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James M. Robins

Publications and source records attributed to James M. Robins.

At least 37 records · Page 2Linked to original sources
arXiv2022

Deep Learning Methods for Proximal Inference via Maximum Moment Restriction

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 structural conditions. However, proximal inference requires solving an ill-posed integral equation. Previous approaches have used a variety of machine learning techniques to estimate a solution to this integral equation, commonly referred to as the bridge function. However, prior work has often been limited by relying on pre-specified kernel functions, which are not data adaptive and struggle to scale to large datasets. In this work, we introduce a flexible and scalable method based on a deep neural network to estimate causal effects in the presence of unmeasured confounding using proximal inference. Our method achieves state of the art performance on two well-established proximal inference benchmarks. Finally, we provide theoretical consistency guarantees for our method.

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arXiv2022

Coherent modeling of longitudinal causal effects on binary outcomes

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, when outcomes are binary, current methods for estimating multiplicative and additive SNMM parameters suffer from variation dependence between the causal parameters and the non-causal nuisance parameters. This leads to a series of difficulties in interpretation, estimation and computation. These difficulties have hindered the uptake of SNMMs in biomedical practice, where binary outcomes are very common. We solve the variation dependence problem for the binary multiplicative SNMM via a reparametrization of the non-causal nuisance parameters. Our novel nuisance parameters are variation independent of the causal parameters, and hence allow for coherent modeling of heterogeneous effects from longitudinal studies with binary outcomes. Our parametrization also provides a key building block for flexible doubly robust estimation of the causal parameters. Along the way, we prove that an additive SNMM with binary outcomes does not admit a variation independent parametrization, thereby justifying the restriction to multiplicative SNMMs.

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arXiv2022

Global sensitivity analysis for studies extending inferences from a randomized trial to a target population

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 inferences from the trial to the target population rely on conditional exchangeability assumptions between randomized and non-randomized individuals. The validity of these assumptions is often uncertain or controversial and investigators need to examine how violation of the assumptions would impact study conclusions. We describe methods for global sensitivity analysis that directly parameterize violations of the assumptions in terms of potential (counterfactual) outcome distributions. Our approach does not require detailed knowledge about the distribution of specific unmeasured effect modifiers or their relationship with the observed variables. We illustrate the methods using data from a trial nested within a cohort of trial-eligible individuals to compare coronary artery surgery plus medical therapy versus medical therapy alone for stable ischemic heart disease.

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arXiv2022

Randomized trials and their observational emulations: a framework for benchmarking and joint analysis

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 compared to benchmark observational analysis methods. In a simplified setting with complete adherence to the assigned treatment strategy and no loss-to-follow-up, we show that benchmarking relies on an exchangeability condition between the populations underlying the trial and its emulation, to account for differences in the distribution of covariates between them. When this exchangeability condition holds, and the usual conditions needed for the estimates from the trial and its emulation to have a causal interpretation also hold, we derive restrictions on the law of the observed data. When the data are compatible with the restrictions, joint analysis of the trial and its emulation is possible. When the data are incompatible with the restrictions, a discrepancy between (1) estimates based on extending inferences from the trial to the population underlying the emulation and (2) the emulation itself may reflect either inability to benchmark (e.g., due to selective participation into the trial) or a failure of the emulation (e.g., due to unmeasured confounding), but we cannot use the data to determine which is the case. Our analysis reveals how benchmarking attempts combine causal assumptions, data analysis methods, and substantive knowledge to examine the validity of observational analysis methods.

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arXiv2022

Estimation of local treatment effects under the binary instrumental variable model

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 effect under the binary instrumental variable model. We discuss the challenges for causal estimation with a binary outcome, and show that surprisingly, it can be more difficult than the case with a continuous outcome. We propose novel modeling and estimating procedures that improve upon existing proposals in terms of model congeniality, interpretability, robustness or efficiency. Our approach is illustrated via simulation studies and a real data analysis.

