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

Important statistical issues pervade the evaluation of training programs’ effects for unemployed people. In particular, the fact that offered wages are observed and well-defined only for subjects w...

Randomized evaluations of educational technology produce log data as a bi-product: highly granular data 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 paper 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., Forthcoming, Journal of Research in Educational Effectiveness

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

Researchers often lack the necessary data to credibly estimate racial discrimination in policing. In particular, police administrative records lack information on civilians police observe but do not investigate. In this article, we show that if police racially discriminate when choosing whom to investigate, analyses using administrative records to estimate racial discrimination in police behavior are statistically biased, and many quantities of interest are unidentified—even among investigated individuals—absent strong and untestable assumptions. Using principal stratification in a causal mediation framework, we derive the exact form of the statistical bias that results from traditional estimation. We develop a bias-correction procedure and nonparametric sharp bounds for race effects, replicate published findings, and show the traditional estimator can severely underestimate levels of racially biased policing or mask discrimination entirely. We conclude by outlining a general and feasible design for future studies that is robust to this inferential snare.

Many research questions concern treatment effects on outcomes that can recur several times in the same individual. For example, medical researchers are interested in treatment effects on hospitalizations in heart failure patients and sports injuries in athletes. Competing events, such as death, complicate causal inference in studies of recurrent events because once a competing event occurs, an individual cannot have more recurrent events. Several statistical estimands have been studied in recurrent event settings, with and without competing events. However, the causal interpretations of these estimands, and the conditions that are required to identify these estimands from observed data, have yet to be formalized. Here we use a formal framework for causal inference to formulate several causal estimands in recurrent event settings, with and without competing events. When competing events exist, we clarify when commonly used classical statistical estimands can be interpreted as causal quantities from the causal mediation literature, such as (controlled) direct effects and total effects. Furthermore, we show that recent results on interventionist mediation estimands allow us to define new causal estimands with recurrent and competing events that may be of particular clinical relevance in many subject matter settings. We use causal directed acyclic graphs and single world intervention graphs to illustrate how to reason about identification conditions for the various causal estimands based on subject matter knowledge. Furthermore, using results on counting processes, we show that our causal estimands and their identification conditions, which are articulated in discrete time, converge to classical continuous time counterparts in the limit of fine discretizations of time. We propose estimators and establish their consistency for the various identifying functionals. Finally, we use the proposed estimators to compute the effect of blood pressure lowering treatment on the recurrence of acute kidney injury using data from the Systolic Blood Pressure Intervention Trial.

This study examines the effects of the Education Welfare Priority Zone Program (ewpzp) on how elementary school students adjust to school in South Korea. Principal stratification and propensity score approaches were employed on a sample of 1,237 students. The results suggest that recipients of Priority Support (ps, a customised care programme offered to ewpzp students with special needs) reported increases in their perceptions of teacher interest. Teacher interest directly and indirectly improved the students’ class attitudes and social skills. Second, non-ps students in ewpzp schools showed appreciable improvement. Suggestions for improving ewpzp implementation are also made based on these findings. Cette étude examine les effets du programme de zone prioritaire d’aide sociale l’éducation (ewpzp) sur la façon dont les élèves de l’école primaire s’adaptent à l’école en Corée du Sud. Les approches de stratification principale et de score de propension ont été employées sur un échantillon de 1 237 élèves. Les résultats suggèrent que les bénéficiaires du soutien prioritaire (ps, un programme de soins personnalisés offert aux élèves de l’ewpzp ayant des besoins spéciaux) ont signalé une augmentation de leur perception de l’intérêt des enseignants. L’intérêt de l’enseignant a directement et indirectement amélioré les attitudes en classe et les compétences sociales des élèves. Ensuite, les élèves non-ps des écoles ewpzp ont montré une amélioration appréciable. Des suggestions pour améliorer la mise en œuvre de l’ewpzp sont également formulées sur la base de ces résultats.

