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The study of treatment effects is often complicated by noncompliance and missing data. In the one-sided noncompliance setting where of interest are the complier and noncomplier average causal effects, we address outcome missingness of the latent missing at random type (LMAR, also known as latent ignorability). That is, conditional on covariates and treatment assigned, the missingness may depend on compliance type. Within the instrumental variable (IV) approach to noncompliance, methods have been proposed for handling LMAR outcome that additionally invoke an exclusion restriction-type assumption on missingness, but no solution has been proposed for when a non-IV approach is used. This article focuses on effect identification in the presence of LMAR outcomes, with a view to flexibly accommodate different principal identification approaches. We show that under treatment assignment ignorability and LMAR only, effect nonidentifiability boils down to a set of two connected mixture equations involving unidentified stratum-specific response probabilities and outcome means. This clarifies that (except for a special case) effect identification generally requires two additional assumptions: a specific missingness mechanism assumption and a principal identification assumption. This provides a template for identifying effects based on separate choices of these assumptions. We consider a range of specific missingness assumptions, including those that have appeared in the literature and some new ones. Incidentally, we find an issue in the existing assumptions, and propose a modification of the assumptions to avoid the issue. Results under different assumptions are illustrated using data from the Baltimore Experience Corps Trial. [ABSTRACT FROM AUTHOR]

When studying the treatment effect on time-to-event outcomes, it is common that some individuals never experience failure events, which suggests that they have been cured. However, the cure status may not be observed due to censoring which makes it challenging to define treatment effects. Current methods mainly focus on estimating model parameters in various cure models, ultimately leading to a lack of causal interpretations. To address this issue, we propose 2 causal estimands, the timewise risk difference and mean survival time difference, in the always-uncured based on principal stratification as a complement to the treatment effect on cure rates. These estimands allow us to study the treatment effects on failure times in the always-uncured subpopulation. We show the identifiability using a substitutional variable for the potential cure status under ignorable treatment assignment mechanism, these 2 estimands are identifiable. We also provide estimation methods using mixture cure models. We applied our approach to an observational study that compared the leukemia-free survival rates of different transplantation types to cure acute lymphoblastic leukemia. Our proposed approach yielded insightful results that can be used to inform future treatment decisions. [ABSTRACT FROM AUTHOR]

Post-randomization events, also known as intercurrent events, such as treatment noncompliance and censoring due to a terminal event, are common in clinical trials. Principal stratification is a framework for causal inference in the presence of intercurrent events. The existing literature on principal stratification lacks generally applicable and accessible methods for time-to-event outcomes. In this paper, we focus on the noncompliance setting. We specify 2 causal estimands for time-to-event outcomes in principal stratification and provide a nonparametric identification formula. For estimation, we adopt the latent mixture modeling approach and illustrate the general strategy with a mixture of Bayesian parametric Weibull-Cox proportional hazards model for the outcome. We utilize the Stan programming language to obtain automatic posterior sampling of the model parameters. We provide analytical forms of the causal estimands as functions of the model parameters and an alternative numerical method when analytical forms are not available. We apply the proposed method to the ADAPTABLE (A spirin D osing: A P atient-Centric T rial A ssessing B enefits and L ong-Term E ffectiveness) trial to evaluate the causal effect of taking 81 versus 325 mg aspirin on the risk of major adverse cardiovascular events. We develop the corresponding R package PStrata. [ABSTRACT FROM AUTHOR]

Point processes are probabilistic tools for modelling event data. While there exists a fast-growing literature on the relationships between point processes, how such relationships connect to causal effects remains unexplored. In the presence of unmeasured confounders, parameters from point process models do not necessarily have causal interpretations. We propose an instrumental variable method for causal inference with point process treatment and outcome. We define causal quantities based on potential outcomes and establish nonparametric identification results with a binary instrumental variable. We extend the traditional Wald estimation to deal with point process treatment and outcome, showing that it should be performed after a Fourier transform of the intention-to-treat effects on the treatment and outcome, and thus takes the form of deconvolution. We refer to this approach as generalized Wald estimation and propose an estimation strategy based on well-established deconvolution methods. [ABSTRACT FROM AUTHOR]

Even in a carefully designed randomised trial, outcomes for some study participants can be missing, or more precisely, ill defined, because participants had died prior to outcome collection. This problem, known as truncation by death, means that the treated and untreated are no longer balanced with respect to covariates determining survival. Therefore, researchers often utilise principal stratification and focus on the Survivor Average Causal Effect (SACE). We present matching-based methods for SACE identification and estimation. We provide identification results motivating the use of matching and discuss practical issues, including the choice of distance measures, matching with replacement, and post-matching estimators. Because the assumptions needed for SACE identification can be too strong, we also present sensitivity analysis techniques and illustrate their use in real data analysis. [ABSTRACT FROM AUTHOR]

