Improving Longitudinal Targeted Maximum Likelihood Estimation in Target Trial Emulation using Joint Calibrated Weights

2026-06-03

AI Summary

This study addresses the limitations of conventional longitudinal targeted maximum likelihood estimation (LTMLE) in target trial emulation, which relies on inverse probability weighting and is prone to instability and bias under model misspecification, particularly in small samples. To enhance robustness and efficiency, the authors propose a joint calibration LTMLE approach that simultaneously balances covariate distributions in both treatment assignment and censoring mechanisms. By integrating marginal structural models with jointly calibrated weights, this method achieves dual balance and demonstrates substantially improved finite-sample performance over standard LTMLE, offering greater precision and stronger resilience to model misspecification. The practical utility of the proposed estimator is illustrated through an analysis of HIV treatment adherence, confirming its value in real-world applications.

Abstract

In target trial emulation (TTE), marginal structural models (MSMs) can be used to characterise per-protocol treatment effects over time. The MSM parameters are often estimated by inverse probability weighting (IPW), with weights estimated by maximum likelihood. However, IPW-based estimators can be unstable in small samples and are sensitive to misspecification of the weight models. An alternative method for estimating the MSM parameters is longitudinal targeted maximum likelihood estimation (LTMLE). LTMLE is double robust and potentially more efficient than IPW. Nevertheless, LTMLE also relies on inverse probability weights and may therefore share the instability of IPW-based estimators. We propose joint calibrated LTMLE, which integrates LTMLE with joint calibrated weights tailored for per-protocol effect estimation in TTE. This calibration of weights improves finite-sample performance by enforcing covariate balance in both the treatment and censoring processes simultaneously. Simulations show that the proposed method has improved efficiency and robustness to weight model misspecification, compared to standard LTMLE. We illustrate the method using a case study to evaluate the effect of highly active antiretroviral therapy on CD4 cell count among HIV-positive women.

Problem

• target trial emulation
• longitudinal targeted maximum likelihood estimation
• inverse probability weighting
• weight model misspecification
• per-protocol effect

Innovation

• joint calibrated weights
• longitudinal targeted maximum likelihood estimation
• target trial emulation
• covariate balance
• double robustness