Search

AbstractOrganizations are increasingly relying on digital communications, such as targeted emails and mobile notifications, to engage with their audiences. Despite the evident advantages like cost-effectiveness and customization, assessing the effectiveness of such communications from observational data poses various statistical challenges. An immediate challenge is to adjust for targeting rules used in these communications. When digital communications involve a sequence of emails or notifications, however, further adjustments are required to correct for selection bias arising from previous communications influencing the subsequent ones and to deal with noncompliance issues, e.g., not opening the email. This paper addresses these challenges in a study of promotional email sequences sent by a US retailer. We use a Bayesian methodology for causal inference from longitudinal data, considering targeting, noncompliance, and sequential confounding with unmeasured variables. The methodology serves three objectives: to evaluate the average treatment effect of any deterministic emailing strategy, to compare the effectiveness of these strategies across varying compliance behaviors, and to infer optimal strategies for distinct customer segments. Our analysis finds, among other things, that certain promotional emails effectively maintain engagement among individuals who have regularly received such incentives, and individuals who consistently open their emails exhibit reduced sensitivity to promotional content. [ABSTRACT FROM AUTHOR]

Data-driven decision making plays an important role even in high stakes settings like medicine and public policy. Learning optimal policies from observed data requires a careful formulation of the utility function whose expected value is maximized across a population. Although researchers typically use utilities that depend on observed outcomes alone, in many settings the decision maker's utility function is more properly characterized by the joint set of potential outcomes under all actions. For example, the Hippocratic principle to "do no harm" implies that the cost of causing death to a patient who would otherwise survive without treatment is greater than the cost of forgoing life-saving treatment. We consider optimal policy learning with asymmetric counterfactual utility functions of this form that consider the joint set of potential outcomes. We show that asymmetric counterfactual utilities lead to an unidentifiable expected utility function, and so we first partially identify it. Drawing on statistical decision theory, we then derive minimax decision rules by minimizing the maximum expected utility loss relative to different alternative policies. We show that one can learn minimax loss decision rules from observed data by solving intermediate classification problems, and establish that the finite sample excess expected utility loss of this procedure is bounded by the regret of these intermediate classifiers. We apply this conceptual framework and methodology to the decision about whether or not to use right heart catheterization for patients with possible pulmonary hypertension. for this article are available online. [ABSTRACT FROM AUTHOR]

AbstractWe analyze the causal effects of taking parental leave on the post-birth hourly wage distribution of parental-leave-eligible mothers in Luxembourg. To deal with selection into parental leave, we match participants with non participants’ rich pre-intervention characteristics obtained from Social Security records for 2005–2010. In addition, we deal with selection into employment by using principal stratification and non parametric bounds. While the key identifying assumptions employed are not refutable (e.g., unconfoundedness and monotonicity), we present suggestive evidence about their plausibility in our context. Inference is for a subpopulation of parental-leave-eligible mothers who are always employed regardless of parental leave participation—about 80% of all eligible mothers. Our estimated bounds on quantile treatment effects of parental leave suggest substantial negative and significant impacts in most quantiles above the median of the wage distribution. These wage penalties, which are bounded between 10 and 26%, appeared present for high-earner mothers 2–5 years after parental leave. [ABSTRACT FROM AUTHOR]

Current instrumental variable methodology focuses mainly on estimating causal effects for a dichotomous or an ordinal treatment variable. Situations with more than two unordered treatments are less explored. The challenge is that assumptions needed to derive point-estimators become increasingly stronger with the number of relevant treatment alternatives. In this article, we aim at deriving causal point-estimators for head-to-head comparisons of the effect of multiple relevant treatments or interventions. We will achieve this with a set of plausible and well-defined rationality assumptions while only considering ordinal instruments. We demonstrate that our methodology provides asymptotically unbiased estimators in the presence of unobserved confounding effects in a simulation study. We then apply the method to compare the effectiveness of five anti-inflammatory drugs in the treatment of rheumatoid arthritis. For this, we use a clinical data set from an observational study in Norway, where price is the primary determinant of the preferred drug and can therefore be considered as an instrument. The developed methodology provides an important addition to the toolbox for causal inference when comparing more than two interventions influenced by an instrumental variable. [ABSTRACT FROM AUTHOR]

