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The article presents a study which illustrates the power of principal stratification in handling partial compliance behavior using a subset of longitudinal data collected from the New York City School Choice Scholarship Program. It states that the School Choice Scholarship Program is intended to evaluate the effects of private schools versus public schools on academic achievement. Analysis of the study uses a pretest score as the only covariate and posttest score as the only result.

Frangakis and Rubin (2002, Biometrics 58, 21–29) proposed a new definition of a surrogate endpoint (a “principal” surrogate) based on causal effects. We introduce an estimand for evaluating a principal surrogate, the causal effect predictiveness (CEP) surface, which quantifies how well causal treatment effects on the biomarker predict causal treatment effects on the clinical endpoint. Although the CEP surface is not identifiable due to missing potential outcomes, it can be identified by incorporating a baseline covariate(s) that predicts the biomarker. Given case–cohort sampling of such a baseline predictor and the biomarker in a large blinded randomized clinical trial, we develop an estimated likelihood method for estimating the CEP surface. This estimation assesses the “surrogate value” of the biomarker for reliably predicting clinical treatment effects for the same or similar setting as the trial. A CEP surface plot provides a way to compare the surrogate value of multiple biomarkers. The approach is illustrated by the problem of assessing an immune response to a vaccine as a surrogate endpoint for infection. [ABSTRACT FROM AUTHOR]

In 2003 Thompson and colleagues reported that daily use of finasteride reduced the prevalence of prostate cancer by 25% compared to placebo. These results were based on the double-blind randomized Prostate Cancer Prevention Trial (PCPT), which followed 18,882 men with no prior or current indications of prostate cancer annually for 7 years. Enthusiasm for the risk reduction afforded by the chemopreventative agent and adoption of its use in clinical practice, however, was severely dampened by the additional finding in the trial of an increased absolute number of high-grade (Gleason score ≥ 7) cancers on the finasteride arm. The question arose as to whether this finding truly implied that finasteride increased the risk of more severe prostate cancer or was a study artifact due to a series of possible postrandomization selection biases, including differences among treatment arms in patient characteristics of cancer cases, differences in biopsy verification of cancer status due to increased sensitivity of prostate-specific antigen under finasteride, differential grading by biopsy due to prostate volume reduction by finasteride, and nonignorable dropout. Via a causal inference approach implementing inverse probability weighted estimating equations, this analysis addresses the question of whether finasteride caused more severe prostate cancer by estimating the mean treatment difference in prostate cancer severity between finasteride and placebo for the principal stratum of participants who would have developed prostate cancer regardless of treatment assignment. We perform sensitivity analyses that sequentially adjust for the numerous potential postrandomization biases conjectured in the PCPT. [ABSTRACT FROM AUTHOR]

This article links the structural equation modeling (SEM) approach with the principal stratification (PS) approach, both of which have been widely used to study the role of intermediate posttreatment outcomes in randomized experiments. Despite the potential benefit of such integration, the 2 approaches have been developed in parallel with little interaction. This article proposes the cross-model translation (CMT) approach, in which parameter estimates are translated back and forth between the PS and SEM models. First, without involving any particular identifying assumptions, translation between PS and SEM parameters is carded out on the basis of their close conceptual connection. Monte Carlo simulations are used to further clarify the relation between the 2 approaches under particular identifying assumptions. The study concludes that, under the common goal of causal inference, what makes a practical difference is the choice of identifying assumptions, not the modeling framework itself. The CMT approach provides a common ground in which the PS and SEM approaches can be jointly considered, focusing on their common inferential problems. [ABSTRACT FROM AUTHOR]

Although experiments are viewed as the gold standard for evaluation, some of their benefits may be lost when, as is common, outcomes are not defined for some sample members. In evaluations of marriage interventions, for example, a key outcome—relationship quality—is undefined when a couple splits up. This article shows how treatment-control differences in mean outcomes can be misleading when outcomes are not defined for everyone and discusses ways to identify the seriousness of the problem. Potential solutions to the problem are described, including approaches that rely on simple treatment-control differences-in-means as well as more complex modeling approaches. [ABSTRACT FROM AUTHOR]