Background Hospitalisation has been widely used as a measure of morbidity in clinical trials for chronic heart failure. As previously reported in the Transthyretin Amyloidosis Cardiomyopathy Clinical Trial (ATTR-ACT), the observed frequency of cardiovascular (CV)-related hospitalisations favoured tafamidis over placebo in all analyses except in the NYHA Class III baseline subgroup with a relative risk of 1.41 [95% CI: 1.05, 1.90]1. However, the evaluation of the causal effect of treatment on hospitalisation is complicated in the presence of death as death precludes further hospitalisation and thus limits the evaluation of hospitalisation rates between groups. This confounding effect of death is particularly relevant in NYHA Class III participants who had higher mortality rates compared to Class I or II participants. Purpose This aim of this study was to assess the impact of the confounding effect of death on CV-related hospitalisation. Methods The effect of tafamidis treatment on CV-related hospitalisations was defined and compared in the subset of participants from either treatment arm who were alive at the end of the study (ie, Month 30); however the subset of participants who survive on the tafamidis arm would be expected to have different characteristics from the subset of participants who survive on the control arm and thus these analyses do not estimate the causal effect. To address this possible survivor bias, we additionally conducted a post hoc principal stratification analysis. Principal stratification is a statistical method to adjust for post treatment events, in this case mortality, by classifying participants according to their potential to survive under each treatment arm. Specifically, we sought to estimate the principal strata effect on CV-related hospitalisations in NYHA Class III participants who would survive irrespective of treatment assignment. Sensitivity analyses were performed to assess the model assumptions. Results The analysis within the subset of participants who survived at Month 30 demonstrated a relative risk of 1.1 (95% CI: 0.56, 2.16) between tafamidis and placebo. The principal stratification analyses of subjects who would survive to 30 months irrespective of treatment estimated a 0.75 (95% CI: 0.44, 1.23) relative risk between tafamidis and placebo, suggesting a 25% reduction in frequency of CV-related hospitalisations in the tafamidis arm. Conclusion The initial data reported in ATTR-ACT likely underestimated the true effect of tafamidis on CV-related hospitalisations due to the confounding effect of death. The analysis of treatment group among observed survivors estimated a smaller relative risk for NYHA Class III; however, this analysis does not fully address the possible survivor bias. The survivor average causal effect, which adjusts for the survival bias demonstrated a reduction in the frequency of CV-related hospitalisation in the tafamidis treated arm for NYHA Class III participants. Funding Acknowledgement Type of funding sources: Private company. Main funding source(s): Pfizer

It is challenging to evaluate causal effects when the outcomes of interest suffer from truncation-by-death in many clinical studies; that is, outcomes cannot be observed if patients die before the time of measurement. To address this problem, it is common to consider average treatment effects by principal stratification, for which, the identifiability results and estimation methods with a binary treatment have been established in previous literature. However, in multiarm studies with more than two treatment options, estimation of causal effects becomes more complicated and requires additional techniques. In this article, we consider identification, estimation, and bounds of causal effects with multivalued ordinal treatments and the outcomes subject to truncation-by-death. We define causal parameters of interest in this setting and show that they are identifiable either using some auxiliary variable or based on linear model assumption. We then propose a semiparametric method for estimating the causal parameters and derive their asymptotic results. When the identification conditions are invalid, we derive sharp bounds of the causal effects by use of covariates adjustment. Simulation studies show good performance of the proposed estimator. We use the estimator to analyze the effects of a four-level chronic toxin on fetal developmental outcomes such as birth weight in rats and mice, with data from a developmental toxicity trial conducted by the National Toxicology Program. Data analyses demonstrate that a high dose of the toxin significantly reduces the weights of pups.

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 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.

While the HVTN 505 trial showed no overall efficacy of the tested vaccine to prevent HIV infection over placebo, markers measuring immune response to vaccination were strongly correlated with infection. This finding generated the hypothesis that some marker-defined vaccinated subgroups were partially protected whereas others had their risk increased. This hypothesis can be assessed using the principal stratification framework (Frangakis and Rubin, 2002) for studying treatment effect modification by an intermediate response variable, using methods in the sub-field of principal surrogate (PS) analysis that studies multiple principal strata. Unfortunately, available methods for PS analysis require an augmented study design not available in HVTN 505, and make untestable structural risk assumptions, motivating a need for more robust PS methods. Fortunately, another sub-field of principal stratification, survivor average causal effect (SACE) analysis (Rubin, 2006) – which studies effects in a single principal stratum – provides many methods not requiring an augmented design and making fewer assumptions. We show how, for a binary intermediate response variable, methods developed for SACE analysis can be adapted to PS analysis, providing new and more robust PS methods. Application to HVTN 505 supports that the vaccine partially protected individuals with vaccine-induced T-cells expressing certain combinations of functions.