The relevance of the epidemiologic concept of preventable fraction to the study of the population-level impact of preventive exposures is unequivocal. Here, we discuss how the preventable fraction can be usefully understood for the class of outcomes that relate to disease progression (e.g., clinical severity given diagnosis), and, under the principal stratification framework, derive an expression for this quantity for this type of outcome. In particular, we show that, in the context of disease progression, the preventable fraction is a function of the effect on the postdiagnosis outcome in the principal stratum in the unexposed group who would have disease regardless of exposure status. This work will facilitate an understanding of the contribution of principal effects to the impact of preventive exposures at the population level. [ABSTRACT FROM AUTHOR]

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]

AbstractThe ICH E9 (R1) addendum on estimands, coupled with recent advancements in causal inference, has prompted a shift toward using model-free treatment effect estimands that are more closely aligned with the underlying scientific question. This represents a departure from traditional, model-dependent approaches where the statistical model often overshadows the inquiry itself. While this shift is a positive development, it has unintentionally led to the prioritization of an estimand’s ability to perfectly answer the key scientific question over its practical learnability from data under plausible assumptions. We illustrate this by scrutinizing assumptions in the recent clinical trials literature on principal stratum estimands, demonstrating that some popular assumptions are not only implausible but often inevitably violated. We advocate for a more balanced approach to estimand formulation, one that carefully considers both the scientific relevance and the practical feasibility of estimation under realistic conditions. [ABSTRACT FROM AUTHOR]

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]

Treatment noncompliance and censoring are two common complications in clinical trials. Motivated by the ADAPTABLE pragmatic clinical trial, we develop methods for assessing treatment effects in the presence of treatment noncompliance with a right-censored survival outcome. We classify the participants into principal strata, defined by their joint potential compliance status under treatment and control. We propose a multiply robust estimator for the causal effects on the survival probability scale within each principal stratum. This estimator is consistent even if one, sometimes two, of the four working models—on the treatment assignment, the principal strata, censoring, and the outcome—is misspecified. A sensitivity analysis strategy is developed to address violations of key identification assumptions, the principal ignorability and monotonicity. We apply the proposed approach to the ADAPTABLE trial to study the causal effect of taking low- versus high-dosage aspirin on all-cause mortality and hospitalization from cardiovascular diseases. [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]

Given a binary treatment and a binary mediator, mediation analysis decomposes the total effect of the treatment on an outcome variable into various sub-effects, and there appeared two-, three-, and four-way decompositions in the literature. Using “principal stratification” based on the potential mediator types, we consider sub-treatment effects for “mediative never-takers, compliers, defiers, and always takers.” In this approach, although it is difficult to pick any one decomposition over the others in general, a particular three-way decomposition becomes well suited, which is thus advocated to use. We present identification conditions for the effects using conditional means, which is then followed by simple estimators that are applicable to any outcome variable (binary, count, continuous, etc.). We also provide simulation and empirical studies.

The selection of the primary endpoint in a clinical trial plays a critical role in determining the trial's success. Ideally, the primary endpoint is the clinically most relevant outcome, also termed the true endpoint. However, practical considerations, like extended follow-up, may complicate this choice, prompting the proposal to replace the true endpoint with so-called surrogate endpoints. Evaluating the validity of these surrogate endpoints is crucial, and a popular evaluation framework is based on the proportion of treatment effect explained (PTE). While methodological advancements in this area have focused primarily on estimation methods, interpretation remains a challenge hindering the practical use of the PTE. We review various ways to interpret the PTE. These interpretations—two causal and one non-causal—reveal connections between the PTE principal surrogacy, causal mediation analysis, and the prediction of trial-level treatment effects. A common limitation across these interpretations is the reliance on unverifiable assumptions. As such, we argue that the PTE is only meaningful when researchers are willing to make very strong assumptions. These challenges are also illustrated in an analysis of three hypothetical vaccine trials. [ABSTRACT FROM AUTHOR]

