James M Robins

Harvard University | Harvard · Department of Epidemiology

Researchers are often interested in estimating the effect of sustained use of a treatment on a health outcome. However, adherence to strict treatment protocols can be challenging for individuals in practice and, when non-adherence is expected, estimates of the effect of sustained use may not be useful for decision making. As an alternative, more re...

In a recent work published in this journal, Philip Dawid has described a graphical causal model based on decision diagrams. This article describes how single-world intervention graphs (SWIGs) relate to these diagrams. In this way, a correspondence is established between Dawid's approach and those based on potential outcomes such as Robins’ finest f...

In this article we develop a feasible version of the assumption-lean tests in Liu et al. 20 that can falsify an analyst's justification for the validity of a reported nominal $(1 - \alpha)$ Wald confidence interval (CI) centered at a double machine learning (DML) estimator for any member of the class of doubly robust (DR) functionals studied by Rot...

In a recent paper published in the Journal of Causal Inference, Philip Dawid has described a graphical causal model based on decision diagrams. We show the relationship of these models to Single World Intervention Graphs (SWIGs). In this way we link Dawid's approach to causal models based on potential outcomes such as Robins' Finest Fully Randomize...

Researchers are often interested in estimating the effect of sustained use of a pharmacological treatment on a health outcome. However, adherence to strict treatment protocols can be challenging for patients in practice and, when non-adherence is expected, estimates of the effect of sustained use may not be useful for decision making. As an alterna...

It is often said that the fundamental problem of causal inference is a missing data problem -- the comparison of responses to two hypothetical treatment assignments is made difficult because for every experimental unit only one potential response is observed. In this paper, we consider the implications of the converse view: that missing data proble...

The case-crossover design (Maclure, 1991) is widely used in epidemiology and other fields to study causal effects of transient treatments on acute outcomes. However, its validity and causal interpretation have only been justified under informal conditions. Here, we place the design in a formal counterfactual framework for the first time. Doing so h...

When individuals participating in a randomized trial differ with respect to the distribution of effect modifiers compared compared with the target population where the trial results will be used, treatment effect estimates from the trial may not directly apply to target population. Methods for extending -- generalizing or transporting -- causal inf...

Researchers are often interested in treatment effects on outcomes that are only defined conditional on posttreatment events. For example, in a study of the effect of different cancer treatments on quality of life at end of follow-up, the quality of life of individuals who die during the study is undefined. In these settings, naive contrasts of outc...

The No Unmeasured Confounding Assumption is widely used to identify causal effects in observational studies. Recent work on proximal inference has provided alternative identification results that succeed even in the presence of unobserved confounders, provided that one has measured a sufficiently rich set of proxy variables, satisfying specific str...

Analyses of biomedical studies often necessitate modeling longitudinal causal effects. The current focus on personalized medicine and effect heterogeneity makes this task even more challenging. Towards this end, structural nested mean models (SNMMs) are fundamental tools for studying heterogeneous treatment effects in longitudinal studies. However,...

In this paper, we generalize methods in the Difference in Differences (DiD) literature by showing that both additive and multiplicative standard and coarse Structural Nested Mean Models (Robins, 1994, 1997, 1998, 2000, 2004; Lok and Degruttola, 2012; Vansteelandt and Joffe, 2014) are identified under parallel trends assumptions. Our methodology ena...

A randomized trial and an analysis of observational data designed to emulate the trial sample observations separately, but have the same eligibility criteria, collect information on some shared baseline covariates, and compare the effects of the same treatments on the same outcomes. Treatment effect estimates from the trial and its emulation can be...

Multiply robust estimators of the longitudinal g-formula have recently been proposed to protect against model misspecification better than the standard augmented inverse probability weighted estimator (Rotnitzky et al., 2017; Luedtke et al., 2018). These multiply robust estimators ensure consistency if one of the models for the treatment process or...

In competing event settings, a counterfactual contrast of cause-specific cumulative incidences quantifies the total causal effect of a treatment on the event of interest. However, effects of treatment on the competing event may indirectly contribute to this total effect, complicating its interpretation. We previously proposed the separable effects...

