Principal stratification--uses and limitations

Interpretations of Studies on SARS-CoV-2 Vaccination and Post-acute COVID-19 Sequelae

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.

Multilevel Resilience and HIV Virologic Suppression Among African American/Black Adults in the Southeastern United States

OBJECTIVE

To assess overall and by neighborhood risk environments whether multilevel resilience resources were associated with HIV virologic suppression among African American/Black adults in the Southeastern United States.

SETTING AND METHODS

This clinical cohort sub-study included 436 African American/Black participants enrolled in two parent HIV clinical cohorts. Resilience was assessed using the Multilevel Resilience Resource Measure (MRM) for African American/Black adults living with HIV, where endorsement of a MRM statement indicated agreement that a resilience resource helped a participant continue HIV care despite challenges or was present in a participant's neighborhood. Modified Poisson regression models estimated adjusted prevalence ratios (aPRs) for virologic suppression as a function of categorical MRM scores, controlling for demographic, clinical, and behavioral characteristics at or prior to sub-study enrollment. We assessed for effect measure modification (EMM) by neighborhood risk environments.

RESULTS

Compared to participants with lesser endorsement of multilevel resilience resources, aPRs for virologic suppression among those with greater or moderate endorsement were 1.03 (95% confidence interval: 0.96-1.11) and 1.03 (0.96-1.11), respectively. Regarding multilevel resilience resource endorsement, there was no strong evidence for EMM by levels of neighborhood risk environments.

CONCLUSIONS

Modest positive associations between higher multilevel resilience resource endorsement and virologic suppression were at times most compatible with the data. However, null findings were also compatible. There was no strong evidence for EMM concerning multilevel resilience resource endorsement, which could have been due to random error. Prospective studies assessing EMM by levels of the neighborhood risk environment with larger sample sizes are needed.

Identification of Vaccine Effects When Exposure Status Is Unknown

Results from randomized controlled trials (RCTs) help determine vaccination strategies and related public health policies. However, defining and identifying estimands that can guide policies in infectious disease settings is difficult, even in an RCT. The effects of vaccination critically depend on characteristics of the population of interest, such as the prevalence of infection, the number of vaccinated, and social behaviors. To mitigate the dependence on such characteristics, estimands, and study designs, that require conditioning or intervening on exposure to the infectious agent have been advocated. But a fundamental problem for both RCTs and observational studies is that exposure status is often unavailable or difficult to measure, which has made it impossible to apply existing methodology to study vaccine effects that account for exposure status. In this study, we present new results on this type of vaccine effects. Under plausible conditions, we show that point identification of certain relative effects is possible even when the exposure status is unknown. Furthermore, we derive sharp bounds on the corresponding absolute effects. We apply these results to estimate the effects of the ChAdOx1 nCoV-19 vaccine on SARS-CoV-2 disease (COVID-19) conditional on postvaccine exposure to the virus, using data from a large RCT.

Social support, psychosocial risks, and cardiovascular health: Using harmonized data from the Jackson Heart Study, Mediators of Atherosclerosis in South Asians Living in America Study, and Multi-Ethnic Study of Atherosclerosis

Purpose

Social support may have benefits on cardiovascular health (CVH). CVH is evaluated using seven important metrics (Life's Simple 7; LS7) established by the American Heart Association (e.g., smoking, diet). However, evidence from longitudinal studies is limited and inconsistent. The objective of this study is to examine the longitudinal relationship between social support and CVH, and assess whether psychosocial risks (e.g., anger and stress) modify the relationship in a racially/ethnically diverse population.

Methods

Participants from three harmonized cohort studies - Jackson Heart Study, Mediators of Atherosclerosis in South Asians Living in America, and Multi-Ethnic Study of Atherosclerosis - were included. Repeated-measures modified Poisson regression models were used to examine the overall relationship between social support (in tertiles) and CVH (LS7 metric), and to assess for effect modification by psychosocial risk.

Results

Among 7724 participants, those with high (versus low) social support had an adjusted prevalence ratio (aPR) and 95% confidence interval (CI) for ideal or intermediate (versus poor) CVH of 0.99 (0.96-1.03). For medium (versus low) social support, the aPR (95% CI) was 1.01 (0.98-1.05). There was evidence for modification by employment and anger. Those with medium (versus low) social support had an aPR (95% CI) of 1.04 (0.99-1.10) among unemployed or low anger participants. Corresponding results for employed or high anger participants were 0.99 (0.94-1.03) and 0.97 (0.91-1.03), respectively.

