Efficient Adjustment Sets for Population Average Causal Treatment Effect Estimation in Graphical Models

The method of covariate adjustment is often used for estimation of total treatment effects from observational studies. Restricting attention to causal linear models, a recent article (Henckel et al., 2019) derived two novel graphical criteria: one to compare the asymptotic variance of linear regression treatment effect estimators that control for certain distinct adjustment sets and another to identify the optimal adjustment set that yields the least squares estimator with the smallest asymptotic variance. In this paper we show that the same graphical criteria can be used in non-parametric causal graphical models when treatment effects are estimated using non-parametrically adjusted estimators of the interventional means. We also provide a new graphical criterion for determining the optimal adjustment set among the minimal adjustment sets and another novel graphical criterion for comparing time dependent adjustment sets. We show that uniformly optimal time dependent adjustment sets do not always exist. For point interventions, we provide a sound and complete graphical criterion for determining when a non-parametric optimally adjusted estimator of an interventional mean, or of a contrast of interventional means, is semiparametric efficient under the non-parametric causal graphical model. In addition, when the criterion is not met, we provide a sound algorithm that checks for possible simplifications of the efficient influence function of the parameter. Finally, we find an interesting connection between identification and efficient covariate adjustment estimation. Specifically, we show that if there exists an identifying formula for an interventional mean that depends only on treatment, outcome and mediators, then the non-parametric optimally adjusted estimator can never be globally efficient under the causal graphical model.Fil: Rotnitzky, Andrea Gloria. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella. Departamento de Economía; ArgentinaFil: Smucler, Ezequiel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella. Departamento de Economía; Argentin

On the analysis of tuberculosis studies with intermittent missing sputum data

In randomized studies evaluating treatments for tuberculosis (TB), individuals are scheduled to be routinely evaluated for the presence of TB using sputum cultures. One important endpoint in such studies is the time of culture conversion, the first visit at which a patient’s sputum culture is negative and remains negative. This article addresses how to draw inference about treatment effects when sputum cultures are intermittently missing on some patients. We discuss inference under a novel benchmark assumption and under a class of assumptions indexed by a treatment-specific sensitivity parameter that quantify departures from the benchmark assumption. We motivate and illustrate our approach using data from a randomized trial comparing the effectiveness of two treatments for adult TB patients in Brazil.Fil: Scharfstein, Daniel. University Johns Hopkins; Estados UnidosFil: Rotnitzky, Andrea Gloria. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella. Departamento de Economía; ArgentinaFil: Abraham, Maria. Statistics Collaborative; Estados UnidosFil: McDermott, Aidan. University Johns Hopkins; Estados UnidosFil: Chaisson, Richard. University Johns Hopkins; Estados UnidosFil: Geiter, Lawrence. Otsuka Novel Products; Estados Unido

Discussion of “Dynamic treatment regimes: Technical challenges and applications”

We thank the editor for organizing this discussion of the article by Laber et al. (2014) (throughout referred to as LLQPM). The authors offer an elegant solution to the inferential problem caused by nonregularity. Our discussion will to a large extent focus on conceptual rather than technical issues, in part because the authors handled the technical matters so decisively and well. In so doing, we recognize that discussion of conceptual issues was not the authors’ goal and that the authors have written elsewhere about many of the issues we raise. Indeed, in our own writing, we have often either ignored the issues we raise or were unable to offer coherent solutions to them. We hope our discussion makes for an interesting and lively interchange.Fil: Robins, James. Harvard University; Estados UnidosFil: Rotnitzky, Andrea Gloria. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella. Departamento de Economía; Argentin

Dynamic regime marginal structural mean models for estimation of optimal dynamic treatment regimes, Part I: main content

Dynamic treatment regimes are set rules for sequential decision making based on patient covariate history. Observational studies are well suited for the investigation of the effects of dynamic treatment regimes because of the variability in treatment decisions found in them. This variability exists because different physicians make different decisions in the face of similar patient histories. In this article we describe an approach to estimate the optimal dynamic treatment regime among a set of enforceable regimes. This set is comprised by regimes defined by simple rules based on a subset of past information. The regimes in the set are indexed by a Euclidean vector. The optimal regime is the one that maximizes the expected counterfactual utility over all regimes in the set. We discuss assumptions under which it is possible to identify the optimal regime from observational longitudinal data. Murphy et al. (2001) developed efficient augmented inverse probability weighted estimators of the expected utility of one fixed regime. Our methods are based on an extension of the marginal structural mean model of Robins (1998, 1999) which incorporate the estimation ideas of Murphy et al. (2001). Our models, which we call dynamic regime marginal structural mean models, are specially suitable for estimating the optimal treatment regime in a moderately small class of enforceable regimes of interest. We consider both parametric and semiparametric dynamic regime marginal structural models. We discuss locally efficient, double-robust estimation of the model parameters and of the index of the optimal treatment regime in the set. In a companion paper in this issue of the journal we provide proofs of the main results