-sided test)**:

- - H0: new - reference <= -margin (new is inferior)

- - H1: new - reference > -margin (new is non-inferior)

- - Alpha is one-sided (typically 0.025).

-

- **Equivalence (TOST)**:

- - H0: |new - reference| >= margin

- - H1: |new - reference| < margin

- - Two one-sided tests, each at alpha (typically 0.05 overall).

-

- **Effect size interpretation**: The margin defines the largest clinically acceptable difference. A smaller margin requires a larger sample. Always justify the margin based on clinical reasoning and prior literature.

-

- ---

-

- ### Test 11: Cox Regression EPV (Events Per Variable)

-

- **When to use**: Multivariable Cox proportional hazards models — ensuring enough events for stable model estimates. Same EPV logic as logistic regression (Test 9), applied to time-to-event outcomes.

-

- **Required parameters**:

- | Parameter | Description | Default |

- |-----------|-------------|---------|

- | `n_predictors` | Number of predictor variables in Cox model | -- |

- | `event_rate` | Expected proportion of subjects experiencing the event | -- |

- | `epv` | Events per variable target | 10 |

- | `attrition_rate` | Expected dropout rate | 0.10 |

-

- **Formula**:

- ```

- N_events = EPV × n_predictors

- N_total = N_events / event_rate

- N_adj = N_total / (1 - attrition_rate)

- ```

-

- **EPV guidelines**:

- - EPV >= 10: minimum for stable estimates (Peduzzi et al., 1995)

- - EPV >= 20: recommended for reliable CI coverage and type I error control

- - EPV < 5: model likely unstable — reduce predictors or use penalized methods

-

- **Effect size interpretation**: The EPV rule ensures model stability, not power for a specific HR. If the user also needs power for detecting a specific HR, combine with Test 7 (log-rank/Schoenfeld) and report the larger N.

-

- **Always report both approaches** (EPV minimum + Schoenfeld power, if HR is available) and recommend the larger N.

-

- ---

-

- ### Test 12: Prediction-Model Development (Riley)

-

- **When to use**: developing a clinical prediction / classification model (including a

- medical-AI model evaluated as one) — the goal is risk prediction *for use*, not a single

- predictor's hypothesis test. EPV-10 (Tests 9/11) is outdated here.

-

- **Approach**: the minimum N is the largest satisfying all four Riley criteria

- simultaneously — global shrinkage ≥ 0.9, apparent–adjusted R² gap ≤ 0.05, precise overall

- risk estimate, and (time-to-event) precise baseline survival. Implemented in R `pmsampsize`.

-

- **Required parameters**: number of **candidate predictor parameters** (count dummy/non-linear

- terms), a conservative expected **C-statistic or Cox-Snell R²** (with its literature source),

- and outcome **prevalence** (binary) or **event rate + mean follow-up** (time-to-event).

-

- Read `${CLAUDE_SKILL_DIR}/references/prediction_model_sample_size.md` for the criteria, the

- `pmsampsize` code, and the reporting requirements. Report N + required events + the binding

- criterion + the assumed C/R² and its source.

-

- ---

-

- ### Test 13: External-Validation Sample Size (Riley)

-

- **When to use**: sizing an **external validation** of an existing prediction/AI model.

-

- **Approach**: size to estimate the key validation metrics *precisely enough to be

- conclusive* — target the CI width of the **C-statistic**, the **calibration slope**, the

- **calibration-in-the-large / O:E ratio**, and (if a utility claim) **net benefit**.

- Implemented in R `pmvalsampsize`. A floor of ≥ 100 events and ≥ 100 non-events applies, but

- the precise target is usually larger.

-

- **Required parameters**: expected **prevalence**, anticipated **C-statistic**, and the

- target CI widths.

-

- Read `${CLAUDE_SKILL_DIR}/references/prediction_model_sample_size.md` for the `pmvalsampsize`

- code. Report the targeted CI widths and the resulting events / non-events.

