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Intercurrent events and estimands play a key role in defining the treatment effects of interest precisely. Sometimes the median or other quantiles of outcomes in a principal stratum according to potential occurrence of intercurrent events are of interest in randomized clinical trials. Naïve analyses such as those based on the observed occurrence of the intercurrent events lead to biased results. Therefore, we propose principal quantile treatment effect estimators that can nonparametrically estimate the distribution of potential outcomes by principal score weighting without relying on the exclusion restriction assumption. Our simulation studies show that the proposed method works in situations where the median or quantiles may be regarded as the preferred population‐level summary over the mean. We illustrate our proposed method by using data from a randomized controlled trial conducted on patients with nonerosive reflux disease. [ABSTRACT FROM AUTHOR]

Principal stratification has become a popular tool to address a broad class of causal inference questions, particularly in dealing with non‐compliance and truncation by death problems. The causal effects within principal strata, which are determined by joint potential values of the intermediate variable, also known as the principal causal effects, are often of interest in these studies. The analysis of principal causal effects from observational studies mostly relies on the ignorability assumption of treatment assignment, which requires practitioners to accurately measure as many covariates as possible so that all potential sources of confounders are captured. However, in practice, collecting all potential confounding factors can be challenging and costly, rendering the ignorability assumption questionable. In this paper, we consider the identification and estimation of causal effects when treatment and principal stratification are confounded by unmeasured confounding. Specifically, we establish the nonparametric identification of principal causal effects using a pair of negative controls to mitigate unmeasured confounding, requiring they have no direct effect on the outcome variable. We also provide an estimation method for principal causal effects. Extensive simulations and a leukemia study are employed for illustration. [ABSTRACT FROM AUTHOR]

In a placebo‐controlled clinical study one may calculate the average treatment effect to convey the effect of the active treatment on some outcome. However, if it is speculated that the treatment only has an effect if the patient responds to the treatment defined by a certain biomarker response, then it is arguably more relevant to estimate the treatment effect among such responders. We present such a causal parameter that is based on principal stratification and is identified under the exclusion of a treatment effect among the nonresponders. We focus on time‐to‐event outcomes allowing for right censoring, and construct a doubly robust and efficient estimator based on the associated efficient influence function. The properties of the estimator are showcased in a simulation study and the methodology is applied to the Leader trial investigating the effect of liraglutide on the occurrence of cardiovascular events. [ABSTRACT FROM AUTHOR]

An important strategy for identifying principal causal effects (popular estimands in settings with noncompliance) is to invoke the principal ignorability (PI) assumption. As PI is untestable, it is important to gauge how sensitive effect estimates are to its violation. We focus on this task for the common one‐sided noncompliance setting where there are two principal strata, compliers and noncompliers. Under PI, compliers and noncompliers share the same outcome‐mean‐given‐covariates function under the control condition. For sensitivity analysis, we allow this function to differ between compliers and noncompliers in several ways, indexed by an odds ratio, a generalized odds ratio, a mean ratio, or a standardized mean difference sensitivity parameter. We tailor sensitivity analysis techniques (with any sensitivity parameter choice) to several types of PI‐based main analysis methods, including outcome regression, influence function (IF) based and weighting methods. We discuss range selection for the sensitivity parameter. We illustrate the sensitivity analyses with several outcome types from the JOBS II study. This application estimates nuisance functions parametrically – for simplicity and accessibility. In addition, we establish rate conditions on nonparametric nuisance estimation for IF‐based estimators to be asymptotically normal – with a view to inform nonparametric inference. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We propose an improved estimator of the complier average causal effect (CACE). Researchers typically choose a presumably consistent estimator for CACE in studies with noncompliance when many other lower variance estimators may be available. We propose a synthetic estimator that combines information across all available estimators, leveraging the efficiency in lower variance estimators while maintaining low bias. Our approach minimizes an estimate of the mean squared error of all convex combinations of the candidate estimators. We derive the asymptotic distribution of the synthetic estimator and demonstrate its good performance in simulation, displaying robustness to inclusion of even high‐bias estimators. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A surrogate endpoint S in a clinical trial is an outcome that may be measured earlier or more easily than the true outcome of interest T. In this work, we extend causal inference approaches to validate such a surrogate using potential outcomes. The causal association paradigm assesses the relationship of the treatment effect on the surrogate with the treatment effect on the true endpoint. Using the principal surrogacy criteria, we utilize the joint conditional distribution of the potential outcomes T, given the potential outcomes S. In particular, our setting of interest allows us to assume the surrogate under the placebo, S(0), is zero‐valued, and we incorporate baseline covariates in the setting of normally distributed endpoints. We develop Bayesian methods to incorporate conditional independence and other modeling assumptions and explore their impact on the assessment of surrogacy. We demonstrate our approach via simulation and data that mimics an ongoing study of a muscular dystrophy gene therapy. [ABSTRACT FROM AUTHOR]

