Best for which estimand? A known-truth benchmark of longitudinal-matching and target-trial-emulation methods for time-varying treatments

Abstract

On a non-collapsible survival mechanism, longitudinal-matching and target-trial-emulation methods are not competing estimators of one truth but answers to different causal questions, so a benchmark that scores them against a single "true hazard ratio" fabricates bias. We provide the direct comparison of relative efficiency, variance estimation, and model sensitivity that reviews find lacking. On a deliberately non-collapsible continuous-time Cox mechanism with known truth, the dominant families (sequential Cox, sequential stratification, risk-set matching, and inverse-probability-of-treatment-weighted (IPTW) marginal structural models) target numerically distinct causal estimands (marginal, conditional, two average-treatment-effect-on-the-treated, and intention-to-treat versus per-protocol). First, we quantify the phantom bias a shared marginal truth fabricates: 0.32-0.33 log-cumulative-hazard-ratio units for the matching estimators and 0.15 for the conditional method; the associational naive time-dependent Cox sits 0.76 away, a total discrepancy compounding the estimand gap with confounding. Second, a rank reversal: the recommended method flips with the target estimand, and a low-variance off-target estimator can still win on mean-squared error. Third, a cross-family variance result: the cluster-robust sandwich is closer to nominal for the trial-stacking estimator (0.90) but under-covers the matching estimators (0.77-0.82), which a prespecified n=500 bootstrap sub-study brings to 0.95-0.96. Fourth, model sensitivity: omitting a confounder induces 0.45-0.50 log-hazard-ratio bias and undercoverage, and intention-to-treat and per-protocol effects diverge as switching increases; a heart-transplant analysis illustrates these. On a second mechanism three of four findings replicate, the rank reversal attenuating and model sensitivity proving calibration-dependent.