We argue that randomized controlled trials (RCTs) are special even among settings where average treatment effects are identified by a nonparametric unconfoundedness assumption. This claim follows from two results of Robins and Ritov (1997): (1) with at least one continuous covariate control, no estimator of the average treatment effect exists which...

We discuss the recent paper on "excursion effect" by T. Qian et al. (2020). We show that the methods presented have close relationships to others in the literature, in particular to a series of papers by Robins, Hern\'{a}n and collaborators on analyzing observational studies as a series of randomized trials. There is also a close relationship to th...

Instrumental variables are widely used to deal with unmeasured confounding in observational studies and imperfect randomized controlled trials. In these studies, researchers often target the so-called local average treatment effect as it is identifiable under mild conditions. In this paper, we consider estimation of the local average treatment effe...

We examine study designs for extending (generalizing or transporting) causal inferences from a randomized trial to a target population. Specifically, we consider nested trial designs, where randomized individuals are nested within a sample from the targetpopulation, and non-nested trial designs, including composite dataset designs, where a randomiz...

We derive new estimators of an optimal joint testing and treatment regime under the no direct effect assumption that a given laboratory, diagnostic, or screening test has no effect on a patient’s clinical outcomes except through the effect of the test results on the choice of treatment. We model the optimal joint strategy with an optimal structural...

The extent and duration of immunity following SARS-CoV-2 infection are critical outstanding questions about the epidemiology of this novel virus, and studies are needed to evaluate the effects of serostatus on reinfection. Understanding the potential sources of bias and methods to alleviate biases in these studies is important for informing their d...

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 nonparametric models, parameters with the mixed bias property admit so-called rate doubly rob...

Among Judea Pearl's many contributions to Causality and Statistics, the graphical d-separation} criterion, the do-calculus and the mediation formula stand out. In this chapter we show that d-separation} provides direct insight into an earlier causal model originally described in terms of potential outcomes and event trees. In turn, the resulting sy...

Judea Pearl's insight that, when errors are assumed independent, the Pure (aka Natural) Direct Effect (PDE) is non-parametrically identified via the Mediation Formula was `path-breaking' in more than one sense! In the same paper Pearl described a thought-experiment as a way to motivate the PDE. Analysis of this experiment led Robins \& Richardson t...

This is the rejoinder to the discussion by Kennedy, Balakrishnan and Wasserman on the paper "On nearly assumption-free tests of nominal confidence interval coverage for causal parameters estimated by machine learning" published in Statistical Science.

We consider the problem of estimating the effects of a binary treatment on a continuous outcome of interest from observational data in the absence of confounding by unmeasured factors. We provide a new estimator of the population average treatment effect (ATE) based on the difference of novel double-robust (DR) estimators of the treatment-specific...

Instrumental variables are widely used to deal with unmeasured confounding in observational studies and imperfect randomized controlled trials. In these studies, researchers often target the so-called local average treatment effect as it is identifiable under mild conditions. In this paper, we consider estimation of the local average treatment effe...

In observational studies, treatments are typically not randomized and therefore estimated treatment effects may be subject to confounding bias. The instrumental variable (IV) design plays the role of a quasi-experimental handle since the IV is associated with the treatment and only affects the outcome through the treatment. In this paper, we presen...

Researchers are often interested in treatment effects on outcomes that are only defined conditional on a post-treatment event status. For example, in a study of the effect of different cancer treatments on quality of life at end of follow-up, the quality of life of individuals who die during the study is undefined. In these settings, a naive contra...

The g‐formula can be used to estimate the survival curve under a sustained treatment strategy. Two available estimators of the g‐formula are non‐iterative conditional expectation and iterative conditional expectation. We propose a version of the iterative conditional expectation estimator and describe its procedures for deterministic and random tre...

In time-to-event settings, the presence of competing events complicates the definition of causal effects. Here we propose the new separable effects to study the causal effect of a treatment on an event of interest. The separable direct effect is the treatment effect on the event of interest not mediated by its effect on the competing event. The sep...

The extent and duration of immunity following SARS-CoV-2 infection are critical outstanding questions about the epidemiology of this novel virus, and studies are needed to evaluate the effects of serostatus on reinfection. Understanding the potential sources of bias and methods to alleviate biases in these studies is important for informing their d...

