# James M. Robins's research while affiliated with Massachusetts Department of Public Health and other places

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## Publications (207)

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...

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 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...

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...

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...

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.

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...

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...

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...

We provide general adaptive upper bounds for estimators of nonparametric functionals based on second order U-statistics arising from finite dimensional approximation of the infinite dimensional models using projection type kernels. An accompanying general adaptive lower bound tool is provided yielding bounds on chi-square divergence between mixture...

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...

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...

We introduce a new method of estimation of parameters in semiparametric 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...

We prove conditional asymptotic normality of a class of quadratic
U-statistics that are dominated by their degenerate second order part and have
kernels that change with the number of observations. These statistics arise in
the construction of estimators in high-dimensional semi- and non-parametric
models, and in the construction of nonparametric c...

Professor Miettinen offers a scathing critique of the criteria used by official bodies to decide for whom and how often breast cancer screening should be offered (Miettinen, 2015). He notes that these bodies often simply synthesize the results of prior randomized clinical trials with very little attention given to the question of whether individual...

We study the adaptive minimax estimation of non-linear integral functionals
of a density and extend the results obtained for linear and quadratic
functionals to general functionals. The typical rate optimal non-adaptive
minimax estimators of "smooth" non-linear functionals are higher order
U-statistics. Since Lepski's method requires tight control...

The objective of many studies in health and social sciences is to evaluate
the causal effect of a treatment or exposure on a specific outcome using
observational data. In such studies, the exposure is typically not randomized
and therefore confounding bias can rarely be ruled out with certainty. The
instrumental variable (IV) design plays the role...

We propose and analyze estimators for statistical functionals of one or more
distributions under nonparametric assumptions. Our estimators are based on the
theory of influence functions, which appear in the semiparametric statistics
literature. Theoretically, we upper bound the rate of convergence for these
estimators, showing that they achieve a p...

Discussion of "Instrumental Variables: An Econometrician's Perspective" by
Guido W. Imbens [arXiv:1410.0163].

We consider estimation of the causal effect of a binary treatment on an outcome, conditionally on covariates, from observational studies or natural experiments in which there is a binary instrument for treatment. We describe a doubly robust, locally efficient estimator of the parameters indexing a model for the local average treatment effect condit...

Methods from causal mediation analysis have generalized the traditional approach to direct and indirect effects in the epidemiologic and social science literature by allowing for interaction and nonlinearities. However, the methods from the causal inference literature have themselves been subject to a major limitation, in that the so-called natural...

This article introduces a new approach to prediction by bringing together two different nonparametric ideas: distribution-free inference and nonparametric smoothing. Specifically, we consider the problem of constructing nonparametric tolerance/prediction sets. We start from the general conformal prediction approach, and we use a kernel density esti...

The paper concerns the probabilistic evaluation of plans in the presence of
unmeasured variables, each plan consisting of several concurrent or sequential
actions. We establish a graphical criterion for recognizing when the effects of
a given plan can be predicted from passive observations on measured variables
only. When the criterion is satisfied...

The standard way to parameterize the distributions represented by a directed
acyclic graph is to insert a parametric family for the conditional distribution
of each random variable given its parents. We show that when one's goal is to
test for or estimate an effect of a sequentially applied treatment, this
natural parameterization has serious defic...

In an attempt to define a postulated effect of lead on male endocrine function, seven men with symptomatic occupational lead intoxication (maximum whole blood lead levels 66-139 micrograms/dl) underwent in-patient endocrine evaluation at the time of diagnosis. Defects in thyroid function, probably of central origin, were present in three patients....

Objective:
To compare regimens consisting of either efavirenz or nevirapine and two or more nucleoside reverse transcriptase inhibitors (NRTIs) among HIV-infected, antiretroviral-naive, and AIDS-free individuals with respect to clinical, immunologic, and virologic outcomes.
Design:
Prospective studies of HIV-infected individuals in Europe and th...

The constraints arising from DAG models with latent variables can be
naturally represented by means of acyclic directed mixed graphs (ADMGs). Such
graphs contain directed and bidirected arrows, and contain no directed cycles.
DAGs with latent variables imply independence constraints in the distribution
resulting from a 'fixing' operation, in which...

Probabilistic inference in graphical models is the task of computing marginal
and conditional densities of interest from a factorized representation of a
joint probability distribution. Inference algorithms such as variable
elimination and belief propagation take advantage of constraints embedded in
this factorization to compute such densities effi...