Inference procedures in sequential trial emulation with survival outcomes: comparing confidence intervals based on the sandwich variance estimator, bootstrap and jackknife

TL;DR

This study compares confidence interval methods in sequential trial emulation with survival outcomes, finding that LEF bootstrap performs best in small samples, while sandwich estimators excel in large samples.

Contribution

It introduces and evaluates the linearised estimating function bootstrap for inference in STE, providing practical guidance for choosing CI methods based on sample size and event rate.

Findings

LEF bootstrap CIs have superior coverage in small/moderate samples.

Sandwich variance estimators perform best with large samples.

LEF bootstrap is faster and less affected by treatment imbalance.

Abstract

Sequential trial emulation (STE) is an approach to estimating causal treatment effects by emulating a sequence of target trials from observational data. In STE, inverse probability weighting is commonly utilised to address time-varying confounding and/or dependent censoring. Then structural models for potential outcomes are applied to the weighted data to estimate treatment effects. For inference, the simple sandwich variance estimator is popular but conservative, while nonparametric bootstrap is computationally expensive, and a more efficient alternative, linearised estimating function (LEF) bootstrap, has not been adapted to STE. We evaluated the performance of various methods for constructing confidence intervals (CIs) of marginal risk differences in STE with survival outcomes by comparing the coverage of CIs based on nonparametric/LEF bootstrap, jackknife, and the sandwich variance estimator through simulations. LEF bootstrap CIs demonstrated the best coverage with small/moderate sample sizes, low event rates and low treatment prevalence, which were the motivating scenarios for STE. They were less affected by treatment group imbalance and faster to compute than nonparametric bootstrap CIs. With large sample sizes and medium/high event rates, the sandwich-variance-estimator-based CIs had the best coverage and were the fastest to compute. These findings offer guidance in constructing CIs in causal survival analysis using STE.