A mixed model approach to estimate the survivor average causal effect in cluster-randomized trials.

In many medical studies, the outcome measure (such as quality of life, QOL) for some study participants becomes informatively truncated (censored, missing, or unobserved) due to death or other forms of dropout, creating a nonignorable missing data problem. In such cases, the use of a composite outcome or imputation methods that fill in unmeasurable QOL values for those who died rely on strong and untestable assumptions and may be conceptually unappealing to certain stakeholders when estimating a treatment effect. The survivor average causal effect (SACE) is an alternative causal estimand that surmounts some of these issues. While principal stratification has been applied to estimate the SACE in individually randomized trials, methods for estimating the SACE in cluster-randomized trials are currently limited. To address this gap, we develop a mixed model approach along with an expectation-maximization algorithm to estimate the SACE in cluster-randomized trials. We model the continuous outcome measure with a random intercept to account for intracluster correlations due to cluster-level randomization, and model the principal strata membership both with and without a random intercept. In simulations, we compare the performance of our approaches with an existing fixed-effects approach to illustrate the importance of accounting for clustering in cluster-randomized trials. The methodology is then illustrated using a cluster-randomized trial of telecare and assistive technology on health-related QOL in the elderly.

Inverse Probability Weighting to Estimate Exposure Effects on the Burden of Recurrent Outcomes in the Presence of Competing Events.

Recurrent events-outcomes that an individual can experience repeatedly over the course of follow-up-are common in epidemiologic and health services research. Studies involving recurrent events often focus on time to first occurrence or on event rates, which assume constant hazards over time. In this paper, we contextualize recurrent event parameters of interest using counterfactual theory in a causal inference framework and describe an approach for estimating a target parameter referred to as the mean cumulative count. This approach leverages inverse probability weights to control measured confounding with an existing (and underutilized) nonparametric estimator of recurrent event burden first proposed by Dong et al. in 2015. We use simulations to demonstrate the unbiased estimation of the mean cumulative count using the weighted Dong-Yasui estimator in a variety of scenarios. The weighted Dong-Yasui estimator for the mean cumulative count allows researchers to use observational data to flexibly estimate and contrast the expected number of cumulative events experienced per individual by a given time point under different exposure regimens. We provide code to ease application of this method.

Assessing intervention effects in a randomized trial within a social network.

Studies of social networks provide unique opportunities to assess the causal effects of interventions that may impact more of the population than just those intervened on directly. Such effects are sometimes called peer or spillover effects, and may exist in the presence of interference, that is, when one individual's treatment affects another individual's outcome. Randomization-based inference (RI) methods provide a theoretical basis for causal inference in randomized studies, even in the presence of interference. In this article, we consider RI of the intervention effect in the eX-FLU trial, a randomized study designed to assess the effect of a social distancing intervention on influenza-like-illness transmission in a connected network of college students. The approach considered enables inference about the effect of the social distancing intervention on the per-contact probability of influenza-like-illness transmission in the observed network. The methods allow for interference between connected individuals and for heterogeneous treatment effects. The proposed methods are evaluated empirically via simulation studies, and then applied to data from the eX-FLU trial.

Testing for heterogeneity in the utility of a surrogate marker.

In studies that require long-term and/or costly follow-up of participants to evaluate a treatment, there is often interest in identifying and using a surrogate marker to evaluate the treatment effect. While several statistical methods have been proposed to evaluate potential surrogate markers, available methods generally do not account for or address the potential for a surrogate to vary in utility or strength by patient characteristics. Previous work examining surrogate markers has indicated that there may be such heterogeneity, that is, that a surrogate marker may be useful (with respect to capturing the treatment effect on the primary outcome) for some subgroups, but not for others. This heterogeneity is important to understand, particularly if the surrogate is to be used in a future trial to replace the primary outcome. In this paper, we propose an approach and estimation procedures to measure the surrogate strength as a function of a baseline covariate W and thus examine potential heterogeneity in the utility of the surrogate marker with respect to W. Within a potential outcome framework, we quantify the surrogate strength/utility using the proportion of treatment effect on the primary outcome that is explained by the treatment effect on the surrogate. We propose testing procedures to test for evidence of heterogeneity, examine finite sample performance of these methods via simulation, and illustrate the methods using AIDS clinical trial data.