-

- ---

-

- ### Test 14: MRMC Reader Study (Obuchowski–Rockette)

-

- **When to use**: sizing a **multi-reader multi-case (MRMC) reader study** — "do readers read

- better *with* the AI", or "is the AI non-inferior to readers". The single-reader AUC-precision

- calculation (Test 1) **under-sizes** this: readers as well as cases are random, so power must

- cover the **reader-variance** term, and a null from an under-sized reader study is *inconclusive,

- not negative*.

-

- **Approach**: invert the OR variance formula over the number of readers `J` and the case counts

- `N⁺`/`N⁻`; report the **`J × N` power grid** (past a modest case count, adding readers usually

- buys more power than adding cases). Requires **variance components** from a pilot or literature —

- the real bottleneck. Implemented in R `RJafroc` / `MRMCaov` / FDA `iMRMC` (integrate; do not

- hand-roll the OR algebra).

-

- **Required parameters**: the **effect** (ΔAUC, or the **non-inferiority margin** — an AI-vs-reader

- claim is usually NI), the expected AUC level, the **variance components** (pilot/literature), the

- **design** (fully-crossed vs crossover-with-washout), and power/α.

-

- Read `${CLAUDE_SKILL_DIR}/references/mrmc_reader_study_sample_size.md` for the framework, the

- readers-vs-cases trade-off, software, and reporting. Reader-study *design internals* live in

- `design-study` (`reader_elicitation_design.md`); an AI-vs-human-expert benchmark routes to

- `/design-ai-benchmarking`.

-

- ---

-

- ### Test 15: Segmentation-metric precision (Dice / HD95 / NSD)

-

- **When to use**: sizing a **segmentation** validation — how many cases to estimate the segmentation

- metric (Dice / HD95 / NSD) precisely enough to be conclusive, or to separate two models. The

- proportion/events calcs (Tests 1, 12–13) do not apply: the outcome is a bounded, skewed per-case

- overlap/boundary score, not a proportion.

-

- **Approach**: precision sizing `n ≈ (1.96·SD/δ)²` from the **pilot/literature SD of per-case Dice**

- (per structure — size on the **worst** structure you must report, not the average); report the CI by

- **bootstrapping per-case values (BCa)** — a t-interval is closed-form but Dice is bounded and

- non-normal near the ceiling, so its coverage is not the coverage you asked for, and BCa must resample

- whole **patients**, not structures. A model comparison on the same cases is **paired** (size on the SD of the per-case

- *difference*, or an NI margin). **Size the external cohort too** — a precise external estimate is the

- #1 acceptance lever.

-

- **Required parameters**: the **per-structure SD of per-case Dice** (pilot/literature), the target

- **precision δ** or **NI margin**, and the metric.

-

- Read `${CLAUDE_SKILL_DIR}/references/segmentation_metric_sample_size.md` for the per-structure and

- paired-comparison detail. The comparator/ablation the size serves lives in `design-study`

- (`combine_models_ablation_design.md`); metric selection is `/model-evaluation`.

-

- ---

-

- ### Test 16: Between-model comparison (is model A really better than B, C, …)

-

- **When to use**: the claim is that **one model outperforms others** — several architectures / families

- compared head-to-head on the same task. Single-model precision (Test 1 AUC, Test 15 Dice) under-sizes

- it: two models can each have a tight CI and still overlap, so the **difference** must be powered.

-

- **Approach**: run all models on the **same cases** (paired / within-case) and size on the **SD of the

- per-case difference** — `σ√(2(1−ρ))`, below either marginal SD once ρ > 0.5, which shared easy/hard cases

- usually clear. Use **DeLong** for a paired ΔAUC (or Obuchowski for the MRMC/clustered case) and a

- **bootstrap of the paired per-case differences** for ΔDice; size so the delta CI excludes zero, or so its

- lower bound clears the NI margin (the whole interval inside ±margin is *equivalence*, a stricter claim).

- For **>2 models**, pre-specify **one primary contrast** (proposed vs a strong, fairly-tuned baseline) at

- full α — or, if all pairwise are confirmatory, pay the **family-wise** correction (higher n per contrast).