Noncompliance issue is common in early phase clinical trials; and may lead to biased estimation of the intent‐to‐treat effect and incorrect conclusions for the clinical trial. In this work, we propose a Bayesian approach for sequentially monitoring the phase II randomized clinical trials that takes account for the noncompliance information. We adopt the principal stratification framework and propose to use Bayesian additive regression trees for selecting useful baseline covariates and estimating the complier average causal effect (CACE) for both efficacy and toxicity outcomes. The decision of early termination or not is then made adaptively based on the estimated CACE from the accumulated data. Simulation studies have confirmed the excellent performance of the proposed design in the presence of noncompliance. [ABSTRACT FROM AUTHOR]

Participants in pragmatic clinical trials often partially adhere to treatment. However, to simplify the analysis, most studies dichotomize adherence (supposing that subjects received either full or no treatment), which can introduce biases in the results. For example, the popular approach of principal stratification is based on the concept that the population can be separated into strata based on how they will react to treatment assignment, but this framework does not include strata in which a partially adhering participant would belong. We expanded the principal stratification framework to allow partial adherers to have their own principal stratum and treatment level. The expanded approach is feasible in pragmatic settings. We have designed a Monte Carlo posterior sampling method to obtain the relevant parameter estimates. Simulations were completed under a range of settings where participants partially adhered to treatment, including a hypothetical setting from a published simulation trial on the topic of partial adherence. The inference method is additionally applied to data from a real randomized clinical trial that features partial adherence. Comparison of the simulation results indicated that our method is superior in most cases to the biased estimators obtained through standard principal stratification. Simulation results further suggest that our proposed method may lead to increased accuracy of inference in settings where study participants only partially adhere to assigned treatment. [ABSTRACT FROM AUTHOR]

Summary: Intercurrent events (ICEs) and missing values are inevitable in clinical trials of any size and duration, making it difficult to assess the treatment effect for all patients in randomized clinical trials. Defining the appropriate estimand that is relevant to the clinical research question is the first step in analyzing data. The tripartite estimands, which evaluate the treatment differences in the proportion of patients with ICEs due to adverse events, the proportion of patients with ICEs due to lack of efficacy, and the primary efficacy outcome for those who can adhere to study treatment under the causal inference framework, are of interest to many stakeholders in understanding the totality of treatment effects. In this manuscript, we discuss the details of how to estimate tripartite estimands based on a causal inference framework and how to interpret tripartite estimates through a phase 3 clinical study evaluating a basal insulin treatment for patients with type 1 diabetes. [ABSTRACT FROM AUTHOR]

In clinical endpoint bioequivalence studies, the observed per-protocol (PP) population (compliers and completers in general) is usually used in the primary analysis for equivalence assessment. However, intercurrent events, ie, missingness and noncompliance, are not properly handled. The resulting estimand is not causal. Previously, we proposed the first causal framework to assess equivalence in the presence of missing data and noncompliance. We proposed a causal survivor average causal effect (SACE) estimand for the difference of means (DOM). In equivalence assessment, DOM is not as widely used as the ratio of means (ROM). However, no existing formula links the observed PP estimand to the SACE estimand for ROM as exists for DOM. Herein, we propose a similar causal framework for ROM using the principal stratification approach, one of the strategies recommended by the International Conference on Harmonisation (ICH) E9 R1 addendum. We quantify the bias of the observed ROM PP estimand for the SACE estimand, which provides a basis to identify three conditions under which the two estimands are equal. We propose a sensitivity analysis method to evaluate the robustness of the current PP estimator to estimate the SACE estimand. We extend Fieller's confidence interval for the SACE estimand using ROM, which can be applied to many settings. Simulation demonstrates that the PP estimator is biased in either directions and may inflate type 1 error and/or change power when the three identified conditions are violated. Our work can be applied to comparative clinical biosimilar studies. [ABSTRACT FROM AUTHOR]