Posttreatment confounding in causal mediation studies: A cutting-edge problem and a novel solution via sensitivity analysis.

In causal mediation studies that decompose an average treatment effect into indirect and direct effects, examples of posttreatment confounding are abundant. In the presence of treatment-by-mediator interactions, past research has generally considered it infeasible to adjust for a posttreatment confounder of the mediator-outcome relationship due to incomplete information: for any given individual, a posttreatment confounder is observed under the actual treatment condition while missing under the counterfactual treatment condition. This paper proposes a new sensitivity analysis strategy for handling posttreatment confounding and incorporates it into weighting-based causal mediation analysis. The key is to obtain the conditional distribution of the posttreatment confounder under the counterfactual treatment as a function of not only pretreatment covariates but also its counterpart under the actual treatment. The sensitivity analysis then generates a bound for the natural indirect effect and that for the natural direct effect over a plausible range of the conditional correlation between the posttreatment confounder under the actual and that under the counterfactual conditions. Implemented through either imputation or integration, the strategy is suitable for binary as well as continuous measures of posttreatment confounders. Simulation results demonstrate major strengths and potential limitations of this new solution. A reanalysis of the National Evaluation of Welfare-to-Work Strategies (NEWWS) Riverside data reveals that the initial analytic results are sensitive to omitted posttreatment confounding.

Single-world intervention graphs for defining, identifying, and communicating estimands in clinical trials.

Confusion often arises when attempting to articulate target estimand(s) of a clinical trial in plain language. We aim to rectify this confusion by using a type of causal graph called the Single-World Intervention Graph (SWIG) to provide a visual representation of the estimand that can be effectively communicated to interdisciplinary stakeholders. These graphs not only display estimands, but also illustrate the assumptions under which a causal estimand is identifiable by presenting the graphical relationships between the treatment, intercurrent events, and clinical outcomes. To demonstrate its usefulness in pharmaceutical research, we present examples of SWIGs for various intercurrent event strategies specified in the ICH E9(R1) addendum, as well as an example from a real-world clinical trial for chronic pain. code to generate all the SWIGs shown is this paper is made available. We advocate clinical trialists adopt the use of SWIGs in their estimand discussions during the planning stages of their studies.

Confounding-adjustment methods for the causal difference in medians.

BACKGROUND: With continuous outcomes, the average causal effect is typically defined using a contrast of expected potential outcomes. However, in the presence of skewed outcome data, the expectation (population mean) may no longer be meaningful. In practice the typical approach is to continue defining the estimand this way or transform the outcome to obtain a more symmetric distribution, although neither approach may be entirely satisfactory. Alternatively the causal effect can be redefined as a contrast of median potential outcomes, yet discussion of confounding-adjustment methods to estimate the causal difference in medians is limited. In this study we described and compared confounding-adjustment methods to address this gap. METHODS: The methods considered were multivariable quantile regression, an inverse probability weighted (IPW) estimator, weighted quantile regression (another form of IPW) and two little-known implementations of g-computation for this problem. Methods were evaluated within a simulation study under varying degrees of skewness in the outcome and applied to an empirical study using data from the Longitudinal Study of Australian Children. RESULTS: Simulation results indicated the IPW estimator, weighted quantile regression and g-computation implementations minimised bias across all settings when the relevant models were correctly specified, with g-computation additionally minimising the variance. Multivariable quantile regression, which relies on a constant-effect assumption, consistently yielded biased results. Application to the empirical study illustrated the practical value of these methods. CONCLUSION: The presented methods provide appealing avenues for estimating the causal difference in medians.

Bayesian causal inference: a critical review.

This paper provides a critical review of the Bayesian perspective of causal inference based on the potential outcomes framework. We review the causal estimands, assignment mechanism, the general structure of Bayesian inference of causal effects and sensitivity analysis. We highlight issues that are unique to Bayesian causal inference, including the role of the propensity score, the definition of identifiability, the choice of priors in both low- and high-dimensional regimes. We point out the central role of covariate overlap and more generally the design stage in Bayesian causal inference. We extend the discussion to two complex assignment mechanisms: instrumental variable and time-varying treatments. We identify the strengths and weaknesses of the Bayesian approach to causal inference. Throughout, we illustrate the key concepts via examples. This article is part of the theme issue 'Bayesian inference: challenges, perspectives, and prospects'.