Conclusion

Overall, we observed no strong evidence for an association between social support and CVH. However, some psychosocial risks may be modifiers. Prospective studies are needed to assess the social support-CVH relationship by psychosocial risks in racially/ethnically diverse populations.

Examining relationships between perceived neighborhood social cohesion and ideal cardiovascular health and whether psychosocial stressors modify observed relationships among JHS, MESA, and MASALA participants

BACKGROUND

Psychosocial stressors increase the risks for cardiovascular disease across diverse populations. However, neighborhood level resilience resources may protect against poor cardiovascular health (CVH). This study used data from three CVH cohorts to examine longitudinally the associations of a resilience resource, perceived neighborhood social cohesion (hereafter referred to as neighborhood social cohesion), with the American Heart Association's Life's Simple 7 (LS7), and whether psychosocial stressors modify observed relationships.

METHODS

We examined neighborhood social cohesion (measured in tertiles) and LS7 in the Jackson Heart Study, Multi-Ethnic Study of Atherosclerosis, and Mediators of Atherosclerosis in South Asians Living in America study. We used repeated-measures, modified Poisson regression models to estimate the relationship between neighborhood social cohesion and LS7 (primary analysis, n = 6,086) and four biological metrics (body mass index, blood pressure, cholesterol, blood glucose; secondary analysis, n = 7,291). We assessed effect measure modification by each psychosocial stressor (e.g., low educational attainment, discrimination).

RESULTS

In primary analyses, adjusted prevalence ratios (aPR) and 95% confidence intervals (CIs) for ideal/intermediate versus poor CVH among high or medium (versus low) neighborhood social cohesion were 1.01 (0.97-1.05) and 1.02 (0.98-1.06), respectively. The psychosocial stressors, low education and discrimination, functioned as effect modifiers. Secondary analyses showed similar findings. Also, in the secondary analyses, there was evidence for effect modification by income.

CONCLUSION

We did not find much support for an association between neighborhood social cohesion and LS7, but did find evidence of effect modification. Some of the effect modification results operated in unexpected directions. Future studies should examine neighborhood social cohesion more comprehensively and assess for effect modification by psychosocial stressors.

Using principal stratification in analysis of clinical trials

The ICH E9(R1) addendum (2019) proposed principal stratification (PS) as one of five strategies for dealing with intercurrent events. Therefore, understanding the strengths, limitations, and assumptions of PS is important for the broad community of clinical trialists. Many approaches have been developed under the general framework of PS in different areas of research, including experimental and observational studies. These diverse applications have utilized a diverse set of tools and assumptions. Thus, need exists to present these approaches in a unifying manner. The goal of this tutorial is threefold. First, we provide a coherent and unifying description of PS. Second, we emphasize that estimation of effects within PS relies on strong assumptions and we thoroughly examine the consequences of these assumptions to understand in which situations certain assumptions are reasonable. Finally, we provide an overview of a variety of key methods for PS analysis and use a real clinical trial example to illustrate them. Examples of code for implementation of some of these approaches are given in Supplemental Materials.

Translating questions to estimands in randomized clinical trials with intercurrent events

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.

Causal inference for semi-competing risks data

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

Estimating the treatment effect for adherers using multiple imputation

Randomized controlled trials are considered the gold standard to evaluate the treatment effect (estimand) for efficacy and safety. According to the recent International Council on Harmonization (ICH)-E9 addendum (R1), intercurrent events (ICEs) need to be considered when defining an estimand, and principal stratum is one of the five strategies to handle ICEs. Qu et al. (2020, Statistics in Biopharmaceutical Research 12:1-18) proposed estimators for the adherer average causal effect (AdACE) for estimating the treatment difference for those who adhere to one or both treatments based on the causal-inference framework, and demonstrated the consistency of those estimators; however, this method requires complex custom programming related to high-dimensional numeric integrations. In this article, we implemented the AdACE estimators using multiple imputation (MI) and constructed confidence intervals (CIs) through bootstrapping. A simulation study showed that the MI-based estimators provided consistent estimators with the nominal coverage probabilities of CIs for the treatment difference for the adherent populations of interest. As an illustrative example, the new method was applied to data from a real clinical trial comparing two types of basal insulin for patients with type 1 diabetes.

