A mixed model approach to estimate the survivor average causal effect in cluster-randomized trials.

In many medical studies, the outcome measure (such as quality of life, QOL) for