Statistical Mediation Analysis for Models with a Binary Mediator and a Binary Outcome: the Differences Between Causal and Traditional Mediation Analysis.

Mediation analysis is an important statistical method in prevention research, as it can be used to determine effective intervention components. Traditional mediation analysis defines direct and indirect effects in terms of linear regression coefficients. It is unclear how these traditional effects are estimated in settings with binary variables. An important recent methodological advancement in the mediation analysis literature is the development of the causal mediation analysis framework. Causal mediation analysis defines causal effects as the difference between two potential outcomes. These definitions can be applied to any mediation model to estimate natural direct and indirect effects, including models with binary variables and an exposure-mediator interaction. This paper aims to clarify the similarities and differences between the causal and traditional effect estimates for mediation models with a binary mediator and a binary outcome. Causal and traditional mediation analyses were applied to an empirical example to demonstrate these similarities and differences. Causal and traditional mediation analysis provided similar controlled direct effect estimates, but different estimates of the natural direct effects, natural indirect effects, and total effect. Traditional mediation analysis methods do not generalize well to mediation models with binary variables, while the natural effect definitions can be applied to any mediation model. Causal mediation analysis is therefore the preferred method for the analysis of mediation models with binary variables.

Estimating vaccine efficacy over time after a randomized study is unblinded.

The COVID-19 pandemic due to the novel coronavirus SARS CoV-2 has inspired remarkable breakthroughs in the development of vaccines against the virus and the launch of several phase 3 vaccine trials in Summer 2020 to evaluate vaccine efficacy (VE). Trials of vaccine candidates using mRNA delivery systems developed by Pfizer-BioNTech and Moderna have shown substantial VEs of 94-95%, leading the US Food and Drug Administration to issue Emergency Use Authorizations and subsequent widespread administration of the vaccines. As the trials continue, a key issue is the possibility that VE may wane over time. Ethical considerations dictate that trial participants be unblinded and those randomized to placebo be offered study vaccine, leading to trial protocol amendments specifying unblinding strategies. Crossover of placebo subjects to vaccine complicates inference on waning of VE. We focus on the particular features of the Moderna trial and propose a statistical framework based on a potential outcomes formulation within which we develop methods for inference on potential waning of VE over time and estimation of VE at any postvaccination time. The framework clarifies assumptions made regarding individual- and population-level phenomena and acknowledges the possibility that subjects who are more or less likely to become infected may be crossed over to vaccine differentially over time. The principles of the framework can be adapted straightforwardly to other trials.

Using principal stratification in analysis of clinical trials.

The ICH E9(R1) addendum (2019) proposed principal stratification (PS) as one of five strategies for dealing with intercurrent events. Therefore, understanding the strengths, limitations, and assumptions of PS is important for the broad community of clinical trialists. Many approaches have been developed under the general framework of PS in different areas of research, including experimental and observational studies. These diverse applications have utilized a diverse set of tools and assumptions. Thus, need exists to present these approaches in a unifying manner. The goal of this tutorial is threefold. First, we provide a coherent and unifying description of PS. Second, we emphasize that estimation of effects within PS relies on strong assumptions and we thoroughly examine the consequences of these assumptions to understand in which situations certain assumptions are reasonable. Finally, we provide an overview of a variety of key methods for PS analysis and use a real clinical trial example to illustrate them. Examples of code for implementation of some of these approaches are given in Supplemental Materials.

Identifying causal mechanisms in psychotherapy: What can we learn from causal mediation analysis?

Despite widespread interest in the development of process-based psychotherapies, little is still known about the underlying processes that underpin our most effective therapies. Statistical mediation analysis is a commonly used analytical method to evaluate how, or by which processes, a therapy causes change in an outcome. Causal mediation analysis (CMA) represents a new advancement in mediation analysis that employs causally defined direct and indirect effects based on potential outcomes. These novel ideas and analytical techniques have been characterized as revolutionary in epidemiology and biostatistics, although they are not (yet) widely known among researchers in clinical psychology. In this paper, I outline the fundamental concepts underlying CMA, clarify the differences between the CMA approach and the traditional approach to mediation, and identify two important data analytical aspects that have been emphasized as a result of these recent advancements. To illustrate the key ideas, assumptions, and mathematical definitions intuitively, an applied clinical example from a previously published randomized controlled trial is used. CMA's main contributions are discussed, as well as some of the key challenges. Finally, it is argued that the most significant contribution of CMA is the formalization of mediation in a unified causal framework with clear assumptions.