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

Confounding is a major concern when using data from observational studies to infer the causal effect of a treatment. Instrumental variables, when available, have been used to construct bound estimates on population average treatment effects when outcomes are binary and unmeasured confounding exists. With continuous outcomes, meaningful bounds are more challenging to obtain because the domain of the outcome is unrestricted. In this paper, we propose to unify the instrumental variable and inverse probability weighting methods, together with suitable assumptions in the context of an observational study, to construct meaningful bounds on causal treatment effects. The contextual assumptions are imposed in terms of the potential outcomes that are partially identified by data. The inverse probability weighting component incorporates a sensitivity parameter to encode the effect of unmeasured confounding. The instrumental variable and inverse probability weighting methods are unified using the principal stratification. By solving the resulting system of estimating equations, we are able to quantify both the causal treatment effect and the sensitivity parameter (i.e. the degree of the unmeasured confounding). We demonstrate our method by analyzing data from the HIV Epidemiology Research Study.

In causal inference, principal stratification is a framework for dealing with a posttreatment intermediate variable between a treatment and an outcome, in which the principal strata are defined by the joint potential values of the intermediate variable. Because the principal strata are not fully observable, the causal effects within them, also known as the principal causal effects, are not identifiable without additional assumptions. Several previous empirical studies leveraged auxiliary variables to improve the inference of principal causal effects. We establish a general theory for identification and estimation of the principal causal effects with auxiliary variables, which provides a solid foundation for statistical inference and more insights for model building in empirical research. In particular, we consider two commonly-used strategies for principal stratification problems: principal ignorability, and the conditional independence between the auxiliary variable and the outcome given principal strata and covariates. For these two strategies, we give non-parametric and semi-parametric identification results without modeling assumptions on the outcome. When the assumptions for neither strategies are plausible, we propose a large class of flexible parametric and semi-parametric models for identifying principal causal effects. Our theory not only establishes formal identification results of several models that have been used in previous empirical studies but also generalizes them to allow for different types of outcomes and intermediate variables.

In this paper, I assess the employment and income effect of divorce for women in West Germany between 2000 and 2005. With newly available administrative data that allows me to adopt a causal approach, I find strong negative employment effects with respect to marginal employment and strong positive effects with respect to regular employment. However, in sum, the overall employment rate (marginal and regular employment combined) is not affected. Furthermore, the lower the labor market attachment before separation is, the more pronounced employment effects are. In addition, I also estimate the impact of divorce on daily gross incomes. I find no convincing evidence for an income effect. I conclude that a divorce might have a pure labor supply effect only.

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., 25 pages, 5 figures, 2 tables

This 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 on the intensity of the implementation of the One-Child 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 sensitivity analysis to assess the key instrumental variable assumption., 33 pages, 6 figures, 1 table

This study introduces a new approach to power analysis in the context of estimating a local average treatment effect (LATE), where the study subjects exhibit noncompliance with treatment assignment. As a result of distributional complications in the LATE context, compared to the simple ATE context, there is currently no standard method of power analysis for the LATE. Moreover, existing methods and commonly used substitutes - which include instrumental variable (IV), intent-to-treat (ITT), and scaled ATE power analyses - require specifying generally unknown variance terms and/or rely upon strong and unrealistic assumptions, thus providing unreliable guidance on the power of tests of the LATE. This study develops a new approach that uses standardized effect sizes to place bounds on the power for the most commonly used estimator of the LATE, the Wald IV estimator, whereby variance terms and distributional parameters need not be specified nor assumed. Instead, in addition to the effect size, sample size, and error tolerance parameters, the only other parameter that must be specified by the researcher is the compliance rate. Additional conditions can also be introduced to further narrow the bounds on the power calculation. The result is a generalized approach to power analysis in the LATE context that is simple to implement., Forthcoming, Statistical Science

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.