We consider estimation, from a double-blind randomized trial, of treatment effect within levels of base-line covariates on an outcome that is measured after a post-treatment event E has occurred in the subpopulation E,E that would experience event E regardless of treatment. Specifically, we consider estimation of the parameters γ indexing models for the outcome mean conditional on treatment and base-line covariates in the subpopulation E,E. Such parameters are not identified from randomized trial data but become identified if additionally it is assumed that the subpopulation E, E of subjects that would experience event E under the second treatment but not under the first is empty and a parametric model for the conditional probability that a subject experiences event E if assigned to the first treatment given that the subject would experience the event if assigned to the second treatment, his or her outcome under the second treatment and his or her pretreatment covariates. We develop a class of estimating equations whose solutions comprise, up to asymptotic equivalence, all consistent and asymptotically normal estimators of γ under these two assumptions. In addition, we derive a locally semiparametric efficient estimator of γ. We apply our methods to estimate the effect on mean viral load of vaccine versus placebo after infection with human immunodeficiency virus (the event E) in a placebo-controlled randomized acquired immune deficiency syndrome vaccine trial. [ABSTRACT FROM AUTHOR]

We consider studies of cohorts of individuals after a critical event, such as an injury, with the following characteristics. First, the studies are designed to measure “input” variables, which describe the period before the critical event, and to characterize the distribution of the input variables in the cohort. Second, the studies are designed to measure “output” variables, primarily mortality after the critical event, and to characterize the predictive (conditional) distribution of mortality given the input variables in the cohort. Such studies often possess the complication that the input data are missing for those who die shortly after the critical event because the data collection takes place after the event. Standard methods of dealing with the missing inputs, such as imputation or weighting methods based on an assumption of ignorable missingness, are known to be generally invalid when the missingness of inputs is nonignorable, that is, when the distribution of the inputs is different between those who die and those who live. To address this issue, we propose a novel design that obtains and uses information on an additional key variable—a treatment or externally controlled variable, which if set at its “effective” level, could have prevented the death of those who died. We show that the new design can be used to draw valid inferences for the marginal distribution of inputs in the entire cohort, and for the conditional distribution of mortality given the inputs, also in the entire cohort, even under nonignorable missingness. The crucial framework that we use is principal stratification based on the potential outcomes, here mortality under both levels of treatment. We also show using illustrative preliminary injury data that our approach can reveal results that are more reasonable than the results of standard methods, in relatively dramatic ways. Thus, our approach suggests that the routine collection of data on variables that could be used as possible treatments in such studies of inputs and mortality should become common. [ABSTRACT FROM AUTHOR]

In this article we present an extended framework based on the principal stratification approach (Frangakis and Rubin, 2002, Biometrics 58, 21–29), for the analysis of data from randomized experiments which suffer from treatment noncompliance, missing outcomes following treatment noncompliance, and “truncation by death.” We are not aware of any previous work that addresses all these complications jointly. This framework is illustrated in the context of a randomized trial of breast self-examination. [ABSTRACT FROM AUTHOR]

In some randomized studies, researchers are interested in determining the effect of treatment assignment on outcomes that may exist only in a subset chosen after randomization. For example, in preventative human immunodeficiency virus (HIV) vaccine efficacy trials, it is of interest to determine whether randomization to vaccine affects postinfection outcomes that may be right-censored. Such outcomes in these trials include time from infection diagnosis to initiation of antiretroviral therapy and time from infection diagnosis to acquired immune deficiency syndrome. Here we present sensitivity analysis methods for making causal comparisons on these postinfection outcomes. We focus on estimating the survival causal effect, defined as the difference between probabilities of not yet experiencing the event in the vaccine and placebo arms, conditional on being infected regardless of treatment assignment. This group is referred to as the always-infected principal stratum. Our key assumption is monotonicity--that subjects randomized to the vaccine arm who become infected would have been infected had they been randomized to placebo. We propose nonparametric, semiparametric, and parametric methods for estimating the survival causal effect. We apply these methods to the first Phase III preventative HIV vaccine trial, VaxGen's trial of AIDSVAX BIB. [ABSTRACT FROM AUTHOR]