A method is proposed to compute more precise standard errors for marketing A/B tests. Incrementality experiments compare customers exposed to a marketing action designed to increase sales with those randomly assigned to a control group. These experiments suffer from noisy responses, which make precise estimation of the average treatment effect (ATE) and marketing return difficult. We develop a model that improves the precision by estimating separate treatment effects for three latent strata defined by potential outcomes in the experiment—customers who would buy regardless of ad exposure, those who would buy only if exposed to ads, and those who would not buy regardless. The overall ATE is estimated by averaging the strata-level effects, and this produces a more precise estimator of the ATE over a wide range of conditions typical of marketing experiments. Analytical results and simulations show that the method decreases the sampling variance of the ATE most when (1) there are large differences in the treatment effect between latent strata and (2) the model used to estimate the strata-level effects is well identified. Applying the procedure to five catalog experiments shows a reduction of 30%–60% in the variance of the overall ATE. This leads to a substantial decrease in decision errors when the estimator is used to determine whether ads should be continued or discontinued. History: Olivier Toubia served as the senior editor. Funding: This work was supported by Adobe Systems [Adobe Digital Experience Research Award]. R. Berman was supported by the United States-Israel Binational Science Foundation [Grant 2020022] and the Wharton Dean's Research Fund, and E. M. Feit was supported by the Dean's Fellowship from LeBow College of Business. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mksc.2022.0297. [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]

This article discusses causal interpretations of epidemiologic studies of the effects of vaccination on sequelae after acute severe acute respiratory syndrome coronavirus 2 infection. To date, researchers have tried to answer several different research questions on this topic. While some studies assessed the impact of postinfection vaccination on the presence of or recovery from post-acute coronavirus disease 2019 syndrome, others quantified the association between preinfection vaccination and postacute sequelae conditional on becoming infected. However, the latter analysis does not have a causal interpretation, except under the principal stratification framework--that is, this comparison can only be interpreted as causal for a nondiscernible stratum of the population. As the epidemiology of coronavirus disease 2019 is now nearly entirely dominated by reinfections, including in vaccinated individuals, and possibly caused by different Omicron subvariants, it has become even more important to design studies on the effects of vaccination on postacute sequelae that address precise causal questions and quantify effects corresponding to implementable interventions. [ABSTRACT FROM AUTHOR]

The COVE trial randomized participants to receive two doses of mRNA-1273 vaccine or placebo on Days 1 and 29 (D1, D29). Anti-SARS-CoV-2 Spike IgG binding antibodies (bAbs), anti-receptor binding domain IgG bAbs, 50% inhibitory dilution neutralizing antibody (nAb) titers, and 80% inhibitory dilution nAb titers were measured at D29 and D57. We assessed these markers as correlates of protection (CoPs) against COVID-19 using stochastic interventional vaccine efficacy (SVE) analysis and principal surrogate (PS) analysis, frameworks not used in our previous COVE immune correlates analyses. By SVE analysis, hypothetical shifts of the D57 Spike IgG distribution from a geometric mean concentration (GMC) of 2737 binding antibody units (BAU)/mL (estimated vaccine efficacy (VE): 92.9% (95% CI: 91.7%, 93.9%)) to 274 BAU/mL or to 27,368 BAU/mL resulted in an overall estimated VE of 84.2% (79.0%, 88.1%) and 97.6% (97.4%, 97.7%), respectively. By binary marker PS analysis of Low and High subgroups (cut-point: 2094 BAU/mL), the ignorance interval (IGI) and estimated uncertainty interval (EUI) for VE were [85%, 90%] and (78%, 93%) for Low compared to [95%, 96%] and (92%, 97%) for High. By continuous marker PS analysis, the IGI and 95% EUI for VE at the 2.5th percentile (519.4 BAU/mL) vs. at the 97.5th percentile (9262.9 BAU/mL) of D57 Spike IgG concentration were [92.6%, 93.4%] and (89.2%, 95.7%) vs. [94.3%, 94.6%] and (89.7%, 97.0%). Results were similar for other D29 and D57 markers. Thus, the SVE and PS analyses additionally support all four markers at both time points as CoPs.

• Many statistical approaches have been applied to vaccine efficacy (VE) trials to evaluate CoPs. • Four distinct statistical frameworks for evaluating CoPs in VE trials are summarized. • Criteria for a 'good CoP' according to the four frameworks are suggested. • This article constitutes a reference resource for promoting harmonization of CoP evaluation. A central goal of vaccine research is to characterize and validate immune correlates of protection (CoPs). In addition to helping elucidate immunological mechanisms, a CoP can serve as a valid surrogate endpoint for an infectious disease clinical outcome and thus qualifies as a primary endpoint for vaccine authorization or approval without requiring resource-intensive randomized, controlled phase 3 trials. Yet, it is challenging to persuasively validate a CoP, because a prognostic immune marker can fail as a reliable basis for predicting/inferring the level of vaccine efficacy against a clinical outcome, and because the statistical analysis of phase 3 trials only has limited capacity to disentangle association from cause. Moreover, the multitude of statistical methods garnered for CoP evaluation in phase 3 trials renders the comparison, interpretation, and synthesis of CoP results challenging. Toward promoting broader harmonization and standardization of CoP evaluation, this article summarizes four complementary statistical frameworks for evaluating CoPs in a phase 3 trial, focusing on the frameworks' distinct scientific objectives as measured and communicated by distinct causal vaccine efficacy parameters. Advantages and disadvantages of the frameworks are considered, dependent on phase 3 trial context, and perspectives are offered on how the frameworks can be applied and their results synthesized. [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]