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arXiv2021

A Formal Causal Interpretation of the Case-Crossover Design

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 helps to clarify its assumptions and interpretation. In particular, when the treatment effect is non-null, we identify a previously unnoticed bias arising from common causes of the outcome at different person-times. We analytically characterize the direction and size of this bias and demonstrate its potential importance with a simulation. We also use our derivation of the limit of the case-crossover estimator to analyze its sensitivity to treatment effect heterogeneity, a violation of one of the informal criteria for validity. The upshot of this work for practitioners is that, while the case-crossover design can be useful for testing the causal null hypothesis in the presence of baseline confounders, extra caution is warranted when using the case-crossover design for point estimation of causal effects.

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arXiv2021

Nonparametric identification is not enough, but randomized controlled trials are

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 is uniformly consistent without further assumptions, (2) knowledge of the propensity score yields a uniformly consistent estimator and honest confidence intervals that shrink at parametric rates with increasing sample size, regardless of how complicated the propensity score function is. We emphasize the latter point, and note that successfully-conducted RCTs provide knowledge of the propensity score to the researcher. We discuss modern developments in covariate adjustment for RCTs, noting that statistical models and machine learning methods can be used to improve efficiency while preserving finite sample unbiasedness. We conclude that statistical inference has the potential to be fundamentally more difficult in observational settings than it is in RCTs, even when all confounders are measured.

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arXiv2021

Multivariate Counterfactual Systems And Causal Graphical Models

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 synthesis leads to a simplification of the do-calculus that clarifies and separates the underlying concepts, and a simple counterfactual formulation of a complete identification algorithm in causal models with hidden variables.

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arXiv2021

An Interventionist Approach to Mediation Analysis

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 to a novel way of conceptualizing direct effects in terms of interventions on an expanded graph in which treatment is decomposed into multiple separable components. We further develop this novel theory here, showing that it provides a self-contained framework for discussing mediation without reference to cross-world (nested) counterfactuals or interventions on the mediator. The theory preserves the dictum `no causation without manipulation' and makes questions of mediation empirically testable in future Randomized Controlled Trials. Even so, we prove the interventionist and nested counterfactual approaches remain tightly coupled under a Non-Parametric Structural Equation Model except in the presence of a `recanting witness.' In fact, our analysis also leads to a simple sound and complete algorithm for determining identification in the (non-interventionist) theory of path-specific counterfactuals.

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arXiv2021

Conditional separable effects

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 contrast of outcomes conditional on the post-treatment variable is not an average causal effect, even in a randomized experiment. Therefore the effect in the principal stratum of those who would have the same value of the post-treatment variable regardless of treatment, such as the always survivors in a truncation by death setting, is often advocated for causal inference. While this principal stratum effect is a well defined causal contrast, it is often hard to justify that it is relevant to scientists, patients or policy makers, and it cannot be identified without relying on unfalsifiable assumptions. Here we formulate alternative estimands, the conditional separable effects, that have a natural causal interpretation under assumptions that can be falsified in a randomized experiment. We provide identification results and introduce different estimators, including a doubly robust estimator derived from the nonparametric influence function. As an illustration, we estimate a conditional separable effect of chemotherapies on quality of life in patients with prostate cancer, using data from a randomized clinical trial.

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arXiv2021

Discussion of 'Estimating time-varying causal excursion effect in mobile health with binary outcomes' by T. Qian et al

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, Hernán and collaborators on analyzing observational studies as a series of randomized trials. There is also a close relationship to the history-restricted and the history-adjusted marginal structural models (MSM). Important differences and their methodological implications are clarified. We also demonstrate that the excursion effect can depend on the design and discuss its suitability for modifying the treatment protocol.

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arXiv2021

Efficient estimation of optimal regimes under a no direct effect assumption

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 regime structural nested mean model (opt-SNMM). The proposed estimators are more efficient than previous estimators of the parameters of an opt-SNMM because they efficiently leverage the `no direct effect (NDE) of testing' assumption. Our methods will be of importance to decision scientists who either perform cost-benefit analyses or are tasked with the estimation of the `value of information' supplied by an expensive diagnostic test (such as an MRI to screen for lung cancer).