A controversial topic in obstetrics is the effect of walking on the probability of Caesarean section among women in labour. A major reason for the controversy is the presence of non-compliance that complicates the estimation of efficacy, the effect of treatment received on outcome. The intent-to-treat method does not estimate efficacy, and estimates of efficacy that are based directly on treatment received may be biased because they are not protected by randomization. However, when non-compliance occurs immediately after randomization, the use of a potential outcomes model with reasonable assumptions has made it possible to estimate efficacy and still to retain the benefits of randomization to avoid selection bias. In this obstetrics application, non-compliance occurs initially and later in one arm. Consequently some parameters cannot be uniquely estimated without making strong assumptions. This difficulty is circumvented by a new study design involving an additional randomization group and a novel potential outcomes model (principal stratification). [ABSTRACT FROM AUTHOR]

It has recently become popular to define treatment effects for subsets of the target population characterized by variables not observable at the time a treatment decision is made. Characterizing and estimating such treatment effects is tricky; the most popular but naive approach inappropriately adjusts for variables affected by treatment and so is biased. We consider several appropriate ways to formalize the effects: principal stratification, stratification on a single potential auxiliary variable, stratification on an observed auxiliary variable and stratification on expected levels of auxiliary variables. We then outline identifying assumptions for each type of estimand. We evaluate the utility of these estimands and estimation procedures for decision making and understanding causal processes, contrasting them with the concepts of direct and indirect effects. We motivate our development with examples from nephrology and cancer screening, and use simulated data and real data on cancer screening to illustrate the estimation methods. [ABSTRACT FROM AUTHOR]

Sensitivity analyses, wherein estimation is performed for each of a range of values of a sensitivity parameter, are of particular use in causal inference, where estimands often are identified because of untestable assumptions. Sensitivity parameters may have counterfactual interpretations, making their elicitation especially challenging. This article describes our experience eliciting a counterfactual sensitivity parameter to be used in the analysis of an ongoing HIV vaccine trial. We include instructions given to 10 subject-matter experts, the chosen ranges of our eight responders and some of their comments, their ranges applied to data from an earlier trial, and a brief discussion of some general issues regarding counterfactual elicitation. [ABSTRACT FROM AUTHOR]

This article introduces methods for use in vaccine clinical trials to help determine whether the immune response to a vaccine is actually causing a reduction in the infection rate. This is not easy because immune response to the (say HIV) vaccine is only observed in the HIV vaccine arm. If we knew what the HIV-specific immune response in placebo recipients would have been, had they been vaccinated, this immune response could be treated essentially like a baseline covariate and an interaction with treatment could be evaluated. Relatedly, the rate of infection by this baseline covariate could be compared between the two groups and a causative role of immune response would be supported if infection risk decreased with increasing HIV immune response only in the vaccine group. We introduce two methods for inferring this HIV-specific immune response. The first involves vaccinating everyone before baseline with an irrelevant vaccine, for example, rabies. Randomization ensures that the relationship between the immune responses to the rabies and HIV vaccines observed in the vaccine group is the same as what would have been seen in the placebo group. We infer a placebo volunteer's response to the HIV vaccine using their rabies response and a prediction model from the vaccine group. The second method entails vaccinating all uninfected placebo patients at the closeout of the trial with the HIV vaccine and recording immune response. We pretend this immune response at closeout is what they would have had at baseline. We can then infer what the distribution of immune response among placebo infecteds would have been. Such designs may help elucidate the role of immune response in preventing infections. More pointedly, they could be helpful in the decision to improve or abandon an HIV vaccine with mediocre performance in a phase III trial. [ABSTRACT FROM AUTHOR]

To support the design of the world's first proof-of-concept (POC) efficacy trial of a cell-mediated immunity-based HIV vaccine, we evaluate eight methods for testing the composite null hypothesis of no-vaccine effect on either the incidence of HIV infection or the viral load set point among those infected, relative to placebo. The first two methods use a single test applied to the actual values or ranks of a burden-of-illness (BOI) outcome that combines the infection and viral load endpoints. The other six methods combine separate tests for the two endpoints using unweighted or weighted versions of the two-part z, Simes', and Fisher's methods. Based on extensive simulations that were used to design the landmark POC trial, the BOI methods are shown to have generally low power for rejecting the composite null hypothesis (and hence advancing the vaccine to a subsequent large-scale efficacy trial). The unweighted Simes' and Fisher's combination methods perform best overall. Importantly, this conclusion holds even after the test for the viral load component is adjusted for bias that can be introduced by conditioning on a postrandomization event (HIV infection). The adjustment is derived using a selection bias model based on the principal stratification framework of causal inference. [ABSTRACT FROM AUTHOR]