Examining Optimism, Psychosocial Risks, and Cardiovascular Health Using Life's Simple 7 Metrics in the Multi-Ethnic Study of Atherosclerosis and the Jackson Heart Study

Background: Optimism has been shown to be positively associated with better cardiovascular health (CVH). However, there is a dearth of prospective studies showing the benefits of optimism on CVH, especially in the presence of adversities, i.e., psychosocial risks. This study examines the prospective relationship between optimism and CVH outcomes based on the Life's Simple 7 (LS7) metrics and whether multilevel psychosocial risks modify the aforementioned relationship. Methods: We examined self-reported optimism and CVH using harmonized data from two U.S. cohorts: Multi-Ethnic Study of Atherosclerosis (MESA) and Jackson Heart Study (JHS). Modified Poisson regression models were used to estimate the relationship between optimism and CVH using LS7 among MESA participants (N = 3,520) and to examine the relationship of interest based on four biological LS7 metrics (body mass index, blood pressure, cholesterol, and blood glucose) among JHS and MESA participants (N = 5,541). For all CVH outcomes, we assessed for effect measure modification by psychosocial risk. Results: Among MESA participants, the adjusted risk ratio (aRR) for ideal or intermediate CVH using LS7 comparing participants who reported high or medium optimism to those with the lowest level of optimism was 1.10 [95% Confidence Interval (CI): 1.04-1.16] and 1.05 (95% CI: 0.99-1.11), respectively. Among MESA and JHS participants, the corresponding aRRs for having all ideal or intermediate (vs. no poor) metrics based on the four biological LS7 metrics were 1.05 (0.98-1.12) and 1.04 (0.97-1.11), respectively. The corresponding aRRs for having lower cardiovascular risk (0-1 poor metrics) based on the four biological LS7 metrics were 1.01 (0.98-1.03) and 1.01 (0.98-1.03), respectively. There was some evidence of effect modification by neighborhood deprivation for the LS7 outcome and by chronic stress for the ideal or intermediate (no poor) metrics outcome based on the four biological LS7 metrics. Conclusion: Our findings suggest that greater optimism is positively associated with better CVH based on certain LS7 outcomes among a racially/ethnically diverse study population. This relationship may be effect measure modified by specific psychosocial risks. Optimism shows further promise as a potential area for intervention on CVH. However, additional prospective and intervention studies are needed.

Causal Inference in Studying the Long-Term Health Effects of Disasters: Challenges and Potential Solutions

Two frequently encountered but underrecognized challenges for causal inference in studying the long-term health effects of disasters among survivors include 1) time-varying effects of disasters on a time-to-event outcome and 2) selection bias due to selective attrition. In this paper, we review approaches for overcoming these challenges and demonstrate application of the approaches to a real-world longitudinal data set of older adults who were directly affected by the 2011 Great East Japan Earthquake and Tsunami (n = 4,857). To illustrate the problem of time-varying effects of disasters, we examined the association between degree of damage due to the tsunami and all-cause mortality. We compared results from Cox regression analysis assuming proportional hazards with those derived using adjusted parametric survival curves allowing for time-varying hazard ratios. To illustrate the problem of selection bias, we examined the association between proximity to the coast (a proxy for housing damage from the tsunami) and depressive symptoms. We corrected for selection bias due to attrition in the 2 postdisaster follow-up surveys (conducted in 2013 and 2016) using multivariable adjustment, inverse probability of censoring weighting, and survivor average causal effect estimation. Our results demonstrate that analytical approaches which ignore time-varying effects on mortality and selection bias due to selective attrition may underestimate the long-term health effects of disasters.

Mediation analysis for mixture Cox proportional hazards cure models

Mediation analysis aims to decompose a total effect into specific pathways and investigate the underlying causal mechanism. Although existing methods have been developed to conduct mediation analysis in the context of survival models, none of these methods accommodates the existence of a substantial proportion of subjects who never experience the event of interest, even if the follow-up is sufficiently long. In this study, we consider mediation analysis for the mixture of Cox proportional hazards cure models that cope with the cure fraction problem. Path-specific effects on restricted mean survival time and survival probability are assessed by introducing a partially latent group indicator and applying the mediation formula approach in a three-stage mediation framework. A Bayesian approach with P-splines for approximating the baseline hazard function is developed to conduct analysis. The satisfactory performance of the proposed method is verified through simulation studies. An application of the Alzheimer's disease (AD) neuroimaging initiative dataset investigates the causal effects of APOE-ϵ4 allele on AD progression.