Valid surrogate endpoints S can be used as a substitute for a true outcome of interest T to measure treatment efficacy in a clinical trial. We propose a causal inference approach to validate a surrogate by incorporating longitudinal measurements of the true outcomes using a mixed modeling approach, and we define models and quantities for validation that may vary across the study period using principal surrogacy criteria. We consider a surrogate‐dependent treatment efficacy curve that allows us to validate the surrogate at different time points. We extend these methods to accommodate a delayed‐start treatment design where all patients eventually receive the treatment. Not all parameters are identified in the general setting. We apply a Bayesian approach for estimation and inference, utilizing more informative prior distributions for selected parameters. We consider the sensitivity of these prior assumptions as well as assumptions of independence among certain counterfactual quantities conditional on pretreatment covariates to improve identifiability. We examine the frequentist properties (bias of point and variance estimates, credible interval coverage) of a Bayesian imputation method. Our work is motivated by a clinical trial of a gene therapy where the functional outcomes are measured repeatedly throughout the trial. [ABSTRACT FROM AUTHOR]

In heterogeneous treatment effect models with endogeneity, identification of the local average treatment effect (LATE) typically relies on the availability of an exogenous instrument monotonically related to treatment participation. First, we demonstrate that a strictly weaker local monotonicity condition—invoked for specific potential outcome values rather than globally—identifies the LATEs on compliers and defiers. Second, we show that our identification results apply to subsets of compliers and defiers when imposing an even weaker local compliers-defiers assumption that allows for both types at any potential outcome value. We propose estimators that are potentially more efficient than two-stage least squares (2SLS) in finite samples, even in cases where 2SLS is consistent. Finally, we provide an empirical application to estimating returns to education using the quarter of birth instrument. [ABSTRACT FROM AUTHOR]

Many studies encounter clustering due to multicenter enrollment and nonmortality outcomes, such as quality of life, that are truncated due to death—that is, missing not at random and nonignorable. Traditional missing-data methods and target causal estimands are suboptimal for statistical inference in the presence of these combined issues, which are especially common in multicenter studies and cluster-randomized trials (CRTs) carried out among the elderly or seriously ill. Using principal stratification, we developed a Bayesian estimator that jointly identifies the always-survivor principal stratum in a clustered/hierarchical data setting and estimates the average treatment effect among them (i.e. the survivor average causal effect (SACE)). In simulations, we observed low bias and good coverage with our method. In a motivating CRT, the SACE and the estimate from complete-case analysis differed in magnitude, but both were small, and neither was incompatible with a null effect. However, the SACE estimate has a clear causal interpretation. The option to assess the rigorously defined SACE estimand in studies with informative truncation and clustering can provide additional insight into an important subset of study participants. Based on the simulation study and CRT reanalysis, we provide practical recommendations for using the SACE in CRTs and software code to support future research. [ABSTRACT FROM AUTHOR]

Despite an increasing reliance on fully-automated algorithmic decision-making in our day-to-day lives, humans still make consequential decisions. While the existing literature focuses on the bias and fairness of algorithmic recommendations, an overlooked question is whether they improve human decisions. We develop a general statistical methodology for experimentally evaluating the causal impacts of algorithmic recommendations on human decisions. We also examine whether algorithmic recommendations improve the fairness of human decisions and derive the optimal decision rules under various settings. We apply the proposed methodology to the first-ever randomized controlled trial that evaluates the pretrial Public Safety Assessment in the United States criminal justice system. Our analysis of the preliminary data shows that providing the PSA to the judge has little overall impact on the judge's decisions and subsequent arrestee behaviour. [ABSTRACT FROM AUTHOR]

Chronic diseases often require continuing care, and early response to treatment can be an important predictor of long‐term efficacy. Often, an apparent lack of early efficacy may lead to discontinuation of treatment, with the decision made either by clinicians or by the patients themselves. Thus, it is important to determine whether or not a desired early outcome corresponds to a beneficial long‐term effect of continuing treatment, and conversely, whether or not the absence of such an outcome corresponds to a lack of long‐term benefit. However, primary clinical trials of such treatments are not commonly designed to answer such questions, for example by randomizing subjects to continue or discontinue treatment after observing early outcomes. We propose an approach to estimating the effect of continuing treatment after observing early outcomes using data from randomized controlled trials in which treatment discontinuation was not part of the design. Our approach estimates average causal effects of continuing treatment on long‐term outcomes in principal strata defined by the potential early outcomes under treatment. For illustration, we estimate the effects of continuing to take gaboxadol to treat insomnia conditional on early improvement in subjective sleep quality after two nights, based on a standard parallel‐arm randomized controlled trial. [ABSTRACT FROM AUTHOR]

The causal effects of Apolipoprotein E $\epsilon4$ allele (APOE) on late-onset Alzheimer's disease (AD) and death are complicated to define because AD may occur under one intervention but not under the other, and because AD occurrence may affect age of death. In this article, this dual outcome scenario is studied using the semi-competing risks framework for time-to-event data. Two event times are of interest: a nonterminal event time (age at AD diagnosis), and a terminal event time (age at death). AD diagnosis time is observed only if it precedes death, which may occur before or after AD. We propose new estimands for capturing the causal effect of APOE on AD and death. Our proposal is based on a stratification of the population with respect to the order of the two events. We present a novel assumption utilizing the time-to-event nature of the data, which is more flexible than the often-invoked monotonicity assumption. We derive results on partial identifiability, suggest a sensitivity analysis approach, and give conditions under which full identification is possible. Finally, we present and implement nonparametric and semiparametric estimation methods under right-censored semi-competing risks data for studying the complex effect of APOE on AD and death. [ABSTRACT FROM AUTHOR]