- For a **ranking** claim, a single-run leaderboard ranks by luck: train over **multiple seeds**

- (Nadeau–Bengio corrected variance for repeated-CV differences) and leave models inside the **Demšar

- critical difference** unranked — not separated by the test is not a demonstrated tie, and Demšar's N

- counts independent datasets, not seeds.

-

- **Required parameters**: the **per-case-difference SD** of the primary metric (pilot / prior head-to-head;

- per structure for segmentation), the metric + paired-CI method, the target **δ or NI margin on the delta**,

- the **number of models + the primary contrast**, and (for ranking) the **seed-to-seed SD**.

-

- Read `${CLAUDE_SKILL_DIR}/references/multi_model_comparison_sample_size.md` for the paired-difference,

- multiplicity, and ranking-stability detail. The fair-comparison design the size serves lives in

- `design-study` (`multi_model_comparison_design.md`); presenting it is `make-figures`

- (`exemplar_plots/model_comparison_leaderboard.md`).

-

- ---

-

- ### Test 17: Segmentation usability (acceptability rate, failure bound, edit time)

-

- **When to use**: the claim is that a segmentation model is **clinically usable** — a share of cases a

- clinician accepts, a bounded catastrophic-failure rate, a time saving — not that its mean metric is

- high. Test 15 sizes a mean Dice to a precision and says nothing about any of these.

-

- **Approach**: an acceptability endpoint is a **proportion**: `n ≈ (z/δ)²·p(1−p)` — ≈138 cases at

- p = 0.90, δ = 0.05, but ≈384 at p = 0.50, so size on the pessimistic p unless a pilot in the same

- anatomy says otherwise, and size **per structure class** (use-as-is rates for one pipeline have run

- from ~40% for target volumes to ~89% for normal tissue). When m readers rate each case the ratings

- are **nested**, not independent: pooling n·m overstates precision by `DE ≈ 1 + (m−1)ρ` (3 readers at

- ρ = 0.5 halves it) — pre-specify either a case-level consensus rule or a mixed-effects/GEE analysis.

- To bound a **catastrophic-failure rate**, zero events in n cases gives an upper bound of ≈ `3/n`

- (**rule of three**), so ≤1% needs ~300 clean cases; a 40–60-case study bounds nothing below ~5–8%.

- For an **edit-time** claim, size the paired per-case time difference (as Test 16) **per structure and

- per site** — pooled savings coexist with structures and centres showing none.

- **Required parameters**: the acceptability scale and which level counts as accepted (*use-as-is* vs

- *after minor edits* are different endpoints), the expected **p** per structure class and target **δ or

- threshold**, the **readers per case** + analysis unit + assumed **ρ**, the **catastrophic bound** you

- must state, and (for work saving) the **SD of the per-case time difference**.

- Read `${CLAUDE_SKILL_DIR}/references/segmentation_acceptability_sample_size.md` for the proportion,

- clustering, rule-of-three and edit-time detail. The usability design the size serves lives in

- `design-study` (`segmentation_failure_characterization_design.md`); presenting it is `make-figures`

- (`exemplar_plots/segmentation_failure_panel.md`).

- ---

- ## Scope Limitations

- ### Supported

- The 11 tests listed above cover the vast majority of sample size calculations needed in medical imaging research, diagnostic accuracy studies, and clinical trials.

- ### NOT Supported

- The following designs require specialized software or biostatistician consultation:

- - **Adaptive trials** (group-sequential, sample size re-estimation)

- - **Cluster-randomized trials** (design effect, ICC-based inflation)

- - **Bayesian sample size determination**

- - **Crossover designs**

- - **Multi-endpoint correction** (mention Bonferroni adjustment if asked, but do not compute corrected sample sizes)

- If the user requests any of these, respond:

- > "This design requires specialized tools beyond this skill's scope. Consider using G*Power software (free, https://www.psychologie.hhu.de/gpower), PASS software, or consulting a biostatistician for [specific design]."

- ---

- 1. Ask the user to describe their study briefly (design, primary outcome, groups).

- 2. Walk through the decision tree to identify the appropriate test.