A novel estimand to adjust for rescue treatment in randomized clinical trials

The interpretation of randomized clinical trial results is often complicated by intercurrent events. For instance, rescue medication is sometimes given to patients in response to worsening of their disease, either in addition to the randomized treatment or in its place. The use of such medication complicates the interpretation of the intention-to-treat analysis. In view of this, we propose a novel estimand defined as the intention-to-treat effect that would have been observed, had patients on the active arm been switched to rescue medication if and only if they would have been switched when randomized to control. This enables us to disentangle the treatment effect from the effect of rescue medication on a patient's outcome, while tempering the strong extrapolations that are typically needed when inferring what the intention-to-treat effect would have been in the absence of rescue medication. We propose a novel inverse probability weighting method for estimating this effect in settings where the decision to initiate rescue medication is made at one prespecified time point. This estimator relies on specific untestable assumptions, in view of which we propose a sensitivity analysis. We use the method for the analysis of a clinical trial conducted by Janssen Pharmaceuticals, in which patients with type 2 diabetes mellitus can switch to rescue medication for ethical reasons. Monte Carlo simulations confirm that the proposed estimator is unbiased in moderate sample sizes.

Quantile regression to estimate the survivor average causal effect of periodontal treatment effects on birthweight and gestational age

BACKGROUND

Survival average causal effect (SACE) can give valid estimates of the periodontal treatment effect on birth outcomes in randomized controlled trials when fetal losses are unequal across the treatment arms. A regression-based method to estimate SACE using ordinary least squares (OLS) regression can be biased if the treatment effect varies across the outcome distribution. In this case quantile regression may be a suitable alternative.

METHODS

We compared OLS and quantile regression models estimating SACE to calculate the effect of periodontal treatment on birthweight and gestational age in secondary analyses of publicly available Obstetrics and Periodontal Therapy (OPT) trial data.

RESULTS

Periodontal treatment tended to increase birthweight and gestational age at the lowest quantiles, remained flat in the middle quantiles, and trended to decrease both birthweight and gestational age in the highest quantiles. In quantile regression models estimating SACE the β-coefficients: 95% confidence intervals (CI) for the 5th, 50th, and 95th percentiles were 277.5:  -141.0 to 696.0 g, 1.4: -107 to 110.3 g, and -84: -344 to 175.3 g for birthweight, and 0.6: -1.0 to 2.2 weeks, -0.1: -0.5 to 0.2 weeks, and -0.6: -1.0 to -0.1 weeks for gestational age. Estimates from OLS models estimating SACE were close to the null, β: 95% CI -4.7: 132.3 to 123.0 g for birthweight, and 0.03: -0.72 to 0.78 weeks for gestational age.

CONCLUSIONS

OLS models to evaluate SACE for periodontal treatment effects on birthweight and gestational age may be biased towards the null. Quantile regression may be a preferable alternative.

Bayesian shrinkage estimation of high dimensional causal mediation effects in omics studies

Causal mediation analysis aims to examine the role of a mediator or a group of mediators that lie in the pathway between an exposure and an outcome. Recent biomedical studies often involve a large number of potential mediators based on high-throughput technologies. Most of the current analytic methods focus on settings with one or a moderate number of potential mediators. With the expanding growth of -omics data, joint analysis of molecular-level genomics data with epidemiological data through mediation analysis is becoming more common. However, such joint analysis requires methods that can simultaneously accommodate high-dimensional mediators and that are currently lacking. To address this problem, we develop a Bayesian inference method using continuous shrinkage priors to extend previous causal mediation analysis techniques to a high-dimensional setting. Simulations demonstrate that our method improves the power of global mediation analysis compared to simpler alternatives and has decent performance to identify true nonnull contributions to the mediation effects of the pathway. The Bayesian method also helps us to understand the structure of the composite null cases for inactive mediators in the pathway. We applied our method to Multi-Ethnic Study of Atherosclerosis and identified DNA methylation regions that may actively mediate the effect of socioeconomic status on cardiometabolic outcomes.