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arXiv2020

Locally Robust Semiparametric Estimation

Many economic and causal parameters depend on nonparametric or high dimensional first steps. We give a general construction of locally robust/orthogonal moment functions for GMM, where moment conditions have zero derivative with respect to first steps. We show that orthogonal moment functions can be constructed by adding to identifying moments the nonparametric influence function for the effect of the first step on identifying moments. Orthogonal moments reduce model selection and regularization bias, as is very important in many applications, especially for machine learning first steps. We give debiased machine learning estimators of functionals of high dimensional conditional quantiles and of dynamic discrete choice parameters with high dimensional state variables. We show that adding to identifying moments the nonparametric influence function provides a general construction of orthogonal moments, including regularity conditions, and show that the nonparametric influence function is robust to additional unknown functions on which it depends. We give a general approach to estimating the unknown functions in the nonparametric influence function and use it to automatically debias estimators of functionals of high dimensional conditional location learners. We give a variety of new doubly robust moment equations and characterize double robustness. We give general and simple regularity conditions and apply these for asymptotic inference on functionals of high dimensional regression quantiles and dynamic discrete choice parameters with high dimensional state variables.

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arXiv2020

On nearly assumption-free tests of nominal confidence interval coverage for causal parameters estimated by machine learning

For many causal effect parameters of interest, doubly robust machine learning (DRML) estimators $\hatψ_{1}$ are the state-of-the-art, incorporating the good prediction performance of machine learning; the decreased bias of doubly robust estimators; and the analytic tractability and bias reduction of sample splitting with cross fitting. Nonetheless, even in the absence of confounding by unmeasured factors, the nominal $(1 - α)$ Wald confidence interval $\hatψ_{1} \pm z_{α/ 2} \widehat{\mathsf{se}} [\hatψ_{1}]$ may still undercover even in large samples, because the bias of $\hatψ_{1}$ may be of the same or even larger order than its standard error of order $n^{-1/2}$. In this paper, we introduce essentially assumption-free tests that (i) can falsify the null hypothesis that the bias of $\hatψ_{1}$ is of smaller order than its standard error, (ii) can provide an upper confidence bound on the true coverage of the Wald interval, and (iii) are valid under the null under no smoothness/sparsity assumptions on the nuisance parameters. The tests, which we refer to as \underline{A}ssumption \underline{F}ree \underline{E}mpirical \underline{C}overage \underline{T}ests (AFECTs), are based on a U-statistic that estimates part of the bias of $\hatψ_{1}$.

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arXiv2020

Generalized interpretation and identification of separable effects in competing event settings

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 (Stensrud et al, 2019) to define direct and indirect effects of the treatment on the event of interest. This definition presupposes a treatment decomposition into two components acting along two separate causal pathways, one exclusively outside of the competing event and the other exclusively through it. Unlike previous definitions of direct and indirect effects, the separable effects can be subject to empirical scrutiny in a study where separate interventions on the treatment components are available. Here we extend and generalize the notion of the separable effects in several ways, allowing for interpretation, identification and estimation under considerably weaker assumptions. We propose and discuss a definition of separable effects that is applicable to general time-varying structures, where the separable effects can still be meaningfully interpreted, even when they cannot be regarded as direct and indirect effects. We further derive weaker conditions for identification of separable effects in observational studies where decomposed treatments are not yet available; in particular, these conditions allow for time-varying common causes of the event of interest, the competing events and loss to follow-up. For these general settings, we propose semi-parametric weighted estimators that are straightforward to implement. As an illustration, we apply the estimators to study the separable effects of intensive blood pressure therapy on acute kidney injury, using data from a randomized clinical trial.

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arXiv2020

Separable Effects for Causal Inference in the Presence of Competing Events

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 separable indirect effect is the treatment effect on the event of interest only through its effect on the competing event. Similar to Robins and Richardson's extended graphical approach for mediation analysis, the separable effects can only be identified under the assumption that the treatment can be decomposed into two distinct components that exert their effects through distinct causal pathways. Unlike existing definitions of causal effects in the presence of competing events, our estimands do not require cross-world contrasts or hypothetical interventions to prevent death. As an illustration, we apply our approach to a randomized clinical trial on estrogen therapy in individuals with prostate cancer.

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arXiv2019

Identification In Missing Data Models Represented By Directed Acyclic Graphs

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 the identifiability of the target distribution within this class of models, and show that the most general identification strategies proposed so far retain a significant gap in that they fail to identify a wide class of identifiable distributions. To address this gap, we propose a new algorithm that significantly generalizes the types of manipulations used in the ID algorithm, developed in the context of causal inference, in order to obtain identification.

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