Causal inference concerns not only the average effect of the treatment on the outcome but also the underlying mechanism through an intermediate variable of interest. Principal stratification characterizes such a mechanism by targeting subgroup causal effects within principal strata, which are defined by the joint potential values of an intermediate variable. Due to the fundamental problem of causal inference, principal strata are inherently latent, rendering it challenging to identify and estimate subgroup effects within them. A line of research leverages the principal ignorability assumption that the latent principal strata are mean independent of the potential outcomes conditioning on the observed covariates. Under principal ignorability, we derive various nonparametric identification formulas for causal effects within principal strata in observational studies, which motivate estimators relying on the correct specifications of different parts of the observed‐data distribution. Appropriately combining these estimators yields triply robust estimators for the causal effects within principal strata. These triply robust estimators are consistent if two of the treatment, intermediate variable and outcome models are correctly specified, and moreover, they are locally efficient if all three models are correctly specified. We show that these estimators arise naturally from either the efficient influence functions in the semiparametric theory or the model‐assisted estimators in the survey sampling theory. We evaluate different estimators based on their finite‐sample performance through simulation and apply them to two observational studies. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We develop a Bayesian nonparametric (BNP) approach to evaluate the causal effect of treatment in a randomized trial where a nonterminal event may be censored by a terminal event, but not vice versa (i.e., semi-competing risks). Based on the idea of principal stratification, we define a novel estimand for the causal effect of treatment on the nonterminal event. We introduce identification assumptions, indexed by a sensitivity parameter, and show how to draw inference using our BNP approach. We conduct simulation studies and illustrate our methodology using data from a brain cancer trial. The R code implementing our model and algorithm is available for download at https://github.com/YanxunXu/BaySemiCompeting. [ABSTRACT FROM AUTHOR]

Summary: In Italian state universities candidate freshmen must take an entrance examination. Candidates who obtain a test score less than or equal to a pre‐fixed threshold may enrol at the university but must comply with an additional compulsory educational obligation, called obblighi formativi aggiuntivi (OFA). The OFA assignment rule appeals to a (sharp) regression discontinuity design with the entrance examination score acting as the forcing variable. We assess causal effects of OFA status by using data from a school of engineering of a specific Italian state university. For subpopulations of units for which our regression discontinuity design can be described as a local randomized experiment, we draw inference on the causal effects of OFA on students' academic performances measured by using two variables: the number of university credits awarded at the end of the first academic year and the corresponding average grade. These outcome variables suffer from the problem of truncation by 'death', because neither is defined for students who decide not to enrol. Moreover, nor is the average grade defined for students who enrol but do not either take or pass any examination in the first academic year. We deal with these issues by using the framework of principal stratification and adopting a Bayesian approach to inference. We find some evidence that the receipt of OFA may negatively affect students' academic performances, although the posterior distributions of the causal estimands have high variability. [ABSTRACT FROM AUTHOR]

Summary: The paper evaluates the effects of being an only child in a family on psychological health, leveraging data on the one‐child policy in China. We use an instrumental variable approach to address the potential unmeasured confounding between the fertility decision and psychological health, where the instrumental variable is an index of the intensity of the implementation of the policy. We establish an analytical link between the local instrumental variable approach and principal stratification to accommodate the continuous instrumental variable. Within the principal stratification framework, we postulate a Bayesian hierarchical model to infer various causal estimands of policy interest while adjusting for the clustering data structure. We apply the method to the data from the China Family Panel Studies and find small but statistically significant negative effects of being an only child on self‐reported psychological health for some subpopulations. Our analysis reveals treatment effect heterogeneity with respect to both observed and unobserved characteristics. In particular, urban males suffer the most from being only children, and the negative effect has larger magnitude if the families were more resistant to the one‐child policy. We also conduct a sensitivity analysis to assess the key instrumental variable assumption. [ABSTRACT FROM AUTHOR]

An objective in randomized clinical trials is the evaluation of "principal surrogates," which consists of analyzing how the treatment effect on a clinical endpoint varies over principal strata subgroups defined by an intermediate response outcome under both or one of the treatment assignments. The latter effect modification estimand has been termed the marginal causal effect predictiveness (mCEP) curve. This objective was addressed in two randomized placebo-controlled Phase 3 dengue vaccine trials for an antibody response biomarker whose sampling design rendered previously developed inferential methods highly inefficient due to a three-phase sampling design. In this design, the biomarker was measured in a case-cohort sample and a key baseline auxiliary strongly associated with the biomarker (the "baseline surrogate measure") was only measured in a further sub-sample. We propose a novel approach to estimation of the mCEP curve in such three-phase sampling designs that avoids the restrictive "placebo structural risk" modeling assumption common to past methods and that further improves robustness by the use of non-parametric kernel smoothing for biomarker density estimation. Additionally, we develop bootstrap-based procedures for pointwise and simultaneous confidence intervals and testing of four relevant hypotheses about the mCEP curve. We investigate the finite-sample properties of the proposed methods and compare them to those of an alternative method making the placebo structural risk assumption. Finally, we apply the novel and alternative procedures to the two dengue vaccine trial data sets. [ABSTRACT FROM AUTHOR]