- 3. Confirm the selected test with the user before proceeding.

- 1. Present the parameter table for the selected test.

- 2. For each parameter without a user-provided value, explain what it means and offer the default.

- 3. Help the user estimate effect sizes from:

- - Prior literature (ask for references)

- - Pilot data

- - Cohen's conventions (as a last resort, with a note that convention-based estimates are less precise)

-

- ### Phase 2b: Retrospective Study — Experience-Based Sample Size Justification

-

- For retrospective studies, formal power analysis is often impractical because the dataset

- already exists. In these cases, an experience-based justification is acceptable for IRB

- and many journals. Offer this path when the user describes a retrospective design.

-

- **Two approaches**:

-

- #### Approach A: Institution Volume-Based

-

- Estimate N from the number of examinations performed at the institution during the study period.

-

- ```

- Total exams in period × prevalence of target condition × (1 - exclusion rate) = Expected N

- ```

-

- - Ask the user for: annual exam volume for the modality, study period length, estimated

- prevalence, and expected exclusion rate

- - This gives a realistic upper bound for N

-

- **IRB justification template**:

- > Based on approximately [X] [modality] examinations performed annually at [institution],

- > and an estimated prevalence of [condition] of [Y]%, we anticipate identifying approximately

- > [N] eligible patients over the [Z]-year study period. After accounting for an estimated

- > [W]% exclusion rate (due to [reasons]), we expect a final sample of approximately [N_adj]

- > patients for analysis.

-

- #### Approach B: Prior Study-Based

-

- Use sample sizes from published studies with similar designs as justification.

-

- - Search for 3-5 comparable studies and report their sample sizes

- - The user's N should be in the same range or larger

- - Cite the specific studies in the IRB justification

-

- **IRB justification template**:

- > Previous studies evaluating [similar topic] with [similar design] enrolled [N1] (Author1

- > et al., Year), [N2] (Author2 et al., Year), and [N3] (Author3 et al., Year) patients.

- > Our anticipated sample of [N] patients is [comparable to / larger than] these prior studies.

- #### When to Use Formal Calculation Instead

- Even for retrospective studies, a formal sample size calculation is preferred when:

- - The study is prospective or will prospectively enroll a subset

- - The primary analysis involves hypothesis testing (not just estimation)

- - The journal explicitly requires power analysis (check Instructions for Authors)

- - The IRB requires it for approval

- In these cases, proceed to Phase 3 with the appropriate test from the decision tree.

- ---

- 1. Read `${CLAUDE_SKILL_DIR}/references/formulas.md` for the exact formula.

- 2. Generate the R code (primary) and Python code (alternative).

- 3. Run the R code via Bash to produce the actual result.

- 4. Present results in the output format below.

- If the user is uncertain about parameters, offer a sensitivity table showing N across a range of plausible values (e.g., varying effect size or power from 0.80 to 0.90).

-

- ---

- ---

-

- ## IRB Justification Text Guidelines

-

- The IRB text must:

- 1. State the required N clearly.

- 2. Name the statistical test and its formula source.

- 3. Specify all assumed parameters (effect size, alpha, power).

- 4. State the attrition adjustment and final enrollment target.

- 5. Cite the methodological reference (e.g., "Schoenfeld, 1981" for survival).

- 6. Use formal, third-person language suitable for an ethics board.

-

- ---

-

- ## Communication Rules

-

- - Communicate with the user in their preferred language.

- - Use English for all statistical terminology, effect size names, and test names.

- - Be explicit about assumptions and their impact on the result.

- - When the user provides vague effect size estimates, flag the uncertainty and suggest a sensitivity analysis.

- - Never fabricate references. Cite only verified methodological sources from `formulas.md`.

-

- ## Anti-Hallucination

-

- - **Never fabricate file paths, URLs, DOIs, or package names.** Verify existence before recommending.

- - **Never invent journal metadata, impact factors, or submission policies** without verification at the journal's website.

- - If a tool, package, or resource does not exist or you are unsure, say so explicitly rather than guessing.