Population stratification is a major concern in genetic association studies. Failure to control it effectively can lead to excess false-positive results and failure to detect true associations. Many methods have been designed to adjust for population stratification, which mainly belong to the following categories: (1) genomic control, (2) structured association, (3) principal component or multidimensional scaling adjustment, (4) stratification score method and (5) other approaches. No method is likely to be superior in all situations. Care needs to be taken to ensure that the assumptions of the method are met and that the method is used for its intended purpose. Keywords: population stratification; genomic control; structured association; principal components; multidimensional scaling; stratification score

Causal knowledge discovery is an essential task in many disciplines. Inferring the knowledge of causal directions from the measurement data of two correlated variables is one of the most basic but non-trivial problems in the research of causal discovery. Most of the existing methods assume that at least one of the variables is strictly measured. In practice, uncertain data with observation error is widely exists and is unavoidable for both the cause and the effect. Correct causal relationships will be blurred by such noise. A causal direction inference method based on the errors-in-variables (EIV) model is proposed in this work. All variables are assumed to be measured with observation errors in the errors-in-variables models. Causal directions will be inferred by computing the correlation coefficients between the regression model functions and the probability density functions on both of the possible causal directions. Experiments are done on artificial data sets and the real world data sets to illustrate the performance of the proposed method.

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. O...

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

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., Comment: Correct a typo in equation (8)

Increasing attention has been focused on the use and validation of surrogate endpoints in cancer clinical trials. Previous literature on validation of surrogate endpoints are classified into four approaches: the proportion explained approach; the indirect effects approach; the meta-analytic approach; and the principal stratification approach. The mainstream in cancer research has seen the application of a meta-analytic approach. However, VanderWeele (2013) showed that all four of these approaches potentially suffer from the surrogate paradox. It was also shown that, if a principal surrogate satisfies additional criteria called one-sided average causal sufficiency, the surrogate cannot exhibit a surrogate paradox. Here, we propose a method for estimating principal effects under a monotonicity assumption. Specifically, we consider cancer clinical trials which compare a binary surrogate endpoint and a time-to-event clinical endpoint under two naturally ordered treatments (e.g. combined therapy vs. monotherapy). Estimation based on a mean score estimating equation will be implemented by the expectation-maximization algorithm. We will also apply the proposed method as well as other surrogacy criteria to evaluate the surrogacy of prostate-specific antigen using data from a phase III advanced prostate cancer trial, clarifying the complementary roles of both the principal stratification and meta-analytic approaches in the evaluation of surrogate endpoints in cancer. Copyright © 2017 John Wiley & Sons, Ltd.

Rates of kidney cancer have been increasing, with small incidental tumors experiencing the fastest growth rates. Much of the increase could be due to increased use of CT scans, MRIs, and ultrasounds for unrelated conditions. Many tumors might never have been detected or become symptomatic in the past. This suggests that many patients might benefit from less aggressive therapy, such as active surveillance by which tumors are surgically removed only if they become sufficiently large. However, it has been difficult for clinicians to identify subgroups of patients for whom treatment might be especially beneficial or harmful. In this work, we use a principal stratification framework to estimate the proportion and characteristics of individuals who have large or small hazard rates of death in two treatment arms. This allows us to assess who might be helped or harmed by aggressive treatment. We also use Weibull mixture models. This work differs from much previous work in that the survival classes upon which principal stratification is based are latent variables. That is, survival class is not an observed variable. We apply this work using Surveillance Epidemiology and End Results-Medicare claims data. Clinicians can use our methods for investigating treatments with heterogeneous effects.

When an initial case-control study is performed, data can be used in a secondary analysis to evaluate the effect of the case-defining event on later outcomes. In this paper, we study the example in ...