In many experiments, researchers would like to compare between treatments and outcome that only exists in a subset of participants selected after randomization. For example, in preventive HIV vaccine efficacy trials it is of interest to determine whether randomization to vaccine causes lower HIV viral load, a quantity that only exists in participants who acquire HIV. To make a causal comparison and account for potential selection bias we propose a sensitivity analysis following the principal stratification framework set forth by Frangakis and Rubin (2002, Biometrics 58, 21–29). Our goal is to assess the average causal effect of treatment assignment on viral load at a given baseline covariate level in the always infected principal stratum (those who would have been infected whether they had been assigned to vaccine or placebo). We assume stable unit treatment values (SUTVA), randomization, and that subjects randomized to the vaccine arm who became infected would also have become infected if randomized to the placebo arm (monotonicity). It is not known which of those subjects infected in the placebo arm are in the always infected principal stratum, but this can be modeled conditional on covariates, the observed viral load, and a specified sensitivity parameter. Under parametric regression models for viral load, we obtain maximum likelihood estimates of the average causal effect conditional on covariates and the sensitivity parameter. We apply our methods to the world's first phase III HIV vaccine trial. [ABSTRACT FROM AUTHOR]

In an increasingly common class of studies, the goal is to evaluate causal effects of treatments that are only partially controlled by the investigator. In such studies there are two conflicting features: (1) a model on the full cohort design and data can identify the causal effects of interest, but can be sensitive to extreme regions of that design's data, where model specification can have more impact; and (2) models on a reduced design (i.e., a subset of the full data), for example, conditional likelihood on matched subsets of data, can avoid such sensitivity, but do not generally identify the causal effects. We propose a framework to assess how inference is sensitive to designs by exploring combinations of both the full and reduced designs. We show that using such a “polydesign” framework generates a rich class of methods that can identify causal effects and that can also be more robust to model specification than methods using only the full design. We discuss implementation of polydesign methods, and provide an illustration in the evaluation of a needle exchange program. [ABSTRACT FROM AUTHOR]

The effects of vaccine on postinfection outcomes, such as disease, death, and secondary transmission to others, are important scientific and public health aspects of prophylactic vaccination. As a result, evaluation of many vaccine effects condition on being infected. Conditioning on an event that occurs posttreatment (in our case, infection subsequent to assignment to vaccine or control) can result in selection bias. Moreover, because the set of individuals who would become infected if vaccinated is likely not identical to the set of those who would become infected if given control, comparisons that condition on infection do not have a causal interpretation. In this article we consider identifiability and estimation of causal vaccine effects on binary postinfection outcomes. Using the principal stratification framework, we define a postinfection causal vaccine efficacy estimand in individuals who would be infected regardless of treatment assignment. The estimand is shown to be not identifiable under the standard assumptions of the stable unit treatment value, monotonicity, and independence of treatment assignment. Thus selection models are proposed that identify the causal estimand. Closed-form maximum likelihood estimators (MLEs) are then derived under these models, including those assuming maximum possible levels of positive and negative selection bias. These results show the relations between the MLE of the causal estimand and two commonly used estimators for vaccine effects on postinfection outcomes. For example, the usual intent-to-treat estimator is shown to be an upper bound on the postinfection causal vaccine effect provided that the magnitude of protection against infection is not too large. The methods are used to evaluate postinfection vaccine effects in a clinical trial of a rotavirus vaccine candidate and in a field study of a pertussis vaccine. Our results show that pertussis vaccination has a significant causal effect in reducing disease severity. [ABSTRACT FROM AUTHOR]