Summary: In some randomized clinical trials, patients may die before the measurement time point of their outcomes. Even though randomization generates comparable treatment and control groups, the remaining survivors often differ significantly in background variables that are prognostic to the outcomes. This is called the truncation by death problem. Under the potential outcomes framework, the only well‐defined causal effect on the outcome is within the subgroup of patients who would always survive under both treatment and control. Because the definition of the subgroup depends on the potential values of the survival status that could not be observed jointly, without making strong parametric assumptions, we cannot identify the causal effect of interest and consequently can only obtain bounds of it. Unfortunately, however, many bounds are too wide to be useful. We propose to use detailed survival information before and after the measurement time point of the outcomes to sharpen the bounds of the subgroup causal effect. Because survival times contain useful information about the final outcome, carefully utilizing them could improve statistical inference without imposing strong parametric assumptions. Moreover, we propose to use a copula model to relax the commonly‐invoked but often doubtful monotonicity assumption that the treatment extends the survival time for all patients. [ABSTRACT FROM AUTHOR]

In causal mediation analysis, the definitions of the natural direct and indirect effects involve potential outcomes that can never be observed, so-called a priori counterfactuals. This conceptual challenge translates into issues in identification, which requires strong and often unverifiable assumptions, including sequential ignorability. Alternatively, we can deal with post-treatment variables using the principal stratification framework, where causal effects are defined as comparisons of observable potential outcomes. We establish a novel bridge between mediation analysis and principal stratification, which helps to clarify and weaken the commonly used identifying assumptions for natural direct and indirect effects. Using principal stratification, we show how sequential ignorability extrapolates from observable potential outcomes to a priori counterfactuals, and propose alternative weaker principal ignorability-type assumptions. We illustrate the key concepts using a clinical trial. [ABSTRACT FROM AUTHOR]

We conduct principal stratification and mediation analysis to investigate to what extent the positive overall effect of treatment on postoperative pain control is mediated by postoperative self administration of intra-venous analgesia by patients in a prospective, randomized, double-blind study. Using the Bayesian approach for inference, we estimate both associative and dissociative principal strata effects arising in principal stratification, as well as natural effects from mediation analysis. We highlight that principal stratification and mediation analysis focus on different causal estimands, answer different causal questions, and involve different sets of structural assumptions. [ABSTRACT FROM AUTHOR]

It is common in medical studies that the outcome of interest is truncated by death, meaning that a subject has died before the outcome could be measured. In this case, restricted analysis among survivors may be subject to selection bias. Hence, it is of interest to estimate the survivor average causal effect, defined as the average causal effect among the subgroup consisting of subjects who would survive under either exposure. In this paper, we consider the identification and estimation problems of the survivor average causal effect. We propose to use a substitution variable in place of the latent membership in the always-survivor group. The identification conditions required for a substitution variable are conceptually similar to conditions for a conditional instrumental variable, and may apply to both randomized and observational studies. We show that the survivor average causal effect is identifiable with use of such a substitution variable, and propose novel model parameterizations for estimation of the survivor average causal effect under our identification assumptions. Our approaches are illustrated via simulation studies and a data analysis. [ABSTRACT FROM AUTHOR]

It is common that, in multiarm randomized trials, the outcome of interest is 'truncated by death', meaning that it is only observed or well-defined conditioning on an intermediate outcome. In this case, in addition to pairwise contrasts, the joint inference for all treatment arms is also of interest. Under a monotonicity assumption we present methods for both pairwise and joint causal analyses of ordinal treatments and binary outcomes in the presence of truncation by death. We illustrate via examples the appropriateness of our assumptions in different scientific contexts. [ABSTRACT FROM AUTHOR]

Recent intervention studies targeted at reducing indoor air pollution have demonstrated both the ability to improve respiratory health outcomes and to reduce particulate matter (PM) levels in the home. However, these studies generally do not address whether it is the reduction in PM levels specifically that improves respiratory health. We apply the method of principal stratification to data from a randomized air cleaner intervention designed to reduce indoor PM in homes of children with asthma. We estimate the health benefit of the intervention among study subjects who would experience a substantial reduction in PM in response to the intervention. For those subjects we find an increase in symptom-free days that is almost three times as large as the overall intention-to-treat effect. We also explore the presence of treatment effects among those subjects whose PM levels would not respond to the air cleaner. This analysis demonstrates the usefulness of principal stratification for environmental intervention trials and its potential for much broader application in this area. [ABSTRACT FROM AUTHOR]

