arXiv subjects

Miguel A. Hernán

Publications and source records attributed to Miguel A. Hernán.

At least 19 recordsLinked to original sources

arXiv2026

Using the target trial framework for combining information: external comparator analyses and other applications

We describe how the target trial framework can be used to plan and report analyses that attempt to answer causal questions by combining information from multiple, diverse sources. Such analyses may involve comparisons of treatments evaluated in different populations, for example when an index trial is combined with other data sources in external comparator analyses, or when extending causal inferences from a randomized trial to a new target population in generalizability and transportability analyses. When planning such analyses, the specification of the target trial supports the explicit definition of the target population with an associated sampling model. We propose this as an additional component for the target trial framework, especially relevant for analyses that combine information, because it influences the choice of eligibility criteria, the specification of the causal model, the choice of causal contrasts, and reasoning about identification strategies. Furthermore, the framework encourages careful mapping of data elements from multiple data sources to a single target trial. This mapping process can highlight potentially irreconcilable misalignments between data sources with respect to specific components of the framework -- for example, in the definitions of eligibility criteria, treatment assignment, and treatment receipt. Such misalignments can arise when attempts to specify a target trial that aligns with a specific data source introduce or worsen misalignments with other proposed data sources. The extent of such misalignments may warrant switching to other data sources, or prospectively obtaining data, to emulate the proposed target trial. We conclude that the target trial framework promotes transparent discussion about the design of and assumptions made in analyses that answer causal questions by combining information from diverse sources.

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arXiv2026

Identification strategies for combining an experimental study with external data

There is increasing interest in combining information from experimental studies, including randomized and single-group trials, with information from external experimental or observational data sources. Such efforts are usually motivated by the desire to compare treatments evaluated in different studies -- for instance, by constructing external comparator groups for some index study -- or to estimate treatment effects with greater precision. Proposals to combine experimental studies with external data were made at least as early as the 1970s, but in recent years have come under increasing consideration within clinical practice and by regulatory agencies involved in drug and device evaluation, particularly with the increasing availability of trial and observational data. In this paper, we describe basic study templates that combine information from experimental studies with external data, and use the potential (counterfactual) outcomes framework to elaborate identification strategies for potential outcome means and average treatment effects. We argue that these identification strategies inherit ideas relevant to the study of causation in single-source studies and the related literature on combining information (e.g., generalizability and transportability methods), but merit consideration as a separate class of causal problems because they differ in terms of their scientific motivations, definitions of the target population, sampling, data structures, and identifiability conditions. In formalizing identification strategies for the analyses described herein, we hope to provide a conceptual foundation to support the systematic use and evaluation of such efforts.

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arXiv2026

Constructing external comparator groups via transportability in mean or in effect measure

Learning about causal effects in target populations and their subsets may be facilitated by combining information from multiple sources. One major class of study designs that combine information involves appending an index study with data from an external comparator, which may facilitate head-to-head comparisons of treatments initially studied in different populations. We delineate external comparator analyses under two distinct, but related, identification strategies. The first strategy relies on exchangeability (transportability) of potential outcome means, which uses information only on the treatments that are to be compared. The second strategy relies on transportability in effect measure, requiring additional use of information on a third treatment common to the populations that have been combined. In a time-fixed setting with a point treatment and non-failure time outcome, we examine identification and estimation under a basic setup where information from an index trial is combined with a second, and external to the index trial, data source. We propose estimators for identifying observed data functionals, with a particular focus on semiparametric efficient augmented weighting estimators that incorporate models for the probability of trial participation, the probability of treatment, and conditional outcome means. We derive the asymptotic properties of these augmented weighting estimators -- including robustness to model misspecification and slower rates of convergence for some nuisance function models -- and use simulation to compare their finite sample performance to estimators based only on outcome modeling or weighting. Last, we provide a practical demonstration of the proposed methods by combining the ACCEPT and PHOENIX 1 randomized trials to evaluate the effect of various biologic agents on plaque psoriasis, a chronic inflammatory disorder.

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arXiv2025

The role of assignment in defining and identifying causal effects in randomized trials

In randomized trials, the per-protocol effect, that is, the effect of being assigned a treatment strategy and receiving treatment according to the assigned strategy, is sometimes thought to reflect the effect of the treatment strategy itself, without intervention on assignment. Here, we argue by example that this is not necessarily the case. We examine a causal structure for a randomized trial where these two causal estimands -- the per-protocol effect and the effect of the treatment strategy -- are not equal, and where their corresponding identifying observed data functionals are not the same, but both require information on assignment for identification. Our example highlights the conceptual difference between the per-protocol effect and the effect of the treatment strategy, the conditions under which these causal estimands are equal, and suggests that in some cases their identification requires information on assignment, even when assignment is randomized. Furthermore, both per-protocol effects and effects of treatment may be unidentifiable without information on treatment assignment, unless one makes additional assumptions -- informally, that assignment does not affect the outcome except through treatment (i.e., an exclusion-restriction assumption), and that assignment is not a confounder of the treatment-outcome association conditional on other variables in the analysis. Our analyses suggest a need to more clearly define the role of assignment when specifying causal effects of interest in randomized trials, which has implications for identification, analysis methods, and the interpretation of trial results.