Grade retention has been controversial for many years, and current calls to end social promotion have lent new urgency to this issue. On the one hand, a policy of retaining in grade those students making slow progress might facilitate instruction by making classrooms more homogeneous academically. On the other hand, grade retention might harm high-risk students by limiting their framing opportunities. Analyzing data from the US Early Childhood Longitudinal Study Kindergarten cohort with the technique of multilevel propensity score stratification, we find no evidence that a policy of grade retention in kindergarten improves average achievement in mathematics or reading. Nor do we find evidence that the policy benefits children who would be promoted under the policy. However, the evidence does suggest that children who are retained learn less than they would have had they instead been promoted. The negative effect of grade retention on those retained has little influence on the overall mean achievement of children attending schools with a retention policy because the fraction of children retained in those schools is quite small. Nevertheless, the effect of retention on the retainees is considerably large. [ABSTRACT FROM AUTHOR]

Causal effects are defined as comparisons of potential outcomes under different treatments on a common set of units. Observed values of the potential outcomes are revealed by the assignment mechanism-a probabilistic model for the treatment each unit receives as a function of covariates and potential outcomes. Fisher made tremendous contributions to causal inference through his work on the design of randomized experiments, but the potential outcomes perspective applies to other complex experiments and nonrandomized studies as well. As noted by Kempthorne in his 1976 discussion of Savage's Fisher lecture, Fisher never bridged his work on experimental design and his work on parametric modeling, a bridge that appears nearly automatic with an appropriate view of the potential outcomes framework, where the potential outcomes and covariates are given a Bayesian distribution to complete the model specification. Also, this framework crisply separates scientific inference for causal effects and decisions based on such inference, a distinction evident in Fisher's discussion of tests of significance versus tests in an accept/reject framework. But Fisher never used the potential outcomes framework, originally proposed by Neyman in the context of randomized experiments, and as a result he provided generally flawed advice concerning the use of the analysis of covariance to adjust for posttreatment concomitants in randomized trials. [ABSTRACT FROM AUTHOR]

The use of the concept of ‘direct’ versus ‘indirect’ causal effects is common, not only in statistics but also in many areas of social and economic sciences. The related terms of ‘biomarkers’ and ‘surrogates’ are common in pharmacological and biomedical sciences. Sometimes this concept is represented by graphical displays of various kinds. The view here is that there is a great deal of imprecise discussion surrounding this topic and, moreover, that the most straightforward way to clarify the situation is by using potential outcomes to define causal effects. In particular, I suggest that the use of principal stratification is key to understanding the meaning of direct and indirect causal effects. A current study of anthrax vaccine will be used to illustrate ideas. [ABSTRACT FROM AUTHOR]

We consider studies for evaluating the short-term effect of a treatment of interest on a time-to-event outcome. The studies we consider are partially controlled in the following sense: (1) Subjects' exposure to the treatment of interest can vary over time, but this exposure is not directly controlled by the study; (2) subjects' follow-up time is not directly controlled by the study; and (3) the study directly controls another factor that can affect subjects' exposure to the treatment of interest as well as subjects' follow-up time. When factors (1) and (2) are both present in the study, evaluating the treatment of interest using standard methods, including instrumental variables, does not generally estimate treatment effects. We develop the methodology for estimating the effect of treatment in this setting of partially controlled studies under explicit assumptions using the framework for principal stratification for causal inference. We illustrate our methods by a study to evaluate the efficacy of the Baltimore Needle Exchange Program to reduce the risk of human immunodeficiency virus (HIV) transmission, using data on distance of the program's sites from the subjects. [ABSTRACT FROM AUTHOR]