In randomized clinical trials, it is often of interest to estimate the effect of treatment on quality of life (QOL), in addition to those on the event itself. When an event occurs in some patients prior to QOL score assessment, investigators may compare QOL scores between patient subgroups defined by the event after randomization. However, owing to postrandomization selection bias, this analysis can mislead investigators about treatment efficacy and result in paradoxical findings. The recent Japanese Osteoporosis Intervention Trial (JOINT‐02), which compared the benefits of a combination therapy for fracture prevention with those of a monotherapy, exemplifies the case in point; the average QOL score was higher in the combination therapy arm for the unfractured subgroup but was lower for the fractured subgroup. To address this issue, principal strata effects (PSEs), which are treatment effects estimated within subgroups of individuals stratified by potential intermediate variable, have been discussed in the literature. In this paper, we describe a simple procedure for estimating the PSEs using marginal structural models. This procedure utilizes SAS code for the estimation. In addition, we present a simple sensitivity analysis method for examining the resulting estimates. The analyses of JOINT‐02 data using these methods revealed that QOL scores were higher in the combination therapy arm than in the monotherapy arm for both subgroups. [ABSTRACT FROM AUTHOR]

Purpose Cancer trials are often open‐label and include patient‐reported outcomes (PROs). Previous work has demonstrated that patients may complete PRO assessments less frequently in the control arm compared with the experimental arm in open‐label trials. Such differential completion may affect PRO results. This paper sought to explore principal stratification methodology to address potential bias caused by the posttreatment intermediate variable of questionnaire completion. Methods: We evaluated six randomized trials (five open‐label and one double‐blind) of anticancer therapies with varying levels of PRO completion submitted to the Food and Drug Administration (FDA). We applied complete case analysis (CCA), multiple imputation (MI), and principal stratification to evaluate PRO results for quality of life (QOL) and the domains of physical, role, and emotional function (PF, RF, and EF). Assignment to potential principal strata was by the expectation maximization algorithm using patient baseline characteristics. Results: Completion rates in the experimental arm ranged from 66% to 94% and 51% to 95% in the control arm. Four trials had negligible completion differences between arms (1%‐2%), and two had large differences favoring the experimental arm (15%‐17%). For trials with negligible completion differences, principal stratification results were similar to CCA and MI results for all domains. Notable differences in point estimates may be observed in trials with large differences in completion rates. However, in the examined trials, the confidence intervals for the principal stratification estimates overlapped with the ones obtained using CCA. Conclusions: The principal stratification estimand may be a useful additional analysis, especially if PRO completion differs between arms. [ABSTRACT FROM AUTHOR]

Subject noncompliance is a common problem in the analysis of randomized clinical trials (RCTs). With cognitive behavioral interventions, the addition of provider noncompliance further complicates making causal inference. As a motivating example, we consider an RCT of a motivational interviewing (MI)-based behavioral intervention for treating problem drug use. Treatment receipt depends on compliance of both a therapist (provider) and a patient (subject), where MI is received when the therapist adheres to the MI protocol and the patient actively participates in the intervention. However, therapists cannot be forced to follow protocol and patients cannot be forced to cooperate in an intervention. In this article, we (1) define a causal estimand of interest based on a principal stratification framework, the average causal effect of treatment among provider-subject pairs that comply with assignment or ACE(cc); (2) explore possible assumptions that identify ACE(cc); (3) develop novel estimators of ACE(cc); (4) evaluate estimators' statistical properties via simulation; and (5) apply our proposed methods for estimating ACE(cc) to data from our motivating example. [ABSTRACT FROM AUTHOR]