Estimating causal effects of internet interventions in the context of nonadherence

A substantial proportion of participants who are offered internet-based psychological treatments in randomized trials do not adhere and may therefore not receive treatment. Despite the availability of justified statistical methods for causal inference in such situations, researchers often rely on analytical strategies that either ignore adherence altogether or fail to provide causal estimands. The objective of this paper is to provide a gentle nontechnical introduction to complier average causal effect (CACE) analysis, which, under clear assumptions, can provide a causal estimate of the effect of treatment for a subsample of compliers. The article begins with a brief review of the potential outcome model for causal inference. After clarifying assumptions and model specifications for CACE in the latent variable framework, data from a previously published trial of an internet-based psychological treatment for irritable bowel syndrome are used to demonstrate CACE-analysis. Several model extensions are then briefly reviewed. The paper offers practical recommendations on how to analyze randomized trials of internet interventions in the context of nonadherence. It is argued that CACE-analysis, whenever it is considered appropriate, should be carried out as a complement to the standard intention-to-treat analysis and that the format of internet-based treatments is particularly well suited to such an analytical approach.

Implementation of tripartite estimands using adherence causal estimators under the causal inference framework

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.

Attributable Risk to Assess the Health Impact of Air Pollution: Advances, Controversies, State of the Art and Future Needs

Despite the increased attention given to the health impact assessment of air pollution and to the strategies to control it in both scientific literature and concrete interventions, the results of the implementations, especially those involving traffic, have not always been satisfactory and there is still disagreement about the most appropriate interventions and the methods to assess their effectiveness. This state-of-the-art article reviews the recent interpretation of the concepts that concern the impact assessment, and compares old and new measurements of attributable risk and attributable fraction. It also summarizes the ongoing discussion about the designs and methods for assessing the air pollution impact with particular attention to improvements due to spatio-temporal analysis and other new approaches, such as studying short term effects in cohorts, and the still discussed methods of predicting the values of attributable risk (AR). Finally, the study presents the more recent analytic perspectives and the methods for directly assessing the effects of not yet implemented interventions on air quality and health, in accordance with the suggestion in the strategic plan 2020-2025 from the Health Effect Institute.

A model-based approach for simulating adaptive clinical studies with surrogate endpoints used for interim decision-making

In clinical trials, when exploring multiple dose groups to establish efficacy and safety on one or more selected doses, adaptive designs with interim dose selection are often used for dropping less effective dose groups. When it takes a long time to observe primary outcomes, utilizing information on a surrogate endpoint available at an earlier interim may be preferred for selecting which dose to continue. We propose a Bayesian model-based approach where historical data can be leveraged to incorporate a correlation model for investigating the design's operating characteristics. Simulation studies were conducted and the method can be readily applied for power and sample size calculations.

A causal framework for classical statistical estimands in failure-time settings with competing events

In failure-time settings, a competing event is any event that makes it impossible for the event of interest to occur. For example, cardiovascular disease death is a competing event for prostate cancer death because an individual cannot die of prostate cancer once he has died of cardiovascular disease. Various statistical estimands have been defined as possible targets of inference in the classical competing risks literature. Many reviews have described these statistical estimands and their estimating procedures with recommendations about their use. However, this previous work has not used a formal framework for characterizing causal effects and their identifying conditions, which makes it difficult to interpret effect estimates and assess recommendations regarding analytic choices. Here we use a counterfactual framework to explicitly define each of these classical estimands. We clarify that, depending on whether competing events are defined as censoring events, contrasts of risks can define a total effect of the treatment on the event of interest or a direct effect of the treatment on the event of interest not mediated by the competing event. In contrast, regardless of whether competing events are defined as censoring events, counterfactual hazard contrasts cannot generally be interpreted as causal effects. We illustrate how identifying assumptions for all of these counterfactual estimands can be represented in causal diagrams, in which competing events are depicted as time-varying covariates. We present an application of these ideas to data from a randomized trial designed to estimate the effect of estrogen therapy on prostate cancer mortality.

BAYESIAN METHODS FOR MULTIPLE MEDIATORS: RELATING PRINCIPAL STRATIFICATION AND CAUSAL MEDIATION IN THE ANALYSIS OF POWER PLANT EMISSION CONTROLS

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.

Analyzing patient-reported outcome data when completion differs between arms in open-label trials: an application of principal stratification

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.

Simple methods for the estimation and sensitivity analysis of principal strata effects using marginal structural models: Application to a bone fracture prevention trial

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.