Background. The phase III Zostavax Efficacy and Safety Trial of 1 dose of licensed zoster vaccine (ZV; Zostavax; Merck) in 50–59-year-olds showed approximately 70% vaccine efficacy (VE) to reduce the incidence of herpes zoster (HZ). An objective of the trial was to assess immune response biomarkers measuring antibodies to varicella zoster virus (VZV) by glycoprotein-based enzyme-linked immunosorbent assay as correlates of protection (CoPs) against HZ.Methods. The principal stratification vaccine efficacy curve framework for statistically evaluating immune response biomarkers as CoPs was applied. The VE curve describes how VE against the clinical end point (HZ) varies across participant subgroups defined by biomarker readout measuring vaccine-induced immune response. The VE curve was estimated using several subgroup definitions.Results. The fold rise in VZV antibody titers from the time before immunization to 6 weeks after immunization was an excellent CoP, with VE increasing sharply with fold rise: VE was estimated at 0% for the subgroup with no rise and at 90% for the subgroup with 5.26-fold rise. In contrast, VZV antibody titers measured 6 weeks after immunization did not predict VE, with similar estimated VEs across titer subgroups.Conclusions. The analysis illustrates the value of the VE curve framework for assessing immune response biomarkers as CoPs in vaccine efficacy trials.Clinical Trials Registration. NCT00534248. [ABSTRACT FROM AUTHOR]

We consider a new approach to identify the causal effects of a binary treatment when the outcome is missing on a subset of units and dependence of nonresponse on the outcome cannot be ruled out even after conditioning on observed covariates. We provide sufficient conditions under which the availability of a binary instrument for nonresponse allows us to derive tighter identification intervals for causal effects in the whole population and to partially identify causal effects in some latent subgroups of units, named Principal Strata, defined by the nonresponse behavior in all possible combinations of treatment and instrument. A simulation study is used to assess the benefits of the presence versus the absence of an instrument for nonresponse. The simulation design is based on real health data, coming from a randomized trial on breast self-examination (BSE) affected by a large proportion of missing outcome data. An instrument for nonresponse is simulated considering alternative scenarios to discuss the key role of the instrument for nonresponse in identifying average causal effects in presence of nonignorable missing outcomes. We also investigate the potential inferential gains from using an instrument for nonresponse adopting a Bayesian approach for inference. In virtue of our theoretical and empirical results, we provide some recommendations on study designs for causal inference. [ABSTRACT FROM AUTHOR]

In clinical trials, a surrogate outcome variable (S) can be measured before the outcome of interest (T) and may provide early information regarding the treatment (Z) effect on T. Using the principal surrogacy framework introduced by Frangakis and Rubin (2002. Principal stratification in causal inference. Biometrics 58, 21–29), we consider an approach that has a causal interpretation and develop a Bayesian estimation strategy for surrogate validation when the joint distribution of potential surrogate and outcome measures is multivariate normal. From the joint conditional distribution of the potential outcomes of T, given the potential outcomes of S, we propose surrogacy validation measures from this model. As the model is not fully identifiable from the data, we propose some reasonable prior distributions and assumptions that can be placed on weakly identified parameters to aid in estimation. We explore the relationship between our surrogacy measures and the surrogacy measures proposed by Prentice (1989. Surrogate endpoints in clinical trials: definition and operational criteria. Statistics in Medicine 8, 431–440). The method is applied to data from a macular degeneration study and an ovarian cancer study. [ABSTRACT FROM AUTHOR]

Principal surrogate (PS) endpoints are relatively inexpensive and easy to measure study outcomes that can be used to reliably predict treatment effects on clinical endpoints of interest. Few statistical methods for assessing the validity of potential PSs utilize time-to-event clinical endpoint information and to our knowledge none allow for the characterization of time-varying treatment effects. We introduce the time-dependent and surrogate-dependent treatment efficacy curve, ${\mathrm {TE}}(t|s)$, and a new augmented trial design for assessing the quality of a biomarker as a PS. We propose a novel Weibull model and an estimated maximum likelihood method for estimation of the ${\mathrm {TE}}(t|s)$ curve. We describe the operating characteristics of our methods via simulations. We analyze data from the Diabetes Control and Complications Trial, in which we find evidence of a biomarker with value as a PS. [ABSTRACT FROM AUTHOR]

. The definitive evaluation of treatment to prevent a chronic disease with low incidence in middle age, such as cancer or cardiovascular disease, requires a trial with a large sample size of perhaps 20000 or more. To help to decide whether to implement a large true end point trial, investigators first typically estimate the effect of treatment on a surrogate end point in a trial with a greatly reduced sample size of perhaps 200 subjects. If investigators reject the null hypothesis of no treatment effect in the surrogate end point trial they implicitly assume that they would probably correctly reject the null hypothesis of no treatment effect for the true end point. Surrogate end point trials are generally designed with adequate power to detect an effect of treatment on the surrogate end point. However, we show that a small surrogate end point trial is more likely than a large surrogate end point trial to give a misleading conclusion about the beneficial effect of treatment on the true end point, which can lead to a faulty (and costly) decision about implementing a large true end point prevention trial. If a small surrogate end point trial rejects the null hypothesis of no treatment effect, an intermediate-sized surrogate end point trial could be a useful next step in the decision-making process for launching a large true end point prevention trial. [ABSTRACT FROM AUTHOR]