Two paradigms for the evaluation of surrogate markers in randomized clinical trials have been proposed: the causal effects paradigm and the causal association paradigm. Each of these paradigms rely on assumptions that must be made to proceed with estimation and to validate a candidate surrogate marker (S) for the true outcome of interest (T). We consider the setting in which S and T are Gaussian and are generated from structural models that include an unobserved confounder. Under the assumed structural models, we relate the quantities used to evaluate surrogacy within both the causal effects and causal association frameworks. We review some of the common assumptions made to aid in estimating these quantities and show that assumptions made within one framework can imply strong assumptions within the alternative framework. We demonstrate that there is a similarity, but not exact correspondence between the quantities used to evaluate surrogacy within each framework, and show that the conditions for identifiability of the surrogacy parameters are different from the conditions, which lead to a correspondence of these quantities. [ABSTRACT FROM AUTHOR]

In a randomized controlled clinical trial that assesses treatment efficacy, a common objective is to assess the association of a measured biomarker response endpoint with the primary study endpoint in the active treatment group, using a case-cohort, case-control, or two-phase sampling design. Methods for power and sample size calculations for such biomarker association analyses typically do not account for the level of treatment efficacy, precluding interpretation of the biomarker association results in terms of biomarker effect modification of treatment efficacy, with detriment that the power calculations may tacitly and inadvertently assume that the treatment harms some study participants. We develop power and sample size methods accounting for this issue, and the methods also account for inter-individual variability of the biomarker that is not biologically relevant (e.g., due to technical measurement error). We focus on a binary study endpoint and on a biomarker subject to measurement error that is normally distributed or categorical with two or three levels. We illustrate the methods with preventive HIV vaccine efficacy trials and include an R package implementing the methods. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We examine the properties of principal scores methods to estimate the causal marginal odds ratio of an intervention for compliers in the context of a randomized controlled trial with non-compliers. The two-stage estimation approach has been proposed for a linear model by Jo and Stuart (Statistics in Medicine 2009; 28:2857-2875) under a principal ignorability (PI) assumption. Using a Monte Carlo simulation study, we compared the performance of several strategies to build and use principal score models and the robustness of the method to violations of underlying assumptions, in particular PI. Results showed that the principal score approach yielded unbiased estimates of the causal marginal log odds ratio under PI but that the method was sensitive to violations of PI, which occurs in particular when confounders are omitted from the analysis. For principal score analysis, probability weighting performed slightly better than full matching or 1:1 matching. Concerning the variables to be included in principal score models, the lowest mean squared error was generally obtained when using the true confounders. Using variables associated with the outcome only but not compliance however yielded very similar performance. [ABSTRACT FROM AUTHOR]

In some two-arm randomized trials, some participants receive the treatment assigned to the other arm as a result of technical problems, refusal of a treatment invitation, or a choice of treatment in an encouragement design. In some before-and-after studies, the availability of a new treatment changes from one time period to this next. Under assumptions that are often reasonable, the latent class instrumental variable (IV) method estimates the effect of treatment received in the aforementioned scenarios involving all-or-none compliance and all-or-none availability. Key aspects are four initial latent classes (sometimes called principal strata) based on treatment received if in each randomization group or time period, the exclusion restriction assumption (in which randomization group or time period is an instrumental variable), the monotonicity assumption (which drops an implausible latent class from the analysis), and the estimated effect of receiving treatment in one latent class (sometimes called efficacy, the local average treatment effect, or the complier average causal effect). Since its independent formulations in the biostatistics and econometrics literatures, the latent class IV method (which has no well-established name) has gained increasing popularity. We review the latent class IV method from a clinical and biostatistical perspective, focusing on underlying assumptions, methodological extensions, and applications in our fields of obstetrics and cancer research. [ABSTRACT FROM AUTHOR]