Researchers are often interested in treatment effects on outcomes that are only defined conditional on a post-treatment event status. 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, a naive contrast of outcomes conditional on the post-treatment variable is not an average causal effect, even in a randomized experiment. Therefore the effect in the principal stratum of those who would have the same value of the post-treatment variable regardless of treatment, such as the always survivors in a truncation by death setting, is often advocated for causal inference. While this principal stratum effect is a well defined causal contrast, it is often hard to justify that it is relevant to scientists, patients or policy makers, and it cannot be identified without relying on unfalsifiable assumptions. Here we formulate alternative estimands, the conditional separable effects, that have a natural causal interpretation under assumptions that can be falsified in a randomized experiment. We provide identification results and introduce different estimators, including a doubly robust estimator derived from the nonparametric influence function. As an illustration, we estimate a conditional separable effect of chemotherapies on quality of life in patients with prostate cancer, using data from a randomized clinical trial.

Dropouts confound the treatment effect when the outcome and the dropout process both depend on subject characteristics. If dropout is unrelated to treatment, there is an unconfounded effect, but it...

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.

Introduction. Medication nonadherence can have a significant negative impact on treatment effectiveness. Standard intention-to-treat analyses conducted alongside clinical trials do not make adjustments for nonadherence. Several methods have been developed that attempt to estimate what treatment effectiveness would have been in the absence of nonadherence. However, health technology assessment (HTA) needs to consider effectiveness under real-world conditions, where nonadherence levels typically differ from those observed in trials. With this analytical requirement in mind, we conducted a review to identify methods for adjusting estimates of treatment effectiveness in the presence of patient nonadherence to assess their suitability for use in HTA. Methods. A “Comprehensive Pearl Growing” technique, with citation searching and reference checking, was applied across 7 electronic databases to identify methodological papers for adjusting time-to-event outcomes for nonadherence using individual patient data. A narrative synthesis of identified methods was conducted. Methods were assessed in terms of their ability to reestimate effectiveness based on alternative, suboptimal adherence levels. Results. Twenty relevant methodological papers covering 12 methods and 8 extensions to those methods were identified. Methods are broadly classified into 4 groups: 1) simple methods, 2) principal stratification methods, 3) generalized methods (g-methods), and 4) pharmacometrics-based methods using pharmacokinetics and pharmacodynamics (PKPD) analysis. Each method makes specific assumptions and has associated limitations. Five of the 12 methods are capable of adjusting for real-world nonadherence, with only g-methods and PKPD considered appropriate for HTA. Conclusion. A range of statistical methods is available for adjusting estimates of treatment effectiveness for nonadherence, but most are not suitable for use in HTA. G-methods and PKPD appear to be more appropriate to estimate effectiveness in the presence of real-world adherence.

Randomized trials are often conducted with separate randomizations across multiple sites such as schools, voting districts, or hospitals. These sites can differ in important ways, including the site’s implementation quality, local conditions, and the composition of individuals. An important question in practice is whether—and under what assumptions—researchers can leverage this cross-site variation to learn more about the intervention. We address these questions in the principal stratification framework, which describes causal effects for subgroups defined by post-treatment quantities. We show that researchers can estimate certain principal causal effects via the multi-site design if they are willing to impose the strong assumption that the site-specific effects are independent of the site-specific distribution of stratum membership. We motivate this approach with a multi-site trial of the Early College High School Initiative, a unique secondary education program with the goal of increasing high school graduation rates and college enrollment. Our analyses corroborate previous studies suggesting that the initiative had positive effects for students who would have otherwise attended a low-quality high school, although power is limited.

Emission control technologies installed on power plants are a key feature of many air pollution regulations in the US. While such regulations are predicated on the presumed relationships between emissions, ambient air pollution, and human health, many of these relationships have never been empirically verified. The goal of this paper is to develop new statistical methods to quantify these relationships. We frame this problem as one of mediation analysis to evaluate the extent to which the effect of a particular control technology on ambient pollution is mediated through causal effects on power plant emissions. Since power plants emit various compounds that contribute to ambient pollution, we develop new methods for multiple intermediate variables that are measured contemporaneously, may interact with one another, and may exhibit joint mediating effects. Specifically, we propose new methods leveraging two related frameworks for causal inference in the presence of mediating variables: principal stratification and causal mediation analysis. We define principal effects based on multiple mediators, and also introduce a new decomposition of the total effect of an intervention on ambient pollution into the natural direct effect and natural indirect effects for all combinations of mediators. Both approaches are anchored to the same observed-data models, which we specify with Bayesian nonparametric techniques. We provide assumptions for estimating principal causal effects, then augment these with an additional assumption required for causal mediation analysis. The two analyses, interpreted in tandem, provide the first empirical investigation of the presumed causal pathways that motivate important air quality regulatory policies.