Cluster randomized trials are commonly used for evaluating treatment effects of a cluster-level intervention. Because subjects are often recruited after cluster randomization, a main complication is the potential for selection bias due to the intervention affecting which subjects are identified as being eligible for receiving the actual treatment. In the presence of such post-randomization selection bias, direct comparison of the observed outcomes among eligible subjects between arms does not yield a valid causal effect estimate. In this note, we define average and quantile causal estimands using principal stratification in the context of post-randomization selection bias, and provide nonparametric identification assumptions and formulas for these estimands. [ABSTRACT FROM AUTHOR]

Three critical issues for causal inference that often occur in modern, complicated experiments are interference, treatment nonadherence, and missing outcomes. A great deal of research efforts has been dedicated to developing causal inferential methodologies that address these issues separately. However, methodologies that can address these issues simultaneously are lacking. We propose a Bayesian causal inference methodology to address this gap. Our methodology extends existing causal frameworks and methods, specifically, two-staged randomized experiments and the principal stratification framework. In contrast to existing methods that invoke strong structural assumptions to identify principal causal effects, our Bayesian approach uses flexible distributional models that can accommodate the complexities of interference and missing outcomes, and that ensure that principal causal effects are weakly identifiable. We illustrate our methodology via simulation studies and a re-analysis of real-life data from an evaluation of India's National Health Insurance Program. Our methodology enables us to identify new active causal effects that were not identified in past analyses. Ultimately, our simulation studies and case study demonstrate how our methodology can yield more informative analyses in modern experiments with interference, treatment nonadherence, missing outcomes, and complicated outcome generation mechanisms. [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]

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]

Researchers are often interested in treatment effects on outcomes that are only defined conditional on posttreatment events. For example, in a study of the effect of different cancer treatments on quality of life at end of follow-up, the quality of life of individuals who die during the study is undefined. In these settings, naive contrasts of outcomes conditional on posttreatment events are not average causal effects, even in randomized experiments. Therefore, the effect in the principal stratum of those who would have the same value of the posttreatment variable regardless of treatment (such as the survivor average causal effect) is often advocated for causal inference. While principal stratum effects are average causal effects, they refer to a subset of the population that cannot be observed and may not exist. Therefore, it is not clear how these effects inform decisions or policies. Here we propose the conditional separable effects, quantifying causal effects of modified versions of the study treatment in an observable subset of the population. These effects, which may quantify direct effects of the study treatment, require transparent reasoning about candidate modified treatments and their mechanisms. We provide identifying conditions and various estimators of these effects along with an applied example. for this article are available online. [ABSTRACT FROM AUTHOR]

In many medical studies, an ultimate failure event, such as death, is likely to be affected by the occurrence and timing of other intermediate clinical events. Both event times are subject to censoring by loss-to-follow-up, but the nonterminal event may be further censored by the occurrence of the primary outcome, but not vice versa. To study the effect of an intervention on both events, the intermediate event may be viewed as a mediator. However, the conventional definitions of direct and indirect effects do not apply, because of the semi-competing risks data structure. We define three principal strata based on whether the potential intermediate event occurs before the potential failure event. This allows us to properly define direct and indirect effects in one stratum, and define total effects for all strata. We discuss the identification conditions for the stratum-specific effects, and propose a semiparametric estimator based on a multivariate logistic stratum membership model and within-stratum proportional hazards models for the event times. By treating the unobserved stratum membership as a latent variable, we propose an expectation-maximization algorithm for the computation. We study the asymptotic properties of the estimators using modern empirical process theory and examine the performance of the estimators in numerical studies. [ABSTRACT FROM AUTHOR]