To estimate causal effects of vaccine on post-infection outcomes, Hudgens and Halloran (2006) defined a post-infection causal vaccine efficacy estimand VEI based on the principal stratification framework. They also derived closed forms for the maximum likelihood estimators of the causal estimand under some assumptions. Extending their research, we propose a Bayesian approach to estimating the causal vaccine effects on binary post-infection outcomes. The identifiability of the causal vaccine effect VEI is discussed under different assumptions on selection bias. The performance of the proposed Bayesian method is compared with the maximum likelihood method through simulation studies and two case studies - a clinical trial of a rotavirus vaccine candidate and a field study of pertussis vaccination. For both case studies, the Bayesian approach provided similar inference as the frequentist analysis. However, simulation studies with small sample sizes suggest that the Bayesian approach provides smaller bias and shorter confidence interval length. [ABSTRACT FROM AUTHOR]

In early-phase clinical trials, interim monitoring is commonly conducted based on the estimated intent-to-treat effect, which is subject to bias in the presence of noncompliance. To address this issue, we propose a Bayesian sequential monitoring trial design based on the estimation of the causal effect using a principal stratification approach. The proposed design simultaneously considers efficacy and toxicity outcomes and utilizes covariates to predict a patient's potential compliance behavior and identify the causal effects. Based on accumulating data, we continuously update the posterior estimates of the causal treatment effects and adaptively make the go/no-go decision for the trial. Numerical results show that the proposed method has desirable operating characteristics and addresses the issue of noncompliance. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Nonadherence to assigned treatment jeopardizes the power and interpretability of intent-to-treat comparisons from clinical trial data and continues to be an issue for effectiveness studies, despite their pragmatic emphasis. We posit that new approaches to design need to complement developments in methods for causal inference to address nonadherence, in both experimental and practice settings. This paper considers the conventional study design for psychiatric research and other medical contexts, in which subjects are randomized to treatments that are fixed throughout the trial and presents an alternative that converts the fixed treatments into an adaptive intervention that reflects best practice. The key element is the introduction of an adaptive decision point midway into the study to address a patient's reluctance to remain on treatment before completing a full-length trial of medication. The clinical uncertainty about the appropriate adaptation prompts a second randomization at the new decision point to evaluate relevant options. Additionally, the standard 'all-or-none' principal stratification (PS) framework is applied to the first stage of the design to address treatment discontinuation that occurs too early for a midtrial adaptation. Drawing upon the adaptive intervention features, we develop assumptions to identify the PS causal estimand and to introduce restrictions on outcome distributions to simplify expectation-maximization calculations. We evaluate the performance of the PS setup, with particular attention to the role played by a binary covariate. The results emphasize the importance of collecting covariate data for use in design and analysis. We consider the generality of our approach beyond the setting of psychiatric research. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Recently, several authors have shown that natural direct and indirect effects (NDEs and NIEs) can be identified under the sequential ignorability assumptions, as long as there is no mediator-outcome confounder that is affected by the treatment. However, if such a confounder exists, NDEs and NIEs will generally not be identified without making additional identifying assumptions. In this article, we propose novel identification assumptions and estimators for evaluating NDEs and NIEs under the usual sequential ignorability assumptions, using the principal stratification framework. It is assumed that the treatment and the mediator are dichotomous. We must impose strong assumptions for identification. However, even if these assumptions were violated, the bias of our estimator would be small under typical conditions, which can be easily evaluated from the observed data. This conjecture is confirmed for binary outcomes by deriving the bounds of the bias terms. In addition, the advantage of our estimator is illustrated through a simulation study. We also propose a method of sensitivity analysis that examines what happens when our assumptions are violated. We apply the proposed method to data from the National Center for Health Statistics. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Previous research has found evidence of an association between indoor air pollution and asthma morbidity in children. Environmental intervention studies have been performed to examine the role of household environmental interventions in altering indoor air pollution concentrations and improving health. Previous environmental intervention studies have found only modest effects on health outcomes and it is unclear if the health benefits provided by environmental modification are comparable with those provided by medication. Traditionally, the statistical analysis of environmental intervention studies has involved performing two intention-to-treat analyses that separately estimate the effect of the environmental intervention on health and the effect of the environmental intervention on indoor air pollution concentrations. We propose a principal stratification approach to examine the extent to which an environmental intervention's effect on health outcomes coincides with its effect on indoor air pollution. We apply this approach to data from a randomized air cleaner intervention trial conducted in a population of asthmatic children living in Baltimore, Maryland, USA. We find that among children for whom the air cleaner reduced indoor particulate matter concentrations, the intervention resulted in a meaningful improvement of asthma symptoms with an effect generally larger than previous studies have shown. A key benefit of using principal stratification in environmental intervention studies is that it allows investigators to estimate causal effects of the intervention for sub-groups defined by changes in the indoor air pollution concentration. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In longitudinal studies, outcomes ascertained at follow-up are typically undefined for individuals who die prior to the follow-up visit. In such settings, outcomes are said to be truncated by death and inference about the effects of a point treatment or exposure, restricted to individuals alive at the follow-up visit, could be biased even if as in experimental studies, treatment assignment were randomized. To account for truncation by death, the survivor average causal effect (SACE) defines the effect of treatment on the outcome for the subset of individuals who would have survived regardless of exposure status. In this paper, the author nonparametrically identifies SACE by leveraging post-exposure longitudinal correlates of survival and outcome that may also mediate the exposure effects on survival and outcome. Nonparametric identification is achieved by supposing that the longitudinal data arise from a certain nonparametric structural equations model and by making the monotonicity assumption that the effect of exposure on survival agrees in its direction across individuals. A novel weighted analysis involving a consistent estimate of the survival process is shown to produce consistent estimates of SACE. A data illustration is given, and the methods are extended to the context of time-varying exposures. We discuss a sensitivity analysis framework that relaxes assumptions about independent errors in the nonparametric structural equations model and may be used to assess the extent to which inference may be altered by a violation of key identifying assumptions. © 2014 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This article discusses joint modeling of compliance and outcome for longitudinal studies when noncompliance is present. We focus on two-arm randomized longitudinal studies in which subjects are randomized at baseline, treatment is applied repeatedly over time, and compliance behaviors and clinical outcomes are measured and recorded repeatedly over time. In the proposed Markov compliance and outcome model, we use the potential outcome framework to define pre-randomization principal strata from the joint distribution of compliance under treatment and control arms, and estimate the effect of treatment within each principal strata. Besides the causal effect of the treatment, our proposed model can estimate the impact of the causal effect of the treatment at a given time on future compliance. Bayesian methods are used to estimate the parameters. The results are illustrated using a study assessing the effect of cognitive behavior therapy on depression. A simulation study is used to assess the repeated sampling properties of the proposed model. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We propose a principal stratification approach to assess causal effects in nonrandomized longitudinal comparative effectiveness studies with a binary endpoint outcome and repeated measures of a continuous intermediate variable. Our method is an extension of the principal stratification approach originally proposed for the longitudinal randomized study 'Prevention of Suicide in Primary Care Elderly: Collaborative Trial' to assess the treatment effect on the continuous Hamilton depression score adjusting for the heterogeneity of repeatedly measured binary compliance status. Our motivation for this work comes from a comparison of the effect of two glucose-lowering medications on a clinical cohort of patients with type 2 diabetes. Here, we consider a causal inference problem assessing how well the two medications work relative to one another on two binary endpoint outcomes: cardiovascular disease-related hospitalization and all-cause mortality. Clinically, these glucose-lowering medications can have differential effects on the intermediate outcome, glucose level over time. Ultimately, we want to compare medication effects on the endpoint outcomes among individuals in the same glucose trajectory stratum while accounting for the heterogeneity in baseline covariates (i.e., to obtain 'principal effects' on the endpoint outcomes). The proposed method involves a three-step model estimation procedure. Step 1 identifies principal strata associated with the intermediate variable using hybrid growth mixture modeling analyses. Step 2 obtains the stratum membership using the pseudoclass technique and derives propensity scores for treatment assignment. Step 3 obtains the stratum-specific treatment effect on the endpoint outcome weighted by inverse propensity probabilities derived from Step 2. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We describe rank-based approaches to assess principal stratification treatment effects in studies where the outcome of interest is only well-defined in a subgroup selected after randomization. Our methods are sensitivity analyses, in that estimands are identified by fixing a parameter and then we investigate the sensitivity of results by varying this parameter over a range of plausible values. We present three rank-based test statistics and compare their performance through simulations, and provide recommendations. We also study three different bootstrap approaches for determining levels of significance. Finally, we apply our methods to two studies: an HIV vaccine trial and a prostate cancer prevention trial. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In longitudinal clinical trials, if a subject drops out due to death, certain responses, such as those measuring quality of life (QoL), will not be defined after the time of death. Thus, standard missing data analyses, e.g., under ignorable dropout, are problematic because these approaches implicitly 'impute' values of the response after death. In this paper we define a new survivor average causal effect for a bivariate response in a longitudinal quality of life study that had a high dropout rate with the dropout often due to death (or tumor progression). We show how principal stratification, with a few sensitivity parameters, can be used to draw causal inferences about the joint distribution of these two ordinal quality of life measures. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Noncompliance to treatment allocation is a key source of complication for causal inference. Efficacy estimation is likely to be compounded by the presence of noncompliance in both treatment arms of clinical trials where the intention-to-treat estimate provides a biased estimator for the true causal estimate even under homogeneous treatment effects assumption. Principal stratification method has been developed to address such posttreatment complications. The present work extends a principal stratification method that adjusts for noncompliance in two-treatment arms trials by developing model selection for covariates predicting compliance to treatment in each arm. We apply the method to analyse data from the Esprit study, which was conducted to ascertain whether unopposed oestrogen (hormone replacement therapy) reduced the risk of further cardiac events in postmenopausal women who survive a first myocardial infarction. We adjust for noncompliance in both treatment arms under a Bayesian framework to produce causal risk ratio estimates for each principal stratum. For mild values of a sensitivity parameter and using separate predictors of compliance in each arm, principal stratification results suggested that compliance with hormone replacement therapy only would reduce the risk for death and myocardial reinfarction by about 47 % and 25 %, respectively, whereas compliance with either treatment would reduce the risk for death by 13 % and reinfarction by 60 % among the most compliant. However, the results were sensitive to the user-defined sensitivity parameter. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In randomized trials to prevent breast milk transmission of human immunodeficiency virus (HIV) from mother to infant, investigators are often interested in assessing the effect of a treatment or intervention on the cumulative risk of HIV infection by time (age) t in infants who are alive and uninfected at a certain time point τ0 < t. Such comparisons are challenging for two reasons. First, infants are typically randomized at birth (time 0 < τ0) such that comparisons between trial arms among the subset of infants alive and uninfected at τ0 are subject to selection bias. Second, in most mother-to-child transmission (MTCT) trials competing risks are often present, such as death or cessation of breastfeeding prior to HIV infection. In this paper, we present methods for assessing the causal effect of a treatment on competing risk outcomes within principal strata. In MTCT trials, the causal effect of interest is that of treatment on the risk of HIV infection by time t > τ0 within the principal stratum of infants who would be alive and uninfected by τ0 regardless of randomization assignment. We develop large sample nonparametric bounds and a semiparametric sensitivity analysis model for drawing inference about this causal effect. We present a simulation study demonstrating that the proposed methods perform well in finite samples. We apply the proposed methods to a large, recent MTCT trial. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Within causal inference, principal stratification (PS) is a popular approach for dealing with intermediate variables, that is, variables affected by treatment that also potentially affect the response. However, when there exists unmeasured confounding in the treatment arms-as can happen in observational studies-causal estimands resulting from PS analyses can be biased. We identify the various pathways of confounding present in PS contexts and their effects for PS inference. We present model-based approaches for assessing the sensitivity of complier average causal effect estimates to unmeasured confounding in the setting of binary treatments, binary intermediate variables, and binary outcomes. These same approaches can be used to assess sensitivity to unknown direct effects of treatments on outcomes because, as we show, direct effects are operationally equivalent to one of the pathways of unmeasured confounding. We illustrate the methodology using a randomized study with artificially introduced confounding and a sensitivity analysis for an observational study of the effects of physical activity and body mass index on cardiovascular disease. Copyright © 2012 John Wiley & Sons, Ltd. [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]