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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]

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]

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]

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]

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]

• 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]

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]

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]

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]

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]

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]

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]

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]

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]

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

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

Abstract Background Attrition due to death and non-attendance are common sources of bias in studies of age-related diseases. A simulation study is presented to compare two methods for estimating the survivor average causal effect (SACE) of a binary exposure (sex-specific dietary iron intake) on a binary outcome (age-related macular degeneration, AMD) in this setting. Methods A dataset of 10,000 participants was simulated 1200 times under each scenario with outcome data missing dependent on measured and unmeasured covariates and survival. Scenarios differed by the magnitude and direction of effect of an unmeasured confounder on both survival and the outcome, and whether participants who died following a protective exposure would also die if they had not received the exposure (validity of the monotonicity assumption). The performance of a marginal structural model (MSM, weighting for exposure, survival and missing data) was compared to a sensitivity approach for estimating the SACE. As an illustrative example, the SACE of iron intake on AMD was estimated using data from 39,918 participants of the Melbourne Collaborative Cohort Study. Results The MSM approach tended to underestimate the true magnitude of effect when the unmeasured confounder had opposing directions of effect on survival and the outcome. Overestimation was observed when the unmeasured confounder had the same direction of effect on survival and the outcome. Violation of the monotonicity assumption did not increase bias. The estimates were similar between the MSM approach and the sensitivity approach assessed at the sensitivity parameter of 1 (assuming no survival bias). In the illustrative example, high iron intake was found to be protective of AMD (adjusted OR 0.57, 95% CI 0.40–0.82) using complete case analysis via traditional logistic regression. The adjusted SACE odds ratio did not differ substantially from the complete case estimate, ranging from 0.54 to 0.58 for each of the SACE methods. Conclusions On average, MSMs with weighting for exposure, missing data and survival produced biased estimates of the SACE in the presence of an unmeasured survival-outcome confounder. The direction and magnitude of effect of unmeasured survival-outcome confounders should be considered when assessing exposure-outcome associations in the presence of attrition due to death.

Principal stratification has recently become a popular tool to address certain causal inference questions, particularly in dealing with post-randomization factors in randomized trials. Here, we analyze the conceptual basis for this framework and invite response to clarify the value of principal stratification in estimating causal effects of interest.

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

Randomized evaluations of educational technology produce log data as a bi-product: highly granular data on student and teacher usage. These datasets could shed light on causal mechanisms, effect heterogeneity, or optimal use. However, there are methodological challenges: implementation is not randomized and is only defined for the treatment group, and log datasets have a complex structure. This article discusses three approaches to help surmount these issues. One approach uses data from the treatment group to estimate the effect of usage on outcomes in an observational study. Another, causal mediation analysis, estimates the role of usage in driving the overall effect. Finally, principal stratification estimates overall effects for groups of students with the same "potential" usage. We analyze hint data from an evaluation of the Cognitive Tutor Algebra I curriculum using these three approaches, with possibly conflicting results: the observational study and mediation analysis suggest that hints reduce posttest scores, while principal stratification finds that treatment effects may be correlated with higher rates of hint requests. We discuss these mixed conclusions and give broader methodological recommendations. [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]

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

The draft ICH E9 (R1) addendum by the International Conference on Harmonisation working group opens for the use of a principal stratum (PS) in the analysis of study data for regulatory purpose, if a relevant estimand can be justified. Inspired by the so-called complier average causal effect and work within this framework, we propose a new estimator—Extrapolation based on propensity to comply—that estimates the treatment effect of an active treatment A relative to a comparator B (active or placebo), in the PS of patients who would comply, if they were treated with treatment A. Sensitivity of the approach to the number of covariates and their ability to predict PS membership is investigated based on data from a placebo-controlled study of brexpiprazole in schizophrenia. The performance of the estimator is compared with another estimator that is also based on principal stratification. A simulation study supports that the proposed estimator has a negligible bias even with a small sample size, except when the covariate predicting compliance is very weak. Not surprisingly, precision of the estimate increases substantially with stronger predictors of compliance. It is shown analytically that the estimator used for comparison is biased in general, and the bias is explicitly derived in a simple case with a binary predictor of compliance. While the proposed methodology is technically easy to implement, choosing predictors for modeling compliance is a key issue in practice. [ABSTRACT FROM AUTHOR]

