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

TL;DR

This paper introduces new power and sample size formulas for causal inference with time-to-event data, applicable to both randomized and observational studies, correcting previous methods and providing practical tools.

Contribution

It derives analytical formulas for sample size and power in causal survival analysis, extending variance theory and offering an online calculator and R package.

Findings

New sample size formula valid at any effect size

Corrects mischaracterization of classic log-rank formulas

Provides tools for both randomized and observational studies

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 analytical 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. We provide an online calculator and an R package 'PSpower' to implement the method.