The precarious state of the educational system in the inner cities of the United States, as well as its potential causes and solutions, have been popular topics of debate in recent years. Part of the difficulty in resolving this debate is the lack of solid empirical evidence regarding the true impact of educational initiatives. The efficacy of so-called "school choice" programs has been a particularly contentious issue. A current multimillion dollar program, the School Choice Scholarship Foundation Program in New York, randomized the distribution of vouchers in an attempt to shed some light on this issue. This is an important time for school choice, because on June 27, 2002 the U.S. Supreme Court upheld the constitutionality of a voucher program in Cleveland that provides scholarships both to secular and religious private schools. Although this study benefits immensely from a randomized design, it suffers from complications common to such research with human subjects: noncompliance with assigned "treatments" and missing data. Recent work has revealed threats to valid estimates of experimental effects that exist in the presence of noncompliance and missing data, even when the goal is to estimate simple intention-to-treat effects. Our goal was to create a better solution when faced with both noncompliance and missing data. This article presents a model that accommodates these complications that is based on the general framework of "principal stratification" and thus relies on more plausible assumptions than standard methodology. Our analyses revealed positive effects on math scores for children who applied to the program from certain types of schools - those with average test scores below the citywide median. Among these children, the effects are stronger for children who applied in the first grade and for African-American children. [ABSTRACT FROM AUTHOR]

Intercurrent (post-treatment) events occur frequently in randomized trials, and investigators often express interest in treatment effects that suitably take account of these events. Contrasts that naively condition on intercurrent events do not have a straight-forward causal interpretation, and the practical relevance of other commonly used approaches is debated. In this work, we discuss how to formulate and choose an estimand, beyond the marginal intention-to-treat effect, from the point of view of a decision maker and drug developer. In particular, we argue that careful articulation of a practically useful research question should either reflect decision making at this point in time or future drug development. Indeed, a substantially interesting estimand is simply a formalization of the (plain English) description of a research question. A common feature of estimands that are practically useful is that they correspond to possibly hypothetical but well-defined interventions in identifiable (sub)populations. To illustrate our points, we consider five examples that were recently used to motivate consideration of principal stratum estimands in clinical trials. In all of these examples, we propose alternative causal estimands, such as conditional effects, sequential regime effects, and separable effects, that correspond to explicit research questions of substantial interest., (© 2022 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.)

Given the latent stratum membership, principal stratification models with continuous outcomes naturally fit in the parametric estimation framework of Gaussian mixtures. However, with models that are not nonparametrically identified, relying on parametric mixture modeling has been mostly discouraged as a way of identifying principal effects. This study revisits this rather deserted use of parametric mixture modeling, which may open up various possibilities in principal stratification modeling. The main problem with using the parametric mixture modeling approach is that it is hard to assess the quality of principal effect estimates given its reliance on parametric conditions. As a way of assessing the estimation quality in this situation, this study proposes that we use parametric mixture modeling in two different ways, with and without the assurance of nonparametric identification. The key identifying assumption employed in this study is the moving exclusion restriction, a flexible version of the standard exclusion restriction assumption. This assumption is used as a temporary vehicle to help assess the quality of principal effect estimates obtained relying on parametric mixture modeling. The study presents promising results, showing the possibility of using parametric mixture modeling as an accessible tool for causal inference., (© 2022 John Wiley & Sons Ltd.)

Treatment noncompliance often occurs in longitudinal randomized controlled trials (RCTs) on human subjects, and can greatly complicate treatment effect assessment. The complier average causal effect (CACE) informs the intervention efficacy for the subpopulation who would comply regardless of assigned treatment and has been considered as patient-oriented treatment effects of interest in the presence of noncompliance. Real-world RCTs evaluating multifaceted interventions often employ multiple study endpoints to measure treatment success. In such trials, limited sample sizes, low compliance rates, and small to moderate effect sizes on individual endpoints can significantly reduce the power to detect CACE when these correlated endpoints are analyzed separately. To overcome the challenge, we develop a multivariate longitudinal potential outcome model with stratification on latent compliance types to efficiently assess multivariate CACEs (MCACE) by combining information across multiple endpoints and visits. Evaluation using simulation data shows a significant increase in the estimation efficiency with the MCACE model, including up to 50% reduction in standard errors (SEs) of CACE estimates and 1-fold increase in the power to detect CACE. Finally, we apply the proposed MCACE model to an RCT on Arthritis Health Journal online tool. Results show that the MCACE analysis detects significant and beneficial intervention effects on two of the six endpoints while estimating CACEs for these endpoints separately fail to detect treatment effect on any endpoint., (© 2022 John Wiley & Sons Ltd.)