The case-crossover design (Maclure, 1991) is widely used in epidemiology and other fields to study causal effects of transient treatments on acute outcomes. However, its validity and causal interpretation have only been justified under informal conditions. Here, we place the design in a formal counterfactual framework for the first time. Doing so h...

In competing event settings, a counterfactual contrast of cause-specific cumulative incidences quantifies the total causal effect of a treatment on the event of interest. However, effects of treatment on the competing event may indirectly contribute to this total effect, complicating its interpretation. We previously proposed the Fseparable effects...

Background and Purpose— Long-term effect of lifestyle changes on stroke incidence has not been estimated in randomized trials. We used observational data to estimate the incidence of stroke under hypothetical lifestyle strategies in the NHS (Nurses’ Health Study). Methods— We considered 3 nondietary strategies (smoking cessation, exercising ≥30 mi...

Background: Weight gain following smoking cessation reduces the incentive to quit, especially among women. Exercise and diet interventions may reduce post-cessation weight gain, but their long-term effect has not been estimated in randomized trials. Methods: We estimated the long-term reduction in post-cessation weight gain among women under smo...

We derive new estimators of an optimal joint testing and treatment regime under the no direct effect (NDE) assumption that a given laboratory, diagnostic, or screening test has no effect on a patient's clinical outcomes except through the effect of the test results on the choice of treatment. We model the optimal joint strategy using an optimal reg...

Missing data is a pervasive problem in data analyses, resulting in datasets that contain censored realizations of a target distribution. Many approaches to inference on the target distribution using censored observed data, rely on missing data models represented as a factorization with respect to a directed acyclic graph. In this paper we consider...

Missing data is a pervasive problem in data analyses, resulting in datasets that contain censored realizations of a target distribution. Many approaches to inference on the target distribution using censored observed data, rely on missing data models represented as a factorization with respect to a directed acyclic graph. In this paper we consider...

When engagement with a randomized trial is driven by factors that affect the outcome or when trial engagement directly affects the outcome independent of treatment, the average treatment effect among trial participants is unlikely to generalize to a target population. In this paper, we use counterfactual and graphical causal models to examine under...

Extending (generalizing or transporting) causal inferences from a randomized trial to a target population requires ``generalizability'' or ``transportability'' assumptions, which state that randomized and non-randomized individuals are exchangeable conditional on baseline covariates. These assumptions are made on the basis of background knowledge,...

We examine study designs for extending (generalizing or transporting) causal inferences from a randomized trial to a target population. Specifically, we consider nested trial designs, where randomized individuals are nested within a sample from the target population, and non-nested trial designs, including composite dataset designs, where a randomi...

For many causal effect parameters $\psi$ of interest doubly robust machine learning estimators $\widehat\psi_1$ are the state-of-the-art, incorporating the benefits of the low prediction error of machine learning algorithms; the decreased bias of doubly robust estimators; and.the analytic tractability and bias reduction of cross fitting. When the p...

In this article we characterize a class of parameters in large non-parametric models that admit rate doubly robust estimators. An estimator of a parameter of interest which relies on non-parametric estimators of two nuisance functions is rate doubly robust if it is consistent and asymptotically normal when one succeeds in estimating both nuisance f...

We consider inference about a scalar parameter under a non-parametric model based on a one-step estimator computed as a plug in estimator plus the empirical mean of an estimator of the parameter's influence function. We focus on a class of parameters that have influence function which depends on two infinite dimensional nuisance functions and such...

Decisions about when to start or switch a therapy often depend on the frequency with which individuals are monitored or tested. For example, the optimal time to switch antiretroviral therapy depends on the frequency with which HIV‐positive individuals have HIV RNA measured. This paper describes an approach to use observational data for the comparis...

Personalized medicine asks if a new treatment will help a particular patient, rather than if it improves the average response in a population. Without a causal model to distinguish these questions, interpretational mistakes arise. These mistakes are seen in an article by Demidenko [2016] that recommends the “D-value,” which is the probability that...