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arXiv2022

Generalizing and transporting inferences about the effects of treatment assignment subject to non-adherence

We discuss the identifiability of causal estimands for generalizability and transportability analyses, both under perfect and imperfect adherence to treatment assignment. We consider a setting where the trial data contain information on baseline covariates, assignment at baseline, intervention at baseline (point treatment), and outcomes; and where the data from non-randomized individuals only contain information on baseline covariates. In this setting, we review identification results under perfect adherence and study two examples in which non-adherence severely limits the ability to transport inferences about the effects of treatment assignment to the target population. In the first example, trial participation has a direct effect on treatment receipt and, through treatment receipt, on the outcome (a "trial engagement effect" via adherence). In the second example, participation in the trial has unmeasured common causes with treatment receipt. In both examples, the effect of assignment on the outcome in the target population is not identifiable. In the first example, however, the effect of joint interventions to scale-up trial activities that affect adherence and assign treatment is identifiable. We conclude that generalizability and transportability analyses should consider trial engagement effects via adherence and selection for participation on the basis of unmeasured factors that influence adherence.

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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

Efficient and robust methods for causally interpretable meta-analysis: transporting inferences from multiple randomized trials to a target population

We present methods for causally interpretable meta-analyses that combine information from multiple randomized trials to estimate potential (counterfactual) outcome means and average treatment effects in a target population. We consider identifiability conditions, derive implications of the conditions for the law of the observed data, and obtain identification results for transporting causal inferences from a collection of independent randomized trials to a new target population in which experimental data may not be available. We propose an estimator for the potential (counterfactual) outcome mean in the target population under each treatment studied in the trials. The estimator uses covariate, treatment, and outcome data from the collection of trials, but only covariate data from the target population sample. We show that it is doubly robust, in the sense that it is consistent and asymptotically normal when at least one of the models it relies on is correctly specified. We study the finite sample properties of the estimator in simulation studies and demonstrate its implementation using data from a multi-center randomized trial.

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arXiv2021

Revisiting the g-null paradox

The parametric g-formula is an approach to estimating causal effects of sustained treatment strategies from observational data. An often cited limitation of the parametric g-formula is the g-null paradox: a phenomenon in which model misspecification in the parametric g-formula is guaranteed under the conditions that motivate its use (i.e., when identifiability conditions hold and measured time-varying confounders are affected by past treatment). Many users of the parametric g-formula know they must acknowledge the g-null paradox as a limitation when reporting results but still require clarity on its meaning and implications. Here we revisit the g-null paradox to clarify its role in causal inference studies. In doing so, we present analytic examples and a simulation-based illustration of the bias of parametric g-formula estimates under the conditions associated with this paradox. Our results highlight the importance of avoiding overly parsimonious models for the components of the g-formula when using this method.

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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

Causal inference with limited resources: proportionally-representative interventions

Investigators often evaluate treatment effects by considering settings in which all individuals are assigned a treatment of interest, assuming that an unlimited number of treatment units are available. However, many real-life treatments are of limited supply and cannot be provided to all individuals in the population. For example, patients on the liver transplant waiting list cannot be assigned a liver transplant immediately at the time they reach highest priority because a suitable organ is not likely to be immediately available. In these cases, investigators may still be interested in the effects of treatment strategies in which a finite number of organs are available at a given time, that is, treatment regimes that satisfy resource constraints. Here, we describe an estimand that can be used to define causal effects of treatment strategies that satisfy resource constraints: proportionally-representative interventions for limited resources. We derive a simple class of inverse probability weighted estimators, and apply one such estimator to evaluate the effect of restricting or expanding utilization of "increased risk" liver organs to treat patients with end-stage liver disease. Our method is designed to evaluate policy-relevant interventions in the setting of finite treatment resources.

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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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arXiv2020

Towards causally interpretable meta-analysis: transporting inferences from multiple studies to a target population

We take steps towards causally interpretable meta-analysis by describing methods for transporting causal inferences from a collection of randomized trials to a new target population, one-trial-at-a-time and pooling all trials. We discuss identifiability conditions for average treatment effects in the target population and provide identification results. We show that assuming inferences are transportable from all trials in the collection to the same target population has implications for the law underlying the observed data. We propose average treatment effect estimators that rely on different working models and provide code for their implementation in statistical software. We discuss how to use the data to examine whether transported inferences are homogeneous across the collection of trials, sketch approaches for sensitivity analysis to violations of the identifiability conditions, and describe extensions to address non-adherence in the trials. Last, we illustrate the proposed methods using data from the HALT-C multi-center trial.

