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

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

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

Causal etiology of the research of James M. Robins

This issue of Statistical Science draws its inspiration from the work of James M. Robins. Jon Wellner, the Editor at the time, asked the two of us to edit a special issue that would highlight the research topics studied by Robins and the breadth and depth of Robins' contributions. Between the two of us, we have collaborated closely with Jamie for nearly 40 years. We agreed to edit this issue because we recognized that we were among the few in a position to relate the trajectory of his research career to date.Fil: Richardson, Thomas S.. University of Washington; Estados UnidosFil: Rotnitzky, Andrea Gloria. Universidad Torcuato Di Tella. Departamento de Economía; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; 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

Evaluation of viable dynamic treatment regimes in a sequentially randomized trial of advanced prostate cancer

We present new statistical analyses of data arising from a clinical trial designed to compare two-stage dynamic treatment regimes (DTRs) for advanced prostate cancer. The trial protocol mandated that patients be initially randomized among four chemotherapies, and that those who responded poorly be re-randomized to one of the remaining candidate therapies. The primary aim was to compare the DTRs' overall success rates, with success defined by the occurrence of successful responses in each of two consecutive courses of the patient's therapy. Of the 150 study participants, 47 did not complete their therapy as per the algorithm. However, 35 of them did so for reasons that precluded further chemotherapy, that is, toxicity and/or progressive disease. Consequently, rather than comparing the overall success rates of the DTRs in the unrealistic event that these patients had remained on their assigned chemotherapies, we conducted an analysis that compared viable switch rules defined by the per-protocol rules but with the additional provision that patients who developed toxicity or progressive disease switch to a non-prespecified therapeutic or palliative strategy. This modification involved consideration of bivariate per-course outcomes encoding both efficacy and toxicity.We used numerical scores elicited from the trial's principal investigator to quantify the clinical desirability of each bivariate per-course outcome, and defined one endpoint as their average over all courses of treatment. Two other simpler sets of scores as well as log survival time were also used as endpoints. Estimation of each DTR-specific mean score was conducted using inverse probability weighted methods that assumed that missingness in the 12 remaining dropouts was informative but explainable in that it only depended on past recorded data.We conducted additional worst-and best-case analyses to evaluate sensitivity of our findings to extreme departures from the explainable dropout assumption.Fil: Wang, Lu. University of Michigan; Estados UnidosFil: Rotnitzky, Andrea Gloria. Universidad Torcuato Di Tella. Departamento de Economía; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Lin, Xihong. Harvard University; Estados UnidosFil: Millikan, Randall. University of Texas; Estados UnidosFil: Thall, Peter. University of Texas; Estados Unido

Estimation of the effect of interventions that modify treatment

Motivated by a study of surgical operating time and post-operative outcomes for lung cancer, we consider the estimation of causal effects of continuous point-exposure treatments. To investigate causality, the standard paradigm postulates a series of treatment-specific counterfactual outcomes and establishes conditions under which we may learn about them from observational study data. While many choices are possible, causal effects are typically defined in terms of variation of the mean of counterfactual outcomes in hypothetical worlds in which specific treatment strategies are ‘applied’ to all individuals. For example, one might compare two worlds: one where each individual receives some specific dose and a second where each individual receives some other dose. For our motivating study, defining causal effects in this way corresponds to (hypothetical) interventions that could not conceivably be implemented in the real world. In this work, we consider an alternative, complimentary framework that investigates variation in the mean of counterfactual outcomes under hypothetical treatment strategies where each individual receives a treatment dose corresponding to that actually received but modified in some pre-specified way. Quantification of this variation is defined in terms of contrasts for specific interventions as well as in terms of the parameters of a new class of marginal structural mean models. Within this framework, we propose three estimators: an outcome regression estimator, an inverse probability of treatment weighted estimator and a doubly robust estimator. We illustrate the methods with an analysis of the motivating data.Fil: Haneuse, Sebastian. Harvard University; Estados UnidosFil: Rotnitzky, Andrea Gloria. Universidad Torcuato Di Tella. Departamento de Economía; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Characterization of parameters with a mixed bias property

