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

2026-05-11

AI Summary

This study addresses the challenge of accurately determining sample size for time-to-event outcomes in causal inference, particularly in observational studies where a general framework has been lacking. Focusing on the marginal hazard ratio, the authors derive an analytical expression for the asymptotic variance of the inverse probability weighted partial likelihood estimator and develop a unified sample size formula applicable to both randomized trials and observational studies. Key innovations include enabling sample size calculation for any prespecified effect size, correcting the common misuse of the log-rank method, introducing an overlap coefficient to quantify covariate balance, and establishing a variance inflation framework compatible with arbitrary propensity score weighting. The resulting formula requires only treatment proportion, effect size, and event rate in randomized trials, and adds only the overlap coefficient in observational settings, substantially enhancing both accuracy and applicability.

Abstract

This paper develops power and sample size formulas for causal inference with time-to-event outcomes. The target estimand is the marginal hazard ratio: the coefficient of a marginal structural Cox proportional hazard model with treatment as the only predictor. We extend the robust sandwich variance theory and derive the analytical form of the asymptotic variance for the inverse probability weighted partial likelihood estimator. Building on this, 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. For observational studies, one additional input suffices: an overlap coefficient summarizing covariate similarity between comparison groups. We further develop a variance inflation approach applicable to any propensity score balancing weights, anchored to the corrected baseline variance.

Problem

• sample size
• power calculation
• causal inference
• time-to-event outcomes
• marginal hazard ratio

Innovation

• marginal hazard ratio
• inverse probability weighting
• sample size calculation
• causal inference
• variance inflation