In time-to-event settings, the presence of competing events complicates the definition of causal effects. Here we propose the new separable effects to study the causal effect of a treatment on an event of interest. The separable direct effect is the treatment effect on the event of interest not mediated by its effect on the competing event. The sep...

Standard approaches to estimating the effect of a time-varying exposure on survival may be biased in the presence of time-varying confounders themselves affected by prior exposure. Methods involving estimation of structural models are becoming more widely used alternatives that do not suffer from this bias. In the case of survival outcomes, these i...

This paper investigates the problem of making inference about a parametric model for the regression of an outcome variable $Y$ on covariates $(V,L)$ when data are fused from two separate sources, one which contains information only on $(V, Y)$ while the other contains information only on covariates. This data fusion setting may be viewed as an extr...

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 m...

Several methods have been proposed for partially or point identifying the average treatment effect (ATE) using instrumental variable (IV) type assumptions. The descriptions of these methods are widespread across the statistical, economic, epidemiologic, and computer science literature, and the connections between the methods have not been readily a...

Researchers are often interested in using observational data to estimate the effect on a health outcome of maintaining a continuous treatment within a pre-specified range over time; e.g. “always exercise at least 30 minutes per day”. There may be many precise interventions that could achieve this range. In this paper we consider representative inte...

We provide adaptive inference methods for linear functionals of sparse linear approximations to the conditional expectation function. Examples of such functionals include average derivatives, policy effects, average treatment effects, and many others. The construction relies on building Neyman-orthogonal equations that are approximately invariant t...

There are many interesting and widely used estimators of a functional with finite semiparametric variance bound that depend on nonparametric estimators of nuisance functions. We use cross-fitting (i.e. sample splitting) to construct novel estimators with fast remainder rates. We give cross-fit doubly robust estimators that use separate subsamples t...

Background: Individual-level simulation models are valuable tools for comparing the impact of clinical or public health interventions on population health and cost outcomes over time. However, a key challenge is ensuring that outcome estimates correctly reflect real-world impacts. Calibration to targets obtained from randomized trials may be insuf...

Pragmatic trials are designed to address real-world questions about care options. This article addresses issues that may arise from per-protocol and intention-to-treat analyses of such trials, outlines alternative analytic approaches, and provides guidance on how to choose among them.

We introduce a new method of estimation of parameters in semi-parametric and nonparametric models. The method is based on estimating equations that are U-statistics in the observations. The U-statistics are based on higher order influence functions that extend ordinary linear influence functions of the parameter of interest, and represent higher de...

Structural nested mean models (SNMMs) are among the fundamental tools for inferring causal effects of time-dependent exposures from longitudinal studies. With binary outcomes, however, current methods for estimating multiplicative and additive SNMM parameters suffer from variation dependence between the causal SNMM parameters and the non-causal nui...

We consider inference under a nonparametric or semiparametric model with likelihood that factorizes as the product of two or more variation-independent factors.We are interested in a finitedimensional parameter that depends on only one of the likelihood factors and whose estimation requires the auxiliary estimation of one or several nuisance functi...

Decision-making requires choosing from treatments on the basis of correctly estimated outcome distributions under each treatment. In the absence of randomized trials, 2 possible approaches are the parametric g-formula and agent-based models (ABMs). The g-formula has been used exclusively to estimate effects in the population from which data were co...

We revisit the classic semiparametric problem of inference on a low dimensional parameter θ0 in the presence of high-dimensional nuisance parameters η0. We depart from the classical setting by allowing for η0 to be so high-dimensional that the traditional assumptions, such as Donsker properties, that limit complexity of the parameter space for this...

We study multiply robust (MR) estimators of the longitudinal g-computation formula of Robins (1986). In the first part of this paper we review and extend the recently proposed parametric multiply robust estimators of Tchetgen-Tchetgen (2009) and Molina, Rotnitzky, Sued and Robins (2017). In the second part of the paper we derive multiply and doubly...

Robins et al. (2008, 2016) applied the theory of higher order influence functions (HOIFs) to derive an estimator of the mean of an outcome Y in a missing data model with Y missing at random conditional on a vector X of continuous covariates; their estimator, in contrast to previous estimators, is semiparametric efficient under minimal conditions. H...