Assays for detecting levels of antiretroviral drugs in study participants are increasingly popular in preexposure prophylaxis (PrEP) trials, since they provide an objective measure of adherence. Current correlation analyses of drug concentration data are prone to bias. In this article, we formulate the causal estimand of prevention efficacy among drug compliers, those who would have had a threshold level of drug concentration had they been assigned to the drug arm of the trial. The identifiability of the causal estimand is facilitated by exploiting the exclusion restriction; that is, drug noncompliers do not acquire any prevention benefit. In addition, we develop an approach to sensitivity analysis that relaxes the exclusion restriction. Applications to published data from 2 PrEP trials, namely the Preexposure Prophylaxis Initiative (iPrEx) trial and the Centre for the AIDS Programme of Research in South Africa (CAPRISA) 004 trial, suggest high efficacy estimates among drug compliers (in the iPrEx trial, odds ratio = 0.097 (95% confidence interval: 0.027, 0.352); in the CAPRISA 004 trial, odds ratio = 0.104 (95% confidence interval: 0.024, 0.447)). In summary, the proposed inferential method provides an unbiased assessment of PrEP efficacy among drug compliers, thus adding to the primary intention-to-treat analysis and correlation analyses of drug concentration data. [ABSTRACT FROM AUTHOR]

The literature on potential outcomes has shown that traditional methods for characterizing surrogate endpoints in clinical trials based only on observed quantities can fail to capture causal relationships between treatments, surrogates, and outcomes. Building on the potential-outcomes formulation of a principal surrogate, we introduce a Bayesian method to estimate the causal effect predictiveness (CEP) surface and quantify a candidate surrogate's utility for reliably predicting clinical outcomes. In considering the full joint distribution of all potentially observable quantities, our Bayesian approach has the following features. First, our approach illuminates implicit assumptions embedded in previously-used estimation strategies that have been shown to result in poor performance. Second, our approach provides tools for making explicit and scientifically-interpretable assumptions regarding associations about which observed data are not informative. Through simulations based on an HIV vaccine trial, we found that the Bayesian approach can produce estimates of the CEP surface with improved performance compared to previous methods. Third, our approach can extend principal-surrogate estimation beyond the previously considered setting of a vaccine trial where the candidate surrogate is constant in one arm of the study. We illustrate this extension through an application to an AIDS therapy trial where the candidate surrogate varies in both treatment arms. [ABSTRACT FROM AUTHOR]

Methods for causal inference regarding health effects of air quality regulations are met with unique challenges because (1) changes in air quality are intermediates on the causal pathway between regulation and health, (2) regulations typically affect multiple pollutants on the causal pathway towards health, and (3) regulating a given location can affect pollution at other locations, that is, there is interference between observations. We propose a principal stratification method designed to examine causal effects of a regulation on health that are and are not associated with causal effects of the regulation on air quality. A novel feature of our approach is the accommodation of a continuously scaled multivariate intermediate response vector representing multiple pollutants. Furthermore, we use a spatial hierarchical model for potential pollution concentrations and ultimately use estimates from this model to assess validity of assumptions regarding interference. We apply our method to estimate causal effects of the 1990 Clean Air Act Amendments among approximately 7 million Medicare enrollees living within 6 miles of a pollution monitor. [ABSTRACT FROM PUBLISHER]

When the true end points (T) are difficult or costly to measure, surrogate markers (S) are often collected in clinical trials to help predict the effect of the treatment (Z). There is great interest in understanding the relationship among S, T, and Z. A principal stratification (PS) framework has been proposed by Frangakis and Rubin (2002) to study their causal associations. In this paper, we extend the framework to a multiple trial setting and propose a Bayesian hierarchical PS model to assess surrogacy. We apply the method to data from a large collection of colon cancer trials in which S and T are binary. We obtain the trial-specific causal measures among S, T, and Z, as well as their overall population-level counterparts that are invariant across trials. The method allows for information sharing across trials and reduces the nonidentifiability problem. We examine the frequentist properties of our model estimates and the impact of the monotonicity assumption using simulations. We also illustrate the challenges in evaluating surrogacy in the counterfactual framework that result from nonidentifiability. [ABSTRACT FROM PUBLISHER]