Dealing with death when studying disease or physiological marker: the stochastic system approach to causality

The stochastic system approach to causality is applied to situations where the risk of death is not negligible. This approach grounds causality on physical laws, distinguishes system and observation and represents the system by multivariate stochastic processes. The particular role of death is highlighted, and it is shown that local influences must be defined on the random horizon of time of death. We particularly study the problem of estimating the effect of a factor V on a process of interest Y, taking death into account. We unify the cases where Y is a counting process (describing an event) and the case where Y is quantitative; we examine the case of observations in continuous and discrete time and we study the issue of whether the mechanism leading to incomplete data can be ignored. Finally, we give an example of a situation where we are interested in estimating the effect of a factor (blood pressure) on cognitive ability in elderly.

Survival-related Selection Bias in Studies of Racial Health Disparities: The Importance of the Target Population and Study Design

The impact of survival-related selection bias has not always been discussed in relevant studies of racial health disparities. Moreover, the analytic approaches most frequently employed in the epidemiologic literature to minimize selection bias are difficult to implement appropriately in racial disparities research. This difficulty stems from the fact that frequently employed analytic techniques require that common causes of survival and the outcome are accurately measured. Unfortunately, such common causes are often unmeasured or poorly measured in racial health disparities studies. In the absence of accurate measures of the aforementioned common causes, redefining the target population or changing the study design represents a useful approach for reducing the extent of survival-related selection bias. To help researchers recognize and minimize survival-related selection bias in racial health disparities studies, we illustrate the aforementioned selection bias and how redefining the target population or changing the study design can be useful.

A Bayesian semiparametric latent variable approach to causal mediation

In assessing causal mediation effects in randomized studies, a challenge is that the direct and indirect effects can vary across participants due to different measured and unmeasured characteristics. In that case, the population effect estimated from standard approaches implicitly averages over and does not estimate the heterogeneous direct and indirect effects. We propose a Bayesian semiparametric method to estimate heterogeneous direct and indirect effects via clusters, where the clusters are formed by both individual covariate profiles and individual effects due to unmeasured characteristics. These cluster-specific direct and indirect effects can be estimated through a set of regression models where specific coefficients are clustered by a stick-breaking prior. To let clustering be appropriately informed by individual direct and indirect effects, we specify a data-dependent prior. We conduct simulation studies to assess performance of the proposed method compared to other methods. We use this approach to estimate heterogeneous causal direct and indirect effects of an expressive writing intervention for patients with renal cell carcinoma.

Links between causal effects and causal association for surrogacy evaluation in a gaussian setting

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.

Bounding the per-protocol effect in randomized trials: an application to colorectal cancer screening

Background

The per-protocol effect is the effect that would have been observed in a randomized trial had everybody followed the protocol. Though obtaining a valid point estimate for the per-protocol effect requires assumptions that are unverifiable and often implausible, lower and upper bounds for the per-protocol effect may be estimated under more plausible assumptions. Strategies for obtaining bounds, known as “partial identification” methods, are especially promising in randomized trials.

Results

We estimated bounds for the per-protocol effect of colorectal cancer screening in the Norwegian Colorectal Cancer Prevention trial, a randomized trial of one-time sigmoidoscopy screening in 98,792 men and women aged 50–64 years. The screening was not available to the control arm, while approximately two thirds of individuals in the treatment arm attended the screening. Study outcomes included colorectal cancer incidence and mortality over 10 years of follow-up. Without any assumptions, the data alone provide little information about the size of the effect. Under the assumption that randomization had no effect on the outcome except through screening, a point estimate for the risk under no screening and bounds for the risk under screening are achievable. Thus, the 10-year risk difference for colorectal cancer was estimated to be at least −0.6 % but less than 37.0 %. Bounds for the risk difference for colorectal cancer mortality (–0.2 to 37.4 %) and all-cause mortality (–5.1 to 32.6 %) had similar widths. These bounds appear helpful in quantifying the maximum possible effectiveness, but cannot rule out harm. By making further assumptions about the effect in the subpopulation who would not attend screening regardless of their randomization arm, narrower bounds can be achieved.

Conclusions

Bounding the per-protocol effect under several sets of assumptions illuminates our reliance on unverifiable assumptions, highlights the range of effect sizes we are most confident in, and can sometimes demonstrate whether to expect certain subpopulations to receive more benefit or harm than others.