When a treatment cannot be enforced, but only encouraged, noncompliance naturally arises. In applied economics, the common empirical strategy for dealing with noncompliance is to rely on Instrumental Variables methods. When the effects are heterogeneous, these methods allow, under a set of assumptions, to identify the causal effect for Compliers, i.e., the subset of units whose treatment is affected by the encouragement. One of the identification assumptions is the Exclusion Restriction (ER), which essentially rules out the possibility of a causal effect for Never Takers, i.e., those whose treatment is not affected by the encouragement. In this paper, we show the consequences of violations of this assumption in the impact evaluation of an intervention implemented in Uganda, where targeted households were encouraged to join a community health financing (CHF) scheme through activities of sensitization. We conduct the analyses using Bayesian model-based principal stratification, first assuming and then relaxing the ER for Never Takers. This allows showing the positive impact of the intervention on the health costs of both Compliers and Never Takers. While the causal effects for the former could be due to the encouragement but also to the actual participation in the scheme, those for the latter are unequivocally attributable to the encouragement. This indicates that sensitization alone is extremely effective in reducing vulnerability against health costs. This finding is of paramount importance for policy-making, as it is much easier and more cost-effective to implement awareness-raising campaigns than CHF schemes. [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]

This study introduces a new approach to power analysis in the context ofestimating a local average treatment effect (LATE), where the study subjectsexhibit noncompliance with treatment assignment. As a result of distributionalcomplications in the LATE context, compared to the simple ATE context, there iscurrently no standard method of power analysis for the LATE. Moreover, existingmethods and commonly used substitutes - which include instrumental variable(IV), intent-to-treat (ITT), and scaled ATE power analyses - require specifyinggenerally unknown variance terms and/or rely upon strong and unrealisticassumptions, thus providing unreliable guidance on the power of tests of theLATE. This study develops a new approach that uses standardized effect sizes toplace bounds on the power for the most commonly used estimator of the LATE, theWald IV estimator, whereby variance terms and distributional parameters neednot be specified nor assumed. Instead, in addition to the effect size, samplesize, and error tolerance parameters, the only other parameter that must bespecified by the researcher is the compliance rate. Additional conditions canalso be introduced to further narrow the bounds on the power calculation. Theresult is a generalized approach to power analysis in the LATE context that issimple to implement.

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]

In observational studies, principal stratification is a well-established method in causal analysis to adjust the treatment effect estimation for post-treatment variables. However, this inference could be challenging when the data have a clustering structure, which is pervasive in observational studies. Adding to the issues is the fact that often the variables associated with the clusters are only recorded as the cluster label due to a budget constraint or measuring difficulties. Furthermore, the true nature of the relationship between these cluster level variables and the outcome may be unclear. Although accommodating this clustering structure via random effects based on the cluster label can address the bias issues, estimating the model is inevitably tedious and overfitting can occur with principal stratification and clustering. In this article, we propose a comprehensive framework for estimating a treatment effect when both post-treatment variable and clustering exist in a data set. Specifically, following the idea of principal stratification, we define the clustering structure as random effects with a spike and slab prior in a Bayesian hierarchical model. As a result, a parsimonious model which only contains clusters with significant effects on the outcome can be obtained without much computational cost. We demonstrate the desirable features of the proposed method with two real data sets, one about academic performance and the other about infant birth weight. To further examine the empirical performance of the proposed method, simulations with data generating mechanisms similar to our data applications, and other four hypothetical data sets are conducted. [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]

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.

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 COVE trial randomized participants to receive two doses of mRNA-1273 vaccine or placebo on Days 1 and 29 (D1, D29). Anti-SARS-CoV-2 Spike IgG binding antibodies (bAbs), anti-receptor binding domain IgG bAbs, 50% inhibitory dilution neutralizing antibody (nAb) titers, and 80% inhibitory dilution nAb titers were measured at D29 and D57. We assessed these markers as correlates of protection (CoPs) against COVID-19 using stochastic interventional vaccine efficacy (SVE) analysis and principal surrogate (PS) analysis, frameworks not used in our previous COVE immune correlates analyses. By SVE analysis, hypothetical shifts of the D57 Spike IgG distribution from a geometric mean concentration (GMC) of 2737 binding antibody units (BAU)/mL (estimated vaccine efficacy (VE): 92.9% (95% CI: 91.7%, 93.9%)) to 274 BAU/mL or to 27,368 BAU/mL resulted in an overall estimated VE of 84.2% (79.0%, 88.1%) and 97.6% (97.4%, 97.7%), respectively. By binary marker PS analysis of Low and High subgroups (cut-point: 2094 BAU/mL), the ignorance interval (IGI) and estimated uncertainty interval (EUI) for VE were [85%, 90%] and (78%, 93%) for Low compared to [95%, 96%] and (92%, 97%) for High. By continuous marker PS analysis, the IGI and 95% EUI for VE at the 2.5th percentile (519.4 BAU/mL) vs. at the 97.5th percentile (9262.9 BAU/mL) of D57 Spike IgG concentration were [92.6%, 93.4%] and (89.2%, 95.7%) vs. [94.3%, 94.6%] and (89.7%, 97.0%). Results were similar for other D29 and D57 markers. Thus, the SVE and PS analyses additionally support all four markers at both time points as CoPs.