Mediation analysis methods used in observational research: a scoping review and recommendations.

BACKGROUND: Mediation analysis methodology underwent many advancements throughout the years, with the most recent and important advancement being the development of causal mediation analysis based on the counterfactual framework. However, a previous review showed that for experimental studies the uptake of causal mediation analysis remains low. The aim of this paper is to review the methodological characteristics of mediation analyses performed in observational epidemiologic studies published between 2015 and 2019 and to provide recommendations for the application of mediation analysis in future studies. METHODS: We searched the MEDLINE and EMBASE databases for observational epidemiologic studies published between 2015 and 2019 in which mediation analysis was applied as one of the primary analysis methods. Information was extracted on the characteristics of the mediation model and the applied mediation analysis method. RESULTS: We included 174 studies, most of which applied traditional mediation analysis methods (n = 123, 70.7%). Causal mediation analysis was not often used to analyze more complicated mediation models, such as multiple mediator models. Most studies adjusted their analyses for measured confounders, but did not perform sensitivity analyses for unmeasured confounders and did not assess the presence of an exposure-mediator interaction. CONCLUSIONS: To ensure a causal interpretation of the effect estimates in the mediation model, we recommend that researchers use causal mediation analysis and assess the plausibility of the causal assumptions. The uptake of causal mediation analysis can be enhanced through tutorial papers that demonstrate the application of causal mediation analysis, and through the development of software packages that facilitate the causal mediation analysis of relatively complicated mediation models.

Assessing Potential Outcomes Mediation in HIV Interventions.

Knowledge of causal processes through mediation analysis can help improve the effectiveness and reduce costs of public health programs, like HIV prevention and treatment interventions. Advancements in mediation using the potential outcomes framework provide a method for estimating the causal effect of interventions on outcomes via a mediating variable. The purpose of this paper is to provide practical information about mediation and the potential outcomes framework that can enhance data analysis and causal inference for intervention studies. Causal mediation effects are defined and then estimated using data from an HIV intervention randomized trial among people who inject drugs (PWID) in Ukraine. Results from a potential outcomes mediation analysis show that the intervention had a total causal effect on incident HIV infection such that participants in the experimental group were 36% less likely to become infected during the 12-month study than those in the control arm, but that neither self-efficacy nor network communication mediated this effect. Because neither putative mediator was significant, measurement and confounding issues should be investigated to rule out these mediators. Other putative mediators, such as injection frequency, route of administration, or HIV knowledge can be considered. Future research is underway to examine additional, multiple mediators explaining efficacy of the current intervention and sensitivity to confounding effects.

A Review of Spatial Causal Inference Methods for Environmental and Epidemiological Applications.

The scientific rigor and computational methods of causal inference have had great impacts on many disciplines but have only recently begun to take hold in spatial applications. Spatial causal inference poses analytic challenges due to complex correlation structures and interference between the treatment at one location and the outcomes at others. In this paper, we review the current literature on spatial causal inference and identify areas of future work. We first discuss methods that exploit spatial structure to account for unmeasured confounding variables. We then discuss causal analysis in the presence of spatial interference including several common assumptions used to reduce the complexity of the interference patterns under consideration. These methods are extended to the spatiotemporal case where we compare and contrast the potential outcomes framework with Granger causality and to geostatistical analyses involving spatial random fields of treatments and responses. The methods are introduced in the context of observational environmental and epidemiological studies and are compared using both a simulation study and analysis of the effect of ambient air pollution on COVID-19 mortality rate. Code to implement many of the methods using the popular Bayesian software OpenBUGS is provided.

Principal stratum strategy: Potential role in drug development.