Trial registration

Clinicaltrials.gov identifier NCT00119912 (registered 6 July 2005)

Electronic supplementary material

The online version of this article (doi:10.1186/s13063-015-1056-8) contains supplementary material, which is available to authorized users.

Simple Estimation of Patient-Oriented Effects From Randomized Trials: An Open and Shut CACE

In randomized controlled trials, the intention-to-treat estimator provides an unbiased estimate of the causal effect of treatment assignment on the outcome. However, patients often want to know what the effect would be if they were to take the treatment as prescribed (the patient-oriented effect), and several researchers have suggested that the more relevant causal effect for this question is the complier average causal effect (CACE), also referred to as the local average treatment effect. Sophisticated approaches to estimating the CACE include Bayesian and frequentist methods for principal stratification, inverse-probability-of-treatment-weighted estimators, and instrumental-variable (IV) analysis. All of these approaches exploit information about adherence to assigned treatment to improve upon the intention-to-treat estimator, but they are rarely used in practice, probably because of their complexity. The IV principal stratification estimator is simple to implement but has had limited use in practice, possibly due to lack of familiarity. Here, we show that the IV principal stratification estimator is a modified per-protocol estimator that should be obtainable from any randomized controlled trial, and we provide a closed form for its robust variance (and its uncertainty). Finally, we illustrate sensitivity analyses we conducted to assess inference in light of potential violations of the exclusion restriction assumption.

Surrogate Endpoint Evaluation: Principal Stratification Criteria and the Prentice Definition

A common problem of interest within a randomized clinical trial is the evaluation of an inexpensive response endpoint as a valid surrogate endpoint for a clinical endpoint, where a chief purpose of a valid surrogate is to provide a way to make correct inferences on clinical treatment effects in future studies without needing to collect the clinical endpoint data. Within the principal stratification framework for addressing this problem based on data from a single randomized clinical efficacy trial, a variety of definitions and criteria for a good surrogate endpoint have been proposed, all based on or closely related to the "principal effects" or "causal effect predictiveness (CEP)" surface. We discuss CEP-based criteria for a useful surrogate endpoint, including (1) the meaning and relative importance of proposed criteria including average causal necessity (ACN), average causal sufficiency (ACS), and large clinical effect modification; (2) the relationship between these criteria and the Prentice definition of a valid surrogate endpoint; and (3) the relationship between these criteria and the consistency criterion (i.e., assurance against the "surrogate paradox"). This includes the result that ACN plus a strong version of ACS generally do not imply the Prentice definition nor the consistency criterion, but they do have these implications in special cases. Moreover, the converse does not hold except in a special case with a binary candidate surrogate. The results highlight that assumptions about the treatment effect on the clinical endpoint before the candidate surrogate is measured are influential for the ability to draw conclusions about the Prentice definition or consistency. In addition, we emphasize that in some scenarios that occur commonly in practice, the principal strata sub-populations for inference are identifiable from the observable data, in which cases the principal stratification framework has relatively high utility for the purpose of effect modification analysis, and is closely connected to the treatment marker selection problem. The results are illustrated with application to a vaccine efficacy trial, where ACN and ACS for an antibody marker are found to be consistent with the data and hence support the Prentice definition and consistency.

Are all biases missing data problems?

Estimating causal effects is a frequent goal of epidemiologic studies. Traditionally, there have been three established systematic threats to consistent estimation of causal effects. These three threats are bias due to confounders, selection, and measurement error. Confounding, selection, and measurement bias have typically been characterized as distinct types of biases. However, each of these biases can also be characterized as missing data problems that can be addressed with missing data solutions. Here we describe how the aforementioned systematic threats arise from missing data as well as review methods and their related assumptions for reducing each bias type. We also link the assumptions made by the reviewed methods to the missing completely at random (MCAR) and missing at random (MAR) assumptions made in the missing data framework that allow for valid inferences to be made based on the observed, incomplete data.

Causal inference methods to assess safety upper bounds in randomized trials with noncompliance

BACKGROUND

Premature discontinuation and other forms of noncompliance with treatment assignment can complicate causal inference of treatment effects in randomized trials. The intent-to-treat analysis gives unbiased estimates for causal effects of treatment assignment on outcome, but may understate potential benefit or harm of actual treatment. The corresponding upper confidence limit can also be underestimated.

