Marginal Structural Models to Estimate the Joint Causal Effect of Nonrandomized Treatments

Abstract

Even in the absence of unmeasured confounding factors or model misspeci cation, standard methods for estimating the causal effect of time-varying treatments on survival are biased when (a) there exists a time-dependent risk factor for survival that also predicts subsequent treatment, and (b) past treatment history predicts subsequent risk factor level. In contrast, methods based on marginal structural models (MSMs) can provide consistent estimates of causal effects when unmeasured confounding and model misspeci cation are absent. MSMs are a new class of causal models whose parameters are estimated using a new class of estimators-inverse-probability-of-treatment weighted estimators. We use a marginal structural Cox proportional hazards model to estimate the joint effect of zidovudine (AZT) and prophylaxis therapy for Pneumocystis carinii pneumonia on the survival of H IV-positive men in the Multicenter A IDS Cohort Study, an observational study of homosexual men. We obtained an estimated causal mortality rate (hazard) ratio of .67 (conservative 95% con dence interval .46-.98) for AZT and of 1.14 (.79, 1.64) for prophylaxis therapy. These estimates will be consistent for the true causal rate ratios when the functional forms chosen for our models are correct and data have been obtained on all time-independent and time-dependent covariates that predict both subsequent treatment and mortality.

Prognosis of patients with advanced gastric cancer by HER2 status and trastuzumab treatment

“…Because the use of trastuzumab and the exposure to platinum agents differed between the groups, we used the TVC analysis to adjust the exposure to agents and comprehensively evaluate the impact of each agent class, regardless of the treatment line. However, TVC analysis is not necessarily adequate under the conditions of our study because its validity may depend on the assumption of a strong association between treatment selection at the time of the events and the history leading up to the events [27]. Other potential confounders, such as PS and the metastatic site, were also considered in the multivariate analyses; owing to the retrospective, non-randomized nature of the study, however, residual confounding effects caused by non-included factors cannot be completely ruled out.…”

Administration of Parenteral Iron and Mortality among Hemodialysis Patients

“…To overcome the limitations of standard software, we used a weighted Poisson regression approximation to a weighted Cox proportional hazards model. The adjusted hazard ratios from these models are numerically comparable to hazard ratios from proportional hazards regression and more closely approximate the results of standard analyses of a randomized trial than do other regression approaches that incorporate time-dependent variables (24,25). The models we fit assumed that the effect of iron did not vary with time since ESRD; we tested this assumption by including a term for the interaction of iron dose and time since ESRD.…”

“…However, the use of these traditional regression methods for controlling confounding by time-varying variables during the iron exposure window could yield biased results because these variables may potentially both predict subsequent iron use and mortality and serve on the causal pathway between iron administration and death. One approach to deal with this type of confounding by time-varying covariates without inappropriately adjusting for any role they may have as intermediate variables is to estimate a modified form of a marginal structural model using weighted Cox proportional hazards regression (21)(22)(23)(24)(25)(26). Using this method, we developed individual-level weights for our mortality model with parameters including rolling 6-mo iron dose, baseline covariates, and levels of timevarying covariates at the start of each 6-mo window.…”

Survival Outcomes of Sipuleucel-T Phase III Studies: Impact of Control-Arm Cross-Over to Salvage Immunotherapy

“…OS therefore remains the most clinically meaningful endpoint in oncology clinical trials (22), and the potential for subsequent therapies to influence it requires careful assessment. Assessing OS in future clinical trials may need to use sophisticated statistical analyses, such as marginal structural models, in which prognostic variables that may also inform treatment decisions (e.g., ECOG status or PSA) are allowed to vary over time (23)(24)(25). More sophisticated models could also account for patient discontinuations that are dependent on treatment assignment and patient noncompliance with dosing (26).…”