Getting it into your agent
One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.
npx skills add PKU-YuanGroup/OpenAI4S --skill bio-clinical-biostatistics-power-and-sample-sizegit clone --depth 1 https://github.com/PKU-YuanGroup/OpenAI4SWrote this? Show the measurements
A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.
[](https://agentmods.dev/skills/pku-yuangroup/openai4s/bio-clinical-biostatistics-power-and-sample-size)<a href="https://agentmods.dev/skills/pku-yuangroup/openai4s/bio-clinical-biostatistics-power-and-sample-size"><img src="https://agentmods.dev/badge/skills/pku-yuangroup/openai4s/bio-clinical-biostatistics-power-and-sample-size/github.svg" alt="Measured on agentmods" height="20"></a>Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.
<a href="https://agentmods.dev/skills/pku-yuangroup/openai4s/bio-clinical-biostatistics-power-and-sample-size"><img src="https://agentmods.dev/badge/skills/pku-yuangroup/openai4s/bio-clinical-biostatistics-power-and-sample-size.svg" alt="Reviewed on agentmods" width="80" height="20"></a>What it costs to keep this loaded
Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5.1 | $0.00125 | $0.08560 |
| Opus 5 | $0.00063 | $0.04280 |
| Sonnet 5 | $0.00025 | $0.01712 |
| Haiku 4.5 | $0.00013 | $0.00856 |
Grade A, and why
bio-clinical-biostatistics-power-sample-size scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 10d ago.
A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.
Nothing flagged
None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.
This is a copy
100% identical to bio-clinical-biostatistics-power-sample-size — 12 lines differ, which has more behind it and is treated as the original. This page carries a canonical link to it rather than competing with it.
How it starts
The opening of the file, as written. The whole thing — 504 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Version Compatibility
Reference examples tested with: statsmodels 0.14+, scipy 1.12+, numpy 1.26+, pandas 2.1+. R packages cited: pwr, gsDesign (Anderson/Merck), gsDesign2, rpact (Wassmer/Brannath), presize, npsurvSS, nph, simtrial.
Before using code patterns, verify installed versions match. If versions differ:
- Python:
pip show <package>thenhelp(module.function)to check signatures - R:
packageVersion('<pkg>')then?function_name
If code throws ImportError, AttributeError, or TypeError, introspect the installed package and adapt the example to match the actual API rather than retrying.
Power and Sample Size for Clinical Trials
"Justify the trial's sample size" -> Compute the n needed to detect a pre-specified alternative δ with power 1-β at significance α, accounting for endpoint distribution, design (superiority/NI/equivalence), expected dropout, multiplicity, and stratification — and distinguish δ (the effect the trial is powered to detect) from MCID (the clinically meaningful difference).
The Foundational Distinction -- δ vs MCID
δ (the alternative effect): what the trial is powered to detect. Usually set above the MCID because sponsors want a strong signal that exceeds noise + design uncertainty.
MCID (Minimum Clinically Important Difference): the smallest effect size considered clinically meaningful. Jaeschke-Singer-Guyatt 1989 Control Clin Trials 10:407 (anchor-based) and Norman-Sloan-Wyrwich 2003 Med Care 41:582 ("the remarkable universality of half a standard deviation") established the modern conventions.
Confusing the two has produced both:
- Underpowered trials where sponsor sets δ = MCID and gets a CI straddling zero
- Overgenerous NI margins where sponsor sets M2 = full MCID (NI margin should be a fraction of MCID)
Postdoc rule of thumb: for superiority, δ >= 1.5 × MCID; for NI, M2 <= 0.5 × MCID.
Algorithmic Taxonomy
| Design | Formula / approach | Software | Strength | Fails when |
|---|---|---|---|---|
| Two-sample t-test, continuous | Cohen's d; n = 2 × (z_α/2 + z_β)² / d² | pwr::pwr.t.test (R); statsmodels.power.tt_ind_solve_power (Py) |
Standard | Heteroscedasticity; non-normal outcomes |
| Two-sample proportions (Fleiss) | Asymptotic normal approximation with/without continuity correction | power.prop.test (R) -- uncorrected; pwr::pwr.2p.test; statsmodels |
Standard | n < 100/arm: continuity correction debate (D'Agostino 1988) |
| Survival (Schoenfeld 1981) | events ≈ 4(z_α/2 + z_β)² / (log HR)² for 1:1 | gsDesign::nSurv; npsurvSS::size_two_arm |
Standard PH-conformant | PH violated (immuno-oncology) under-estimates by 20-50% |
| Survival under non-PH (Lakatos 1988) | Markov chain accommodating time-varying HR, accrual, dropout | gsDesign::nSurv; npsurvSS; simtrial |
Handles immuno-oncology delayed effects | Requires explicit specification of HR(t) and accrual |
| MaxCombo SS under NPH | Simulation-based; pre-specify weight family | nphRCT; simtrial |
Robust to NPH pattern | Computationally heavier |
| Non-inferiority fixed-margin | n = (z_α + z_β)² × variance / M² | pwr::pwr.t2n.test adapted; rpact::getSampleSizeMeans |
Pre-discounted M | Constancy assumption violation invisible |
| Non-inferiority synthesis | Pool historical control-vs-placebo + current test-vs-control | gsDesign::ssTwoArmTest |
More efficient than fixed-margin | Constancy assumption MUST hold exactly |
| Equivalence TOST | Two one-sided tests at α each | pwr::pwr.t.test adapted; presize |
No multiplicity adjustment needed | Wrong question when superiority/NI is intended |
| Group-sequential | Lan-DeMets spending function | rpact; gsDesign |
Interim analyses; early stopping | More complex SAP |
| Sample-size re-estimation (Mehta-Pocock) | Promising-zone conditional power | rpact::getSampleSizeMeans with reestimation |
Recovers power if interim shows promise | Unblinded SSR scares FDA |
| Cluster-randomised | Adjust for design effect = 1 + (m-1)ICC | clusterPower; pwr adapted |
Standard | ICC misspecification |
What ships with it
2 files beside SKILL.md in the same directory: the scripts, references and assets a skill reads on demand. Not counted in the per-session cost; read them before you install if any of them is executable.
What this file has done since we first saw it
Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.
- 10d ago First seen · 504 lines · 125 tokens per session scan A 7d62ed11d3bf
bio-clinical-biostatistics-power-sample-size is a skill published in the GitHub repository PKU-YuanGroup/OpenAI4S (409 stars, last pushed 2d ago), licensed MIT. It adds 125 tokens to every session and 8,560 once invoked, about $0.0006 per session on Opus 5. A static security scan graded it A with 0 findings. It is 100% identical to bio-clinical-biostatistics-power-sample-size, differing in 12 lines, and is treated as a copy.
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