Background: Clinical guidelines vary with respect to the optimal monitoring frequency of HIV-positive individuals. We compared dynamic monitoring strategies based on time-varying CD4 cell counts in virologically suppressed HIV-positive individuals. Methods: In this observational study, we used data from prospective studies of HIV-positive indivi...

Directed acyclic graph (DAG) models may be characterized in at least four different ways: via a factorization, the d-separation criterion, the moralization criterion, and the local Markov property. As pointed out by Robins (1986, 1999), Verma and Pearl (1990), and Tian and Pearl (2002b), marginals of DAG models also imply equality constraints that...

Drawing causal inference with observational studies is the central pillar of many disciplines. One sufficient condition for identifying the causal effect is that the treatment-outcome relationship is unconfounded conditional on the observed covariates. It is often believed that the more covariates we condition on, the more plausible this unconfound...

Weight gain after smoking cessation can lessen the health benefits of, and reduce the incentives for, quitting smoking. Randomized clinical trials of smoking cessation have estimated this weight gain only over short periods of follow-up. We provide an estimate of long-term post-cessation weight gain in the Framingham Heart Study, a prospective obse...

Introduction Because a comparison of noninitiators and initiators of treatment may be hopelessly confounded, guidelines for the conduct of observational research often recommend using an “active” comparator group consisting of people who initiate a treatment other than the medication of interest. In this paper, we discuss the conditions under which...

Objective To compare regimens consisting of either ritonavir-boosted atazanavir or efavirenz and a nucleoside reverse transcriptase inhibitor (NRTI) backbone with respect to clinical, immunologic, and virologic outcomes. Design Prospective studies of human immunodeficiency virus (HIV)-infected individuals in Europe and the United States included i...

We provide general adaptive upper bounds for estimating nonparametric functionals based on second order U-statistics arising from finite dimensional approximation of the infinite dimensional models. We then provide examples of functionals for which the theory produces rate optimally matching adaptive upper and lower bounds. Our results are automati...

Missing data occur frequently in empirical studies in health and social sciences, often compromising our ability to make accurate inferences. An outcome is said to be missing not at random (MNAR) if, conditional on the observed variables, the missing data mechanism still depends on the unobserved outcome. In such settings, identification is general...

In this Viewpoint, JoAnn Manson and colleagues discuss the risk of postrandomization “confounding,” a bias that can be introduced in long-duration trials of sustained interventions, using statin initiation after randomization in Women’s Health Initiative trials as an example.Randomized clinical trials (RCTs) are considered the “gold standard” for e...

Objective: To illustrate an approach to compare CD4 cell count and HIV-RNA monitoring strategies in HIV-positive individuals on antiretroviral therapy (ART). Design: Prospective studies of HIV-positive individuals in Europe and the USA in the HIV-CAUSAL Collaboration and The Center for AIDS Research Network of Integrated Clinical Systems. Metho...

Instrumental variables are widely used for estimating causal effects in the presence of unmeasured confounding. The discrete instrumental variable model has testable implications on the law of the observed data. To date, however, assessments of instrumental validity are typically based solely on subject matter arguments rather than these testable i...

Ideally, questions about comparative effectiveness or safety would be answered using an appropriately designed and conducted randomized experiment. When we cannot conduct a randomized experiment, we analyze observational data. Causal inference from large observational databases (big data) can be viewed as an attempt to emulate a randomized experime...

Robins et al, 2008, published a theory of higher order influence functions for inference in semi- and non-parametric models. This paper is a comprehensive manuscript from which Robins et al, was drawn. The current paper includes many results and proofs that were not included in Robins et al due to space limitation. Particular results contained in t...

Background: When a clinical treatment fails or shows suboptimal results, the question of when to switch to another treatment arises. Treatment switching strategies are often dynamic because the time of switching depends on the evolution of an individual's time-varying covariates. Dynamic strategies can be directly compared in randomized trials. Fo...

This article introduces fundamental concepts for making inferences about treatments with values that may change over time. We define time-varying treatments and confounders, and provide a classification of treatment strategies. We also describe key identifiability conditions, and the bias of traditional adjustment methods when the time-varying conf...