In randomized clinical trials, researchers are often interested in identifying an inexpensive intermediate study endpoint (typically a biomarker) that is a strong effect modifier of the treatment effect on a longer-term clinical endpoint of interest. Motivated by randomized placebo-controlled preventive vaccine efficacy trials, within the principal stratification framework a pseudo-score type estimator has been proposed to estimate disease risks conditional on the counter-factual biomarker of interest under each treatment assignment to vaccine or placebo, yielding an estimator of biomarker conditional vaccine efficacy. This method can be used for trial designs that use baseline predictors of the biomarker and/or designs that vaccinate disease-free placebo recipients at the end of the trial. In this article, we utilize the pseudo-score estimator to estimate the biomarker conditional vaccine efficacy adjusting for baseline covariates. We also propose a perturbation resampling method for making simultaneous inference on conditional vaccine efficacy over the values of the biomarker. We illustrate our method with datasets from two phase 3 dengue vaccine efficacy trials.

The hazard ratio is one of the most commonly reported measures of treatment effect in randomised trials, yet the source of much misinterpretation. This point was made clear by Hernan (Epidemiology (Cambridge, Mass) 21(1):13-15, 2010) in a commentary, which emphasised that the hazard ratio contrasts populations of treated and untreated individuals who survived a given period of time, populations that will typically fail to be comparable-even in a randomised trial-as a result of different pressures or intensities acting on different populations. The commentary has been very influential, but also a source of surprise and confusion. In this note, we aim to provide more insight into the subtle interpretation of hazard ratios and differences, by investigating in particular what can be learned about a treatment effect from the hazard ratio becoming 1 (or the hazard difference 0) after a certain period of time. We further define a hazard ratio that has a causal interpretation and study its relationship to the Cox hazard ratio, and we also define a causal hazard difference. These quantities are of theoretical interest only, however, since they rely on assumptions that cannot be empirically evaluated. Throughout, we will focus on the analysis of randomised experiments.

Summary 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.

Students in Algebra I classrooms typically learn at different rates and struggle at different points in the curriculum—a common challenge for math teachers. Cognitive Tutor Algebra I (CTA1), an educational computer program, addresses such student heterogeneity via what they term “mastery learning,” where students progress from one section of the curriculum to the next by demonstrating appropriate “mastery” at each stage. However, when students are unable to master a section’s skills even after trying many problems, they are automatically promoted to the next section anyway. Does promotion without mastery impair the program’s effectiveness? ¶ At least in certain domains, CTA1 was recently shown to improve student learning on average in a randomized effectiveness study. This paper uses student log data from that study in a continuous principal stratification model to estimate the relationship between students’ potential mastery and the CTA1 treatment effect. In contrast to extant principal stratification applications, a student’s propensity to master worked sections here is never directly observed. Consequently we embed an item-response model, which measures students’ potential mastery, within the larger principal stratification model. We find that the tutor may, in fact, be more effective for students who are more frequently promoted (despite unsuccessfully completing sections of the material). However, since these students are distinctive in their educational strength (as well as in other respects), it remains unclear whether this enhanced effectiveness can be directly attributed to aspects of the mastery learning program.

The proposed addendum to the International Conference on Harmonization document, Statistical Principles for Clinical Trials, can be read in two ways. There is a new framework for talking about estimands, but is it about fitting present methods into the framework? Or is it about changing methods? My answer: some of each. Where different methods are needed, there are challenging problems in estimating some desirable estimands, but there may also be desirable estimands that can be estimated easily and robustly.