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arXiv2019

Guidelines for estimating causal effects in pragmatic randomized trials

Pragmatic randomized trials are designed to provide evidence for clinical decision-making rather than regulatory approval. Common features of these trials include the inclusion of heterogeneous or diverse patient populations in a wide range of care settings, the use of active treatment strategies as comparators, unblinded treatment assignment, and the study of long-term, clinically relevant outcomes. These features can greatly increase the usefulness of the trial results for patients, clinicians, and other stakeholders. However, these features also introduce an increased risk of non-adherence, which reduces the value of the intention-to-treat effect as a patient-centered measure of causal effect. In these settings, the per-protocol effect provides useful complementary information for decision making. Unfortunately, there is little guidance for valid estimation of the per-protocol effect. Here, we present our full guidelines for analyses of pragmatic trials that will result in more informative causal inferences for both the intention-to-treat effect and the per-protocol effect.

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arXiv2019

A causal framework for classical statistical estimands in failure time settings with competing events

In failure-time settings, a competing risk event is any event that makes it impossible for the event of interest to occur. For example, cardiovascular disease death is a competing event for prostate cancer death because an individual cannot die of prostate cancer once he has died of cardiovascular disease. Various statistical estimands have been defined as possible targets of inference in the classical competing risks literature. Many reviews have described these statistical estimands and their estimating procedures with recommendations about their use. However, this previous work has not used a formal framework for characterizing causal effects and their identifying conditions, which makes it difficult to interpret effect estimates and assess recommendations regarding analytic choices. Here we use a counterfactual framework to explicitly define each of these classical estimands. We clarify that, depending on whether competing events are defined as censoring events, contrasts of risks can define a total effect of the treatment on the event of interest, or a direct effect of the treatment on the event of interest not mediated through the competing event. In contrast, regardless of whether competing events are defined as censoring events, counterfactual hazard contrasts cannot generally be interpreted as causal effects. We illustrate how identifying assumptions for all of these counterfactual estimands can be represented in causal diagrams in which competing events are depicted as time-varying covariates. We present an application of these ideas to data from a randomized trial designed to estimate the effect of estrogen therapy on prostate cancer mortality.

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arXiv2019

gfoRmula: An R package for estimating effects of general time-varying treatment interventions via the parametric g-formula

Researchers are often interested in using longitudinal data to estimate the causal effects of hypothetical time-varying treatment interventions on the mean or risk of a future outcome. Standard regression/conditioning methods for confounding control generally fail to recover causal effects when time-varying confounders are themselves affected by past treatment. In such settings, estimators derived from Robins's g-formula may recover time-varying treatment effects provided sufficient covariates are measured to control confounding by unmeasured risk factors. The package gfoRmula implements in R one such estimator: the parametric g-formula. This estimator easily adapts to binary or continuous time-varying treatments as well as contrasts defined by static or dynamic, deterministic or random treatment interventions, as well as interventions that depend on the natural value of treatment. The package accommodates survival outcomes as well as binary or continuous end of follow-up outcomes. For survival outcomes, the package has different options for handling competing events. This paper describes the gfoRmula package, along with motivating background, features, and examples.

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arXiv2019

Generalizing causal inferences from randomized trials: counterfactual and graphical identification

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 what conditions we can generalize causal inferences from a randomized trial to the target population of trial-eligible individuals. We offer an interpretation of generalizability analyses using the notion of a hypothetical intervention to "scale-up" trial engagement to the target population. We consider the interpretation of generalizability analyses when trial engagement does or does not directly affect the outcome, highlight connections with censoring in longitudinal studies, and discuss identification of the distribution of counterfactual outcomes via g-formula computation and inverse probability weighting. Last, we show how the methods can be extended to address time-varying treatments, non-adherence, and censoring.

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arXiv2019

Sensitivity analysis using bias functions for studies extending inferences from a randomized trial to a target population

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, which is often uncertain or controversial, and need to be subjected to sensitivity analysis. We present simple methods for sensitivity analyses that do not require detailed background knowledge about specific unknown or unmeasured determinants of the outcome or modifiers of the treatment effect. Instead, our methods directly parameterize violations of the assumptions using bias functions. We show how the methods can be applied to non-nested trial designs, where the trial data are combined with a separately obtained sample of non-randomized individuals, as well as to nested trial designs, where a clinical trial is embedded within a cohort sampled from the target population. We illustrate the methods using data from a clinical trial comparing treatments for chronic hepatitis C infection.

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