PURPOSE

To compare estimates of the hazard ratio and upper bound of the two-sided 95% confidence interval from causal inference methods that account for noncompliance with those from the intent-to-treat analysis.

METHODS

We used simulations with parameters chosen to reflect cardiovascular safety trials of diabetes drugs, with a focus on upper bound estimates relative to 1.3, based on regulatory guidelines. A total of 1000 simulations were run under each parameter combination for a hypothetical trial of 10,000 total subjects randomly assigned to active treatment or control at 1:1 ratio. Noncompliance was considered in the form of treatment discontinuation and cross-over at specified proportions, with an assumed true hazard ratio of 0.9, 1, and 1.3, respectively. Various levels of risk associated with being a non-complier (independent of treatment status) were evaluated. Hazard ratio and upper bound estimates from causal survival analysis and intent-to-treat were obtained from each simulation and summarized under each parameter setting.

RESULTS

Causal analysis estimated the true hazard ratio with little bias in almost all settings examined. Intent-to-treat was unbiased only when the true hazard ratio = 1; otherwise it underestimated both benefit and harm. When upper bound estimates from intent-to-treat were ≥1.3, corresponding estimates from causal analysis were also ≥1.3 in almost 100% of the simulations, regardless of the true hazard ratio. When upper bound estimates from intent-to-treat were <1.3 and the true hazard ratio = 1, corresponding upper bound estimates from causal analysis were ≥1.3 in up to 66% of the simulations under some settings.

LIMITATIONS

Simulations cannot cover all scenarios for noncompliance in real randomized trials.

CONCLUSION

Causal survival analysis was superior to intent-to-treat in estimating the true hazard ratio with respect to bias in the presence of noncompliance. However, its large variance should be considered for safety upper bound exclusion especially when the true hazard ratio = 1. Our simulations provided a broad reference for practical considerations of bias-variance trade-off in dealing with noncompliance in cardiovascular safety trials of diabetes drugs. Further research is warranted for the development and application of causal inference methods in the evaluation of safety upper bounds.

Estimating the health benefit of reducing indoor air pollution in a randomized environmental intervention

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

Inference for environmental intervention studies using principal stratification

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

Comparing and combining biomarkers as principal surrogates for time-to-event clinical endpoints

Principal surrogate endpoints are useful as targets for phase I and II trials. In many recent trials, multiple post-randomization biomarkers are measured. However, few statistical methods exist for comparison of or combination of biomarkers as principal surrogates, and none of these methods to our knowledge utilize time-to-event clinical endpoint information. We propose a Weibull model extension of the semi-parametric estimated maximum likelihood method that allows for the inclusion of multiple biomarkers in the same risk model as multivariate candidate principal surrogates. We propose several methods for comparing candidate principal surrogates and evaluating multivariate principal surrogates. These include the time-dependent and surrogate-dependent true and false positive fraction, the time-dependent and the integrated standardized total gain, and the cumulative distribution function of the risk difference. We illustrate the operating characteristics of our proposed methods in simulations and outline how these statistics can be used to evaluate and compare candidate principal surrogates. We use these methods to investigate candidate surrogates in the Diabetes Control and Complications Trial.

A principal stratification approach for evaluating natural direct and indirect effects in the presence of treatment-induced intermediate confounding

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

Sharpening bounds on principal effects with covariates

Estimation of treatment effects in randomized studies is often hampered by possible selection bias induced by conditioning on or adjusting for a variable measured post-randomization. One approach to obviate such selection bias is to consider inference about treatment effects within principal strata, that is, principal effects. A challenge with this approach is that without strong assumptions principal effects are not identifiable from the observable data. In settings where such assumptions are dubious, identifiable large sample bounds may be the preferred target of inference. In practice these bounds may be wide and not particularly informative. In this work we consider whether bounds on principal effects can be improved by adjusting for a categorical baseline covariate. Adjusted bounds are considered which are shown to never be wider than the unadjusted bounds. Necessary and sufficient conditions are given for which the adjusted bounds will be sharper (i.e., narrower) than the unadjusted bounds. The methods are illustrated using data from a recent, large study of interventions to prevent mother-to-child transmission of HIV through breastfeeding. Using a baseline covariate indicating low birth weight, the estimated adjusted bounds for the principal effect of interest are 63% narrower than the estimated unadjusted bounds.

Surrogacy assessment using principal stratification when surrogate and outcome measures are multivariate normal

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