We provide an introduction to causal inference with longitudinal data and discuss the complexities of analysis and interpretation when exposures can vary over time. We consider what types of causal questions can be addressed with the standard regression-based analyses and what types of covariate control and control for the prior values of outcome and exposure must be made to reason about causal effects. We also consider newer classes of causal models, including marginal structural models, that can assess questions of the joint effects of time-varying exposures and can take into account feedback between the exposure and outcome over time. Such feedback renders cross-sectional data ineffective for drawing inferences about causation. The challenges are illustrated by analyses concerning potential effects of religious service attendance on depression, in which there may in fact be effects in both directions with service attendance preventing the subsequent depression, but depression itself leading to lower levels of the subsequent religious service attendance. Longitudinal designs, with careful control for prior exposures, outcomes, and confounders, and suitable methodology, will strengthen research on mental health, religion and health, and in the biomedical and social sciences generally.

In randomized controlled trials, the evaluation of an overall treatment effect is often followed by effect modification or subgroup analyses, where the possibility of a different magnitude or direction of effect for varying values of a covariate is explored. While studies of effect modification are typically restricted to pretreatment covariates, longitudinal experimental designs permit the examination of treatment effect modification by intermediate outcomes, where intermediates are measured after treatment but before the final outcome. We present a novel application of generalized structural mean models (GSMMs) for simultaneously assessing effect modification by post-treatment covariates and accounting for noncompliance to assigned treatment status. The proposed approach may also be used to identify post-treatment effect modifiers in the absence of noncompliance. The methods are evaluated using a simulation study that demonstrates that our approach retains consistent estimation of effect modification by intermediate variables that are affected by treatment and also predict outcomes. We illustrate the method using a randomized trial designed to promote re-employment through teaching skills to enhance self-esteem and inoculate job seekers against setbacks in the job search process. Our analysis provides some evidence that the intervention was much less successful among subjects that displayed higher levels of depression at intermediate post-treatment waves of the study. We also compare the assumptions of our approach and principal stratification as alternatives to account for differences in effects by intermediate variables.

Recent approaches in causal inference have proposed estimating average causal effects that are local to some subpopulation, often for reasons of efficiency. These inferential targets are sometimes data-adaptive, in that they are dependent on the empirical distribution of the data. In this short note, we show that if researchers are willing to adapt the inferential target on the basis of efficiency, then extraordinary gains in precision can potentially be obtained. Specifically, when causal effects are heterogeneous, any asymptotically normal and root- n $n$ consistent estimator of the population average causal effect is superefficient for a data-adaptive local average causal effect.

In clinical trials, a surrogate outcome ( S) can be measured before the outcome of interest ( T) and may provide early information regarding the treatment ( Z) effect on T. Many methods of surrogacy validation rely on models for the conditional distribution of T given Z and S. However, S is a post-randomization variable, and unobserved, simultaneous predictors of S and T may exist, resulting in a non-causal interpretation. Frangakis and Rubin developed the concept of principal surrogacy, stratifying on the joint distribution of the surrogate marker under treatment and control to assess the association between the causal effects of treatment on the marker and the causal effects of treatment on the clinical outcome. Working within the principal surrogacy framework, we address the scenario of an ordinal categorical variable as a surrogate for a censored failure time true endpoint. A Gaussian copula model is used to model the joint distribution of the potential outcomes of T, given the potential outcomes of S. Because the proposed model cannot be fully identified from the data, we use a Bayesian estimation approach with prior distributions consistent with reasonable assumptions in the surrogacy assessment setting. The method is applied to data from a colorectal cancer clinical trial, previously analyzed by Burzykowski et al.