In clinical trials, placebo response is considered a beneficial effect arising from multiple factors, including the patient's expectations for the treatment. Its presence makes the classical parallel study design suboptimal and can bias the inference. The sequential parallel comparison design (SPCD), a two-stage design where the first stage is a classical parallel study design, followed by another parallel design among placebo subjects from the first stage, was proposed to address the shortcomings of the classical design. In SPCD, in lieu of treatment effect, a weighted average of the mean treatment difference in Stage I among all randomized subjects and the mean treatment difference in Stage II among placebo non-responders was proposed as the efficacy measure. However, by linking two possibly different populations, this weighted average lacks interpretability, and the choice of weight remains controversial. In this work, under the principal stratification framework, we propose a causal estimand for the treatment effect under each of three clinically important principal strata: Always Responders, Never Responders, and Drug-only Responders. To make the stratum treatment effect identifiable, we introduce a set of assumptions and two sensitivity parameters. By further considering the strata as latent characteristics, the sensitivity parameters can be estimated. An extensive simulation study is conducted to evaluate the operating characteristics of the proposed method. Finally, we apply our method on the ADAPT-A study data to assess the benefit of low-dose aripiprazole adjunctive to antidepressant therapy treatment., (© 2022 John Wiley & Sons Ltd.)

In vaccine studies, an important research question is to study effect modification of clinical treatment efficacy by intermediate biomarker-based principal strata. In settings where participants entering a trial may have prior exposure and therefore variable baseline biomarker values, clinical treatment efficacy may further depend jointly on a biomarker measured at baseline and measured at a fixed time after vaccination. This makes it important to conduct a bivariate effect modification analysis by both the intermediate biomarker-based principal strata and the baseline biomarker values. Existing research allows this assessment if the sampling of baseline and intermediate biomarkers follows a monotone pattern, i.e., if participants who have the biomarker measured post-randomization would also have the biomarker measured at baseline. However, additional complications in study design could happen in practice. For example, in a dengue correlates study, baseline biomarker values were only available from a fraction of participants who have biomarkers measured post-randomization. How to conduct the bivariate effect modification analysis in these studies remains an open research question. In this article, we propose approaches for bivariate effect modification analysis in the complicated sampling design based on an estimated likelihood framework. We demonstrate advantages of the proposed method over existing methods through numerical studies and illustrate our method with data sets from two phase 3 dengue vaccine efficacy trials., (© The Author 2020. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

Background: In cluster randomized trials, patients are typically recruited after clusters are randomized, and the recruiters and patients may not be blinded to the assignment. This often leads to differential recruitment and consequently systematic differences in baseline characteristics of the recruited patients between intervention and control arms, inducing post-randomization selection bias. We aim to rigorously define causal estimands in the presence of selection bias. We elucidate the conditions under which standard covariate adjustment methods can validly estimate these estimands. We further discuss the additional data and assumptions necessary for estimating causal effects when such conditions are not met., Methods: Adopting the principal stratification framework in causal inference, we clarify there are two average treatment effect (ATE) estimands in cluster randomized trials: one for the overall population and one for the recruited population. We derive analytical formula of the two estimands in terms of principal-stratum-specific causal effects. Furthermore, using simulation studies, we assess the empirical performance of the multivariable regression adjustment method under different data generating processes leading to selection bias., Results: When treatment effects are heterogeneous across principal strata, the average treatment effect on the overall population generally differs from the average treatment effect on the recruited population. A naïve intention-to-treat analysis of the recruited sample leads to biased estimates of both average treatment effects. In the presence of post-randomization selection and without additional data on the non-recruited subjects, the average treatment effect on the recruited population is estimable only when the treatment effects are homogeneous between principal strata, and the average treatment effect on the overall population is generally not estimable. The extent to which covariate adjustment can remove selection bias depends on the degree of effect heterogeneity across principal strata., Conclusion: There is a need and opportunity to improve the analysis of cluster randomized trials that are subject to post-randomization selection bias. For studies prone to selection bias, it is important to explicitly specify the target population that the causal estimands are defined on and adopt design and estimation strategies accordingly. To draw valid inferences about treatment effects, investigators should (1) assess the possibility of heterogeneous treatment effects, and (2) consider collecting data on covariates that are predictive of the recruitment process, and on the non-recruited population from external sources such as electronic health records.