Background: Although there are discussions regarding standards of the analysis of patient-reported outcomes and quality of life (QOL) in oncology clinical trials, that of QOL with death events is not within their scope. For example, ignoring death can lead to bias in the QOL analysis for patients with moderate or high mortality rates in the palliative care setting. This is discussed in the estimand framework but is controversial. Information loss by summary measures under the estimand framework may make it challenging for clinicians to interpret the QOL analysis results. This study illustrated the use of graphical displays in the framework. They can be helpful for discussions between clinicians and statisticians and decision-making by stakeholders.Methods: We reviewed the time-to-deterioration analysis, prioritized composite outcome approach, semi-competing risk analysis, survivor analysis, linear mixed model for repeated measures, and principal stratification approach. We summarized attributes of estimands and graphs in the statistical analysis and evaluated them in various hypothetical randomized controlled trials.Results: Graphs for each analysis method provide different information and impressions. In the time-to-deterioration analysis, it was not easy to interpret the difference in the curves as an effect on QOL. The prioritized composite outcome approach provided new insights for QOL considering death by defining better conditions based on the distinction of OS and QOL. The semi-competing risk analysis provided different insights compared with the time-to-deterioration analysis and prioritized composite outcome approach. Due to the missing assumption, graphs by the linear mixed model for repeated measures should be carefully interpreted, even for descriptive purposes. The principal stratification approach provided pure comparison, but the interpretation was difficult because the target population was unknown.Conclusions: Graphical displays can capture different aspects of treatment effects that should be described in the estimand framework. [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]

Background: The Tafamidis in Transthyretin Cardiomyopathy Clinical Trial (ATTR-ACT) demonstrated the effectiveness of tafamidis for the treatment of patients with transthyretin amyloid cardiomyopathy (ATTR-CM). Tafamidis reduced mortality in all subgroups of patients studied. Tafamidis also reduced observed frequency of cardiovascular (CV)-related hospitalizations in all subgroups except those who were New York Heart Association (NYHA) class III at baseline who, paradoxically, had a higher frequency of CV-related hospitalizations than placebo. Given the greater mortality rate with placebo, this analysis assessed the impact of the confounding effect of death on the frequency of CV-related hospitalization in ATTR-ACT. Methods: In ATTR-ACT, patients with ATTR-CM were randomized to tafamidis (n = 264) or placebo (n = 177) for 30 months. Post hoc analyses first defined and compared the effect of tafamidis treatment in the subset of NYHA class III patients from each treatment arm alive at month 30. The impact of a potential survivor bias was then adjusted for using principal stratification, estimating the frequency of CV-related hospitalization in NYHA class III patients who would have survived regardless of assigned treatment group (defined as the survivor average causal effect [SACE]). Results: In the subset of NYHA class III patients alive at month 30, tafamidis reduced the relative risk of CV-related hospitalization versus placebo (relative risk: 0.95 [95% CI: 0.55–1.65]). In the principal stratification analyses of those patients who would survive to 30 months regardless of treatment, tafamidis treatment was associated with a 24% lower risk of CV-related hospitalization (relative risk: 0.76 [95% CI: 0.45–1.24]). Similarly, there was a larger reduction in CV-related hospitalization frequency with tafamidis in NYHA class I or II patients in the SACE than was initially observed in ATTR-ACT. Conclusions: Initial data from ATTR-ACT likely underestimated the effect of tafamidis on CV-related hospitalizations due to the confounding effect of death. When SACE was used to adjust for survivor bias, there was a 24% reduction in the frequency of CV-related hospitalization in NYHA class III patients treated with tafamidis. [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]

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]