Encouragement design studies are particularly useful for estimating the effect of an intervention that cannot itself be randomly administered to some and not to others. They require a randomly selected group receive extra encouragement to undertake the treatment of interest, where the encouragement typically takes the form of additional information or incentives. We consider a “clustered encouragement design” (CED), where the randomization is at the level of the clusters (e.g. physicians), but the compliance with assignment is at the level of the units (e.g. patients) within clusters. Noncompliance and missing data are particular problems in encouragement design studies, where encouragement to take the treatment, rather than the treatment itself, is randomized. The motivating study looks at whether computer-based care suggestions can improve patient outcomes in veterans with chronic heart failure. Since physician adherence has been inadequate, the original study focused on methods to improve physician adherence, although an equally important question is whether physician adherence improves patient outcomes. Here, we reanalyze the data to determine the effect of physician adherence on patient outcomes. We propose causal inference methodology for the effect of a treatment versus a control in a randomized CED study with all-or-none compliance at the unit level. These methods extend the current approaches to account for nonignorable missing data and use an alternative approach to inference using multiple imputation methods, which have been successfully applied to a wide variety of missing data problems and have recently been applied to the potential outcomes framework of causal inference (Taylor and Zhou, 2009b). [ABSTRACT FROM AUTHOR]

Recently, , Biometrics 96-103) proposed a model for the causal effect of receiving treatment when there is all-or-none compliance in one randomization group, with maximum likelihood estimation based on convex programming. We discuss an alternative approach that involves a model for all-or-none compliance in two randomization groups and estimation via a perfect fit or an expectation-maximization algorithm for count data. We believe this approach is easier to implement, which would facilitate the reproduction of calculations. [ABSTRACT FROM AUTHOR]

Given a randomized treatment Z, a clinical outcome Y, and a biomarker S measured some fixed time after Z is administered, we may be interested in addressing the surrogate endpoint problem by evaluating whether S can be used to reliably predict the effect of Z on Y. Several recent proposals for the statistical evaluation of surrogate value have been based on the framework of principal stratification. In this article, we consider two principal stratification estimands: joint risks and marginal risks. Joint risks measure causal associations (CAs) of treatment effects on S and Y, providing insight into the surrogate value of the biomarker, but are not statistically identifiable from vaccine trial data. Although marginal risks do not measure CAs of treatment effects, they nevertheless provide guidance for future research, and we describe a data collection scheme and assumptions under which the marginal risks are statistically identifiable. We show how different sets of assumptions affect the identifiability of these estimands; in particular, we depart from previous work by considering the consequences of relaxing the assumption of no individual treatment effects on Y before S is measured. Based on algebraic relationships between joint and marginal risks, we propose a sensitivity analysis approach for assessment of surrogate value, and show that in many cases the surrogate value of a biomarker may be hard to establish, even when the sample size is large. [ABSTRACT FROM AUTHOR]

Structural mean models (SMMs) were originally formulated to estimate causal effects among those selecting treatment in randomized controlled trials affected by nonignorable noncompliance. It has already been established that SMMs can identify these causal effects in randomized placebo-controlled trials under fairly weak assumptions. SMMs are now being used to analyze other types of study where identification depends on a no effect modification assumption. We highlight how this assumption depends crucially on the unknown causal model that generated the data, and so is difficult to justify. However, we also highlight that, if treatment selection is monotonic, additive and multiplicative SMMs do identify local (or complier) causal effects, but that the double-logistic SMM estimator does not without further assumptions. We clarify the proper interpretation of inferences from SMMs by means of an application and a simulation study. [ABSTRACT FROM PUBLISHER]

Data analysis for randomized trials including multitreatment arms is often complicated by subjects who do not comply with their treatment assignment. We discuss here methods of estimating treatment efficacy for randomized trials involving multitreatment arms subject to non-compliance. One treatment effect of interest in the presence of non-compliance is the complier average causal effect, which is defined as the treatment effect for subjects who would comply regardless of the treatment assigned. Following the idea of principal stratification, we define principal compliance in trials with three treatment arms, extend the complier average causal effect and define causal estimands of interest in this setting. In addition, we discuss structural assumptions that are needed for estimation of causal effects and the identifiability problem that is inherent in this setting from both a Bayesian and a classical statistical perspective. We propose a likelihood-based framework that models potential outcomes in this setting and a Bayes procedure for statistical inference. We compare our method with a method-of-moments approach that was proposed by Cheng and Small in 2006 by using a hypothetical data set, and we further illustrate our approach with an application to a behavioural intervention study. [ABSTRACT FROM AUTHOR]

In the past decade, several principal stratification–based statistical methods have been developed for testing and estimation of a treatment effect on an outcome measured after a postrandomization event. Two examples are the evaluation of the effect of a cancer treatment on quality of life in subjects who remain alive and the evaluation of the effect of an HIV vaccine on viral load in subjects who acquire HIV infection. However, in general the developed methods have not addressed the issue of missing outcome data, and hence their validity relies on a missing completely at random (MCAR) assumption. Because in many applications the MCAR assumption is untenable, while a missing at random (MAR) assumption is defensible, we extend the semiparametric likelihood sensitivity analysis approach of Gilbert and others (2003) and Jemiai and Rotnitzky (2005) to allow the outcome to be MAR. We combine these methods with the robust likelihood–based method of Little and An (2004) for handling MAR data to provide semiparametric estimation of the average causal effect of treatment on the outcome. The new method, which does not require a monotonicity assumption, is evaluated in a simulation study and is applied to data from the first HIV vaccine efficacy trial. [ABSTRACT FROM PUBLISHER]

