Analysis of Longitudinal Marginal Structural Models

In this article we construct and study estimators of the causal effect of a time-dependent treatment on survival in longitudinal studies. We employ a particular marginal structural model (MSM), and follow a general methodology for constructing estimating functions in censored data models. The inverse probability of treatment weighted (IPTW) estimator is used as an initial estimator and the corresponding treatment-orthogonalized, one-step estimator is consistent and asymptotically linear when the treatment mechanism is consistently estimated. We extend these methods to handle informative censoring. A simulation study demonstrates that the the treatment-orthogonalized, one-step estimator is superior to the IPTW estimator in terms of efficiency. The proposed methodology is employed to estimate the causal effect of exercise on mortality in a longitudinal study of seniors in Sonoma County

History-Adjusted Marginal Structural Models to Estimate Time-Varying Effect Modification

Much of epidemiology and clinical medicine is focused on the estimation of treatments or interventions administered over time. In such settings of longitudinal treatment, time-dependent confounding is often an important source of bias. Marginal structural models are a powerful tool for estimating the causal effect of a treatment using observational data, particularly when time-dependent confounding is present. Recent statistical work presented a generalization of marginal structural models, called history-adjusted marginal structural models. Unlike standard marginal structural models, history-adjusted marginal structural models can be used to estimate modification of treatment effects by time-varying covariates. Estimation of time-dependent causal effect modification is frequently of great practical relevance. For example, clinical researchers are often interested in how the prognostic significance of a biomarker for treatment response can change over time. This article provides a practical introduction to the implementation and interpretation of history-adjusted marginal structural models. The method is illustrated using a clinical question drawn from the treatment of HIV infection. Observational cohort data from San Francisco, California, collected between 2000 and 2004, are used to estimate the effect of time until switching antiretroviral therapy regimen among patients receiving a non-suppressive regimen, and how this effect differs depending on CD4 T cell count

Marginal Structural Models with Counterfactual Effect Modifiers

In health and social sciences, research questions often involve systematic assessment of the modification of treatment causal effect by patient characteristics, in longitudinal settings with time-varying or post-intervention effect modifiers of interest. In this work, we investigate the robust and efficient estimation of the so-called Counterfactual-History-Adjusted Marginal Structural Model (van der Laan and Petersen (2007)), which models the conditional intervention-specific mean outcome given modifier history in an ideal experiment where, possible contrary to fact, the subject was assigned the intervention of interest, including the treatment sequence in the conditioning history. We establish the semiparametric efficiency theory for these models, and present a substitution-based, semiparametric efficient and doubly robust estimator using the targeted maximum likelihood estimation methodology (TMLE, e.g. van der Laan and Rubin (2006), van der Laan and Rose (2011)). To facilitate implementation in applications where the effect modifier is high dimensional, our third contribution is a projected influence curve (and the corresponding TMLE estimator), which retains most of the robustness of its efficient peer and can be easily implemented in applications where the use of the efficient influence curve becomes taxing. In addition to these two robust estimators, we also present an Inverse-Probability-Weighted (IPW) estimator (e.g. Robins (1997a), Hernan, Brumback, and Robins (2000)), and a non-targeted G-computation estimator (Robins (1986)). The comparative performance of these estimators are assessed in a simulation study. The use of the TMLE estimator (based on the projected influence curve) is illustrated in a secondary data analysis for the Sequenced Treatment Alternatives to Relieve Depression (STAR*D) trial

History-Adjusted Marginal Structural Models: Optimal Treatment Strategies

Much of clinical medicine involves choosing a future treatment plan that is expected to optimize a patient\u27s long-term outcome, and modifying this treatment plan over time in response to changes in patient characteristics. However, dynamic treatment regimens, or decision rules for altering treatment in response to time-varying covariates, are rarely estimated based on observational data. In a companion paper, we introduced a generalization of Marginal Structural Models, named History-Adjusted Marginal Structural Models, that estimate modification of causal effects by time-varying covariates. Here, we illustrate how History-Adjusted Marginal Structural Models can be used to identify a specific type of optimal dynamic treatment regimen. Estimation and interpretation of this dynamic treatment regimen are illustrated using an example drawn from the treatment of HIV infection using antiretroviral drugs

Double Robust Estimation in Longitudinal Marginal Structural Models

Consider estimation of causal parameters in a marginal structural model for the discrete intensity of the treatment specific counting process (e.g. hazard of a treatment specific survival time) based on longitudinal observational data on treatment, covariates and survival. We assume the sequential randomization assumption (SRA) on the treatment assignment mechanism and the so called experimental treatment assignment assumption which is needed to identify the causal parameters from the observed data distribution. Under SRA, the likelihood of the observed data structure factorizes in the auxiliary treatment mechanism and the partial likelihood consisting of the product over time of conditional distributions of covariate and survival at a specific time, given the past. Due to the curse of dimensionality, without assuming lower dimensional models for either the partial likelihood or the treatment mechanism, there exist no regular asymptotically linear estimators with reasonable practical performance (van der Laan and Robins [2002]). In this article, we define three estimators the Inverse Probability of Treatment weighted (IPTW) estimator based on a maximum likelihood estimator of the treatment mechanism according to a model, the maximum likelihood estimator (MLE) based on a maximum likelihood estimator of the partial likleihood according to a model, and a double robust (DL) estimator based on the maximum likelihood estimator of the treatment mechanism and the maximum likelihood estimator of the partial likelihood. The double robust estimator is obtained by following a general methodology for constructing double robust estimating functions in censored data models as described in van der Laan and Robins [2002]. We propose specific implementation of this estimator based on Monte-Carlo simulation methods, which makes the estimator computationally tractable and maximally robust. The double-robust estimator is consistent and asymptotically linear when either the treatment mechanism or the partial likelihood of the observed data is consistently estimated. We extend the estimator to handle informative censoring. We illustrate the practical performance of the DR estimator relative to the IPTW and ML estimators in a simulation study. The proposed methodology is also applied to estimate the causal effect of exercise on physical functioning in a longitudinal study of seniors in Sonoma County