Pith Number

pith:IBWGQQ37

pith:2026:IBWGQQ37PGD4SQCKASGV37LPVS

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Sample size and power calculations for causal inference with time-to-event outcomes

Bo Liu, Chengxin Yang, Fan Li

A new sample size formula for marginal hazard ratios in time-to-event causal inference applies to both randomized trials and observational studies.

arxiv:2605.10088 v2 · 2026-05-11 · stat.ME

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Claims

C1strongest claim

We derive a new sample size formula valid at any prespecified effect size, applicable to both randomized trials and observational studies. For randomized trials, the formula requires only the canonical inputs of treatment proportion, effect size, and event rate. The new formula corrects the mischaracterization of classic log-rank-based formulas.

C2weakest assumption

The marginal structural Cox model satisfies the proportional hazards assumption and the asymptotic variance derivation for the IPW partial likelihood estimator holds under the stated regularity conditions; the overlap coefficient is assumed to be correctly estimated from the data.

C3one line summary

Derives new analytical sample size formulas for the marginal hazard ratio under IPW estimation in Cox models, correcting classic log-rank formulas for RCTs and adding an overlap measure for observational data.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:16.731847Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

406c68437f7987c9404a048d5dfd6facbe767187b2f36ce63a62eeec4375c5dc

Aliases

arxiv: 2605.10088 · arxiv_version: 2605.10088v2 · doi: 10.48550/arxiv.2605.10088 · pith_short_12: IBWGQQ37PGD4 · pith_short_16: IBWGQQ37PGD4SQCK · pith_short_8: IBWGQQ37

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/IBWGQQ37PGD4SQCKASGV37LPVS \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 406c68437f7987c9404a048d5dfd6facbe767187b2f36ce63a62eeec4375c5dc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "73f363e92ae5d5aa1e7fdd4734aa752ca656da4644046e9c7176a758b09b5096",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ME",
    "submitted_at": "2026-05-11T07:07:23Z",
    "title_canon_sha256": "fcd14b00cdb2c5ba590a87959a8ec5164ca8295ab6032679d5c3b1d1e51bec4c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.10088",
    "kind": "arxiv",
    "version": 2
  }
}