Exploration of causal mechanisms is often important for researchers and policymakers to understand how an intervention works and how it can be improved. This task can be crucial in clustered encouragement designs (CEDs). Encouragement design studies arise frequently when the treatment cannot be enforced because of ethical or practical constraints and an encouragement intervention (information campaigns, incentives, etc.) is conceived with the purpose of increasing the uptake of the treatment of interest. By design, encouragements always entail the complication of noncompliance. Encouragements can also give rise to a variety of mechanisms, particularly when encouragement is assigned at the cluster level. Social interactions among units within the same cluster can result in spillover effects. Disentangling the effect of encouragement through spillover effects from that through the enhancement of the treatment would give better insight into the intervention and it could be compelling for planning the scaling-up phase of the program. Building on previous works on CEDs and noncompliance, we use the principal stratification framework to define stratum-specific causal effects, that is, effects for specific latent subpopulations, defined by the joint potential compliance statuses under both encouragement conditions. We show how the latter stratum-specific causal effects are related to the decomposition commonly used in the literature and provide flexible homogeneity assumptions under which an extrapolation across principal strata allows one to disentangle the effects. Estimation of causal estimands can be performed with Bayesian inferential methods using hierarchical models to account for clustering. We illustrate the proposed methodology by analyzing a cluster randomized experiment implemented in Zambia and designed to evaluate the impact on malaria prevalence of an agricultural loan program intended to increase the bed net coverage. Farmer households assigned to the program could take advantage of a deferred payment and a discount in the purchase of new bed nets. Our analysis shows a lack of evidence of an effect of the offering of the program to a cluster of households through spillover effects, that is, through a greater bed net coverage in the neighborhood. Supplementary materials for this article are available online.

In this article, causal inference in randomized studies with recurrent events data and all-or-none compliance is considered. We use the counting process to analyze the recurrent events data and propose a causal proportional intensity model. The maximum likelihood approach is adopted to estimate the parameters of the proposed causal model. To overcome the computational difficulties created by the mixture structure of the problem, we develop an expectation-maximization (EM) algorithm. The resulting estimators are shown to be consistent and asymptotically normal. We further estimate the complier average causal effect (CACE), which is defined as the difference of the average numbers of recurrence between treatment and control groups within the complier class. The corresponding inferential procedures are established. Some simulation studies are conducted to assess the finite sample performance of the proposed approach.

This paper reexamines the literature on the impact of migration on household members left behind at origin. The empirical problem previous studies address is the self-selection of households into migration, i.e. the endogenous decision as to whether or not send a migrant. Yet, the subsequent selection of which family members migrate and which stay behind generates additional identification problems that have remained largely ignored. To tackle this second form of selectivity within the households, I model the behavior of families using latent stratification and potential outcome (Imbens and Angrist, 1994; Rubin, 1974). I show that the point-identification of the causal impact of migration requires strong behavioral assumptions rarely satisfied even with ideal experimental data. As a practical solution, I derive non parametric bounds under different sets of weaker assumptions. Using Mexican panel data, I show that standard estimates ignoring the intra-household selection into migration may suffer from substantial bias.

In a world increasingly globalized, multiple language skills can create more employment opportunities. Several countries include language training programs in active labor market programs for the unemployed. We analyze the effects of a language training program on the re-employment probability and hourly wages of the unemployed simultaneously, using high-quality administrative data from Luxembourg. We address selection into training by exploiting the rich administrative information available, and account for the complication that wages are "truncated" by unemployment by adopting a principal stratification framework. Estimation is undertaken with a mixture model likelihood-based approach.To improve inference, we use the individual's hours worked as a secondary outcome and a stochastic dominance assumption. These two features considerably ameliorate the multimodality problem commonly encountered in mixture models. We also conduct sensitivity analysis to assess the unconfoundedness assumption employed. Our results strongly suggest a positive effect (of up to 12.7 percent) of the language training programs on the re-employment probability, but no effects on wages for those who are observed employed regardless of training participation. It appears that, in the context of an open and multilingual economy, language training improve employability but the language skills acquired are not sufficiently rewarded to be reflected in higher wages.

Researchers often lack the necessary data to credibly estimate racial discrimination in policing. In particular, police administrative records lack information on civilians that police observe but do not investigate. In this paper, we show that if police racially discriminate when choosing whom to investigate, analyses using administrative records to estimate racial discrimination in police behavior are statistically biased, rendering many quantities of interest unidentified---even among investigated individuals---absent strong and untestable assumptions. Using principal stratification in a causal mediation framework, we derive the exact form of the statistical bias that results from traditional estimation. We develop a bias-correction procedure and nonparametric sharp bounds for race effects, replicate published findings, and show the traditional estimator can severely underestimate levels of racially biased policing or mask discrimination entirely. We conclude by outlining a general and feasible design for future studies that is robust to this inferential snare.