This article proposes new tests to compare the vaccine and placebo groups in randomized vaccine trials when a small fraction of volunteers become infected. A simple approach that is consistent with the intent-to-treat principle is to assign a score, say W, equal to 0 for the uninfecteds and some postinfection outcome for the infecteds. One can then test the equality of this skewed distribution of W between the two groups. This burden of illness (BOI) test was introduced by Chang, Guess, and Heyse (1994, Statistics in Medicine 13, 1807–1814). If infections are rare, the massive number of 0s in each group tends to dilute the vaccine effect and this test can have poor power, particularly if the X's are not close to zero. Comparing X in just the infecteds is no longer a comparison of randomized groups and can produce misleading conclusions. Gilbert, Bosch, and Hudgens (2003, Biometrics 59, 531–541) and Hudgens, Hoering, and Self (2003, Statistics in Medicine 22, 2281–2298) introduced tests of the equality of X in a subgroup—the principal stratum of those “doomed” to be infected under either randomization assignment. This can be more powerful than the BOI approach, but requires unexaminable assumptions. We suggest new “chop-lump” Wilcoxon and t-tests (CLW and CLT) that can be more powerful than the BOI tests in certain situations. When the number of volunteers in each group are equal, the chop-lump tests remove an equal number of zeros from both groups and then perform a test on the remaining W's, which are mostly >0. A permutation approach provides a null distribution. We show that under local alternatives, the CLW test is always more powerful than the usual Wilcoxon test provided the true vaccine and placebo infection rates are the same. We also identify the crucial role of the “gap” between 0 and the X's on power for the t-tests. The chop-lump tests are compared to established tests via simulation for planned HIV and malaria vaccine trials. A reanalysis of the first phase III HIV vaccine trial is used to illustrate the method. [ABSTRACT FROM AUTHOR]

We consider the analysis of clinical trials that involve randomization to an active treatment ( T = 1) or a control treatment ( T = 0), when the active treatment is subject to all-or-nothing compliance. We compare three approaches to estimating treatment efficacy in this situation: as-treated analysis, per-protocol analysis, and instrumental variable (IV) estimation, where the treatment effect is estimated using the randomization indicator as an IV. Both model- and method-of-moment based IV estimators are considered. The assumptions underlying these estimators are assessed, standard errors and mean squared errors of the estimates are compared, and design implications of the three methods are examined. Extensions of the methods to include observed covariates are then discussed, emphasizing the role of compliance propensity methods and the contrasting role of covariates in these extensions. Methods are illustrated on data from the Women Take Pride study, an assessment of behavioral treatments for women with heart disease. [ABSTRACT FROM AUTHOR]

In many studies, the aim is to learn about the direct exposure effect, that is, the effect not mediated through an intermediate variable. For example, in circulation disease studies it may be of interest to assess whether a suitable level of physical activity can prevent disease, even if it fails to prevent obesity. It is well known that stratification on the intermediate may introduce a so-called posttreatment selection bias. To handle this problem, we use the framework of principal stratification ( Frangakis and Rubin, 2002 , Biometrics 58, 21–29) to define a causally relevant estimand—the principal stratum direct effect (PSDE). The PSDE is not identified in our setting. We propose a method of sensitivity analysis that yields a range of plausible values for the causal estimand. We compare our work to similar methods proposed in the literature for handling the related problem of “truncation by death.” [ABSTRACT FROM AUTHOR]

We consider a Markov structure for partially unobserved time-varying compliance classes in the Imbens–Rubin (1997, The Annals of Statistics 25, 305–327) compliance model framework. The context is a longitudinal randomized intervention study where subjects are randomized once at baseline, outcomes and patient adherence are measured at multiple follow-ups, and patient adherence to their randomized treatment could vary over time. We propose a nested latent compliance class model where we use time-invariant subject-specific compliance principal strata to summarize longitudinal trends of subject-specific time-varying compliance patterns. The principal strata are formed using Markov models that relate current compliance behavior to compliance history. Treatment effects are estimated as intent-to-treat effects within the compliance principal strata. [ABSTRACT FROM AUTHOR]

Randomized clinical trials are a powerful tool for investigating causal treatment effects, but in human trials there are oftentimes problems of noncompliance which standard analyses, such as the intention-to-treat or as-treated analysis, either ignore or incorporate in such a way that the resulting estimand is no longer a causal effect. One alternative to these analyses is the complier average causal effect (CACE) which estimates the average causal treatment effect among a subpopulation that would comply under any treatment assigned. We focus on the setting of a randomized clinical trial with crossover treatment noncompliance (e.g., control subjects could receive the intervention and intervention subjects could receive the control) and outcome nonresponse. In this article, we develop estimators for the CACE using multiple imputation methods, which have been successfully applied to a wide variety of missing data problems, but have not yet been applied to the potential outcomes setting of causal inference. Using simulated data we investigate the finite sample properties of these estimators as well as of competing procedures in a simple setting. Finally we illustrate our methods using a real randomized encouragement design study on the effectiveness of the influenza vaccine. [ABSTRACT FROM AUTHOR]

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]

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]

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]

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]