Abstract–Biomarker measurements can be relatively easy and quick to obtain and are useful to investigate whether a compound works as intended on a mechanistic, pharmacological level. In some situations, it is realistic to assume that patients, whose post-baseline biomarker levels indicate that they do not sufficiently respond to the drug, are also unlikely to respond on clinically relevant long-term outcomes (such as time-to-event). However, the determination of the treatment effect in the subgroup of patients that would be biomarker responders, if given treatment, is not straightforward in a parallel groups trial: it is unclear which patients on placebo would have responded had they been given the treatment, so that naive comparisons between treatment and placebo will not estimate the treatment effect of interest. The purpose of this article is to investigate assumptions necessary to obtain causal conclusions in such a setting, using the formalism and existing strategies from causal inference. Three approaches for estimation of subgroup effects will be developed and illustrated using simulations and a case-study. [ABSTRACT FROM AUTHOR]

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

Individualizing treatment according to patients' characteristics is central for personalized or precision medicine. There has been considerable recent research in developing statistical methods to determine optimal personalized treatment strategies by modeling the outcome of patients according to relevant covariates under each of the alternative treatments, and then relying on so-called predicted individual treatment effects. In this paper, we use potential outcomes and principal stratification frameworks and develop a multinomial model for left and right-censored data to estimate the probability that a patient is a responder given a set of baseline covariates. The model can apply to RCT or observational study data. This method is based on the monotonicity assumption, which implies that no patients would respond to the control treatment but not to the experimental one. We conduct a simulation study to evaluate the properties of the proposed estimation method. Results showed that the predictions of the probability of being a responder were well calibrated even if we observed variability and a small bias when many parameters were estimated. We finally applied the method to a cohort study on the selection of patients for additional radiotherapy after resection of a soft-tissue sarcoma. [ABSTRACT FROM AUTHOR]

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

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

In clinical endpoint bioequivalence (BE) studies, the primary analysis for assessing equivalence between a generic and an innovator product is based on the observed per-protocol (PP) population (usually completers and compliers). However, missing data and noncompliance are post-randomization intercurrent events and may introduce selection bias. Therefore, PP analysis is generally not causal. The FDA Missing Data Working Group recommended using "causal estimands of primary interest." In this paper, we propose a principal stratification causal framework and co-primary causal estimands to test equivalence, which was also recommended by the recently published ICH E9 (R1) addendum to address intercurrent events. We identify three conditions under which the current PP estimator is unbiased for one of the proposed co-primary causal estimands - the "Survivor Average Causal Effect" (SACE) estimand. Simulation shows that when these three conditions are not met, the PP estimator is biased and may inflate Type 1 error and/or change power. We also propose a tipping point sensitivity analysis to evaluate the robustness of the current PP estimator in testing equivalence when the sensitivity parameters deviate from the three identified conditions, but stay within a clinically meaningful range. Our work is the first causal equivalence assessment in equivalence studies with intercurrent events. [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]

Researchers addressing posttreatment complications in randomized trials often turn to principal stratification to define relevant assumptions and quantities of interest. One approach for the subsequent estimation of causal effects in this framework is to use methods based on the “principal score,” the conditional probability of belonging to a certain principal stratum given covariates. These methods typically assume that stratum membership is as good as randomly assigned, given these covariates. We clarify the key assumption in this context, known as principal ignorability, and argue that versions of this assumption are quite strong in practice. We describe these concepts in terms of both one- and two-sided noncompliance and propose a novel approach for researchers to “mix and match” principal ignorability assumptions with alternative assumptions, such as the exclusion restriction. Finally, we apply these ideas to randomized evaluations of a job training program and an early childhood education program. Overall, applied researchers should acknowledge that principal score methods, while useful tools, rely on assumptions that are typically hard to justify in practice. [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]