In this article we study a class of parameters with the so-called ‘mixed bias property’. For parameters with this property, the bias of the semiparametric efficient one step estimator is equal to the mean of the product of the estimation errors of two nuisance functions. In non-parametric models, parameters with the mixed bias property admit so-called rate doubly robust estimators, i.e. estimators that are consistent and asymptotically normal when one succeeds in estimating both nuisance functions at sufficiently fast rates, with the possibility of trading off slower rates of convergence for the estimator of one of the nuisance functions with faster rates for the estimator of the other nuisance. We show that the class of parameters with the mixed bias property strictly includes two recently studied classes of parameters which, in turn, include many parameters of interest in causal inference. We characterize the form of parameters with the mixed bias property and of their influence functions. Furthermore, we derive two functional moment equations, each being solved at one of the two nuisance functions, as well as, two functional loss functions, each being minimized at one of the two nuisance functions. These loss functions can be used to derive loss based penalized estimators of the nuisance functions.Fil: Rotnitzky, Andrea Gloria. Universidad Torcuato Di Tella. Departamento de Economía; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Smucler, Ezequiel. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Robins, James. Harvard University; Estados Unido

Multiple robust estimation of marginal structural mean models for unconstrained outcomes

We consider estimation, from longitudinal observational data, of the parameters of marginal structural mean models for unconstrained outcomes. Current proposals include inverse probability of treatment weighted and double robust (DR) estimators. A difficulty with DR estimation is that it requires postulating a sequence of models, one for the each mean of the counterfactual outcome given covariate and treatment history up to each exposure time point. Most natural models for such means are often incompatible. Robins et al., (2000b) proposed a parameterization of the likelihood which implies compatible parametric models for such means. Their parameterization has not been exploited to construct DR estimators and one goal of this article is to fill this gap. More importantly, exploiting this parameterization we propose a multiple robust (MR) estimator that confers even more protection against model misspecification than DR estimators. Our methods are easy to implement as they are based on the iterative fit of a sequence of weighted regressions.Fil: Babino, Lucía. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Ecología, Genética y Evolución de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Ecología, Genética y Evolución de Buenos Aires; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; ArgentinaFil: Rotnitzky, Andrea Gloria. Universidad Torcuato Di Tella. Departamento de Economía; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Robins, James. Harvard University. Harvard School of Public Health; Estados Unido

Optimal auxiliary-covariate-based two-phase sampling design for semiparametric efficient estimation of a mean or mean difference, with application to clinical trials

To address the objective in a clinical trial to estimate the mean or mean difference of an expensive endpoint Y, one approach employs a two-phase sampling design, wherein inexpensive auxiliary variables W predictive of Y are measured in everyone, Y is measured in a random sample, and the semiparametric efficient estimator is applied. This approach is made efficient by specifying the phase two selection probabilities as optimal functions of the auxiliary variables and measurement costs. While this approach is familiar to survey samplers, it apparently has seldom been used in clinical trials, and several novel results practicable for clinical trials are developed. We perform simulations to identify settings where the optimal approach significantly improves efficiency compared to approaches in current practice. We provide proofs and R code. The optimality results are developed to design an HIV vaccine trial, with objective to compare the mean 'importance-weighted' breadth (Y) of the T-cell response between randomized vaccine groups. The trial collects an auxiliary response (W) highly predictive of Y and measures Y in the optimal subset. We show that the optimal design-estimation approach can confer anywhere between absent and large efficiency gain (up to 24 % in the examples) compared to the approach with the same efficient estimator but simple random sampling, where greater variability in the cost-standardized conditional variance of Y given W yields greater efficiency gains. Accurate estimation of E[Y|W] is important for realizing the efficiency gain, which is aided by an ample phase two sample and by using a robust fitting method.Fil: Gilbert, Peter B.. Fred Hutchinson Cancer Research Center; Estados Unidos. University of Washington; Estados UnidosFil: Yu, Xuesong. Fred Hutchinson Cancer Research Center; Estados UnidosFil: Rotnitzky, Andrea Gloria. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella; Argentina. Harvard University. Harvard School of Public Health; Estados Unido