A randomized trial allows estimation of the causal effect of an intervention compared to a control in the overall population and in subpopulations defined by baseline characteristics. Often, however, clinical questions also arise regarding the treatment effect in subpopulations of patients, which would experience clinical or disease related events post-randomization. Events that occur after treatment initiation and potentially affect the interpretation or the existence of the measurements are called intercurrent events in the ICH E9(R1) guideline. If the intercurrent event is a consequence of treatment, randomization alone is no longer sufficient to meaningfully estimate the treatment effect. Analyses comparing the subgroups of patients without the intercurrent events for intervention and control will not estimate a causal effect. This is well known, but post-hoc analyses of this kind are commonly performed in drug development. An alternative approach is the principal stratum strategy, which classifies subjects according to their potential occurrence of an intercurrent event on both study arms. We illustrate with examples that questions formulated through principal strata occur naturally in drug development and argue that approaching these questions with the ICH E9(R1) estimand framework has the potential to lead to more transparent assumptions as well as more adequate analyses and conclusions. In addition, we provide an overview of assumptions required for estimation of effects in principal strata. Most of these assumptions are unverifiable and should hence be based on solid scientific understanding. Sensitivity analyses are needed to assess robustness of conclusions.

Using the potential outcome framework to estimate optimal sample size for cluster randomized trials: a simulation-based algorithm.

In cluster randomized trials (CRTs) groups rather than individuals are randomized to different interventions. Individuals' responses within clusters are commonly more similar than those across clusters. This dependency introduces complexity when calculating the number of clusters required to reach a specified statistical power for nominal significance levels and effect sizes. Current CRTs' sample size estimation approaches rely on asymptotic-based formulae or Monte Carlo methods. We propose a new Monte Carlo procedure which is based on the potential outcomes framework. By explicitly defining the causal estimand, the data generating, the sampling, and the treatment assignment mechanisms, this procedure allows for sample size calculations in a broad range of study designs including sample size calculations in finite and infinite populations. It can also address financial and administrative considerations by allowing for unequal allocation of clusters. The R package CRTsampleSearch implements the method and we provide examples for using this package.

Invited Commentary: Counterfactuals in Social Epidemiology-Thinking Outside of "the Box".

There are tensions inherent between many of the social exposures examined within social epidemiology and the assumptions embedded in quantitative potential-outcomes-based causal inference framework. The potential-outcomes framework characteristically requires a well-defined hypothetical intervention. As noted by Galea and Hernán (Am J Epidemiol. 2020;189(3):167-170), for many social exposures, such well-defined hypothetical exposures do not exist or there is no consensus on what they might be. Nevertheless, the quantitative potential-outcomes framework can still be useful for the study of some of these social exposures by creative adaptations that 1) redefine the exposure, 2) separate the exposure from the hypothetical intervention, or 3) allow for a distribution of hypothetical interventions. These various approaches and adaptations are reviewed and discussed. However, even these approaches have their limits. For certain important historical and social determinants of health such as social movements or wars, the quantitative potential-outcomes framework with well-defined hypothetical interventions is the wrong tool. Other modes of inquiry are needed.

Sharp bounds on the relative treatment effect for ordinal outcomes.

For ordinal outcomes, the average treatment effect is often ill-defined and hard to interpret. Echoing Agresti and Kateri, we argue that the relative treatment effect can be a useful measure, especially for ordinal outcomes, which is defined as γ=pr{Yi(1)>Yi(0)}-pr{Yi(1)

Formulating causal questions and principled statistical answers.

Although review papers on causal inference methods are now available, there is a lack of introductory overviews on what they can render and on the guiding criteria for choosing one particular method. This tutorial gives an overview in situations where an exposure of interest is set at a chosen baseline ("point exposure") and the target outcome arises at a later time point. We first phrase relevant causal questions and make a case for being specific about the possible exposure levels involved and the populations for which the question is relevant. Using the potential outcomes framework, we describe principled definitions of causal effects and of estimation approaches classified according to whether they invoke the no unmeasured confounding assumption (including outcome regression and propensity score-based methods) or an instrumental variable with added assumptions. We mainly focus on continuous outcomes and causal average treatment effects. We discuss interpretation, challenges, and potential pitfalls and illustrate application using a "simulation learner," that mimics the effect of various breastfeeding interventions on a child's later development. This involves a typical simulation component with generated exposure, covariate, and outcome data inspired by a randomized intervention study. The simulation learner further generates various (linked) exposure types with a set of possible values per observation unit, from which observed as well as potential outcome data are generated. It thus provides true values of several causal effects. R code for data generation and analysis is available on www.ofcaus.org, where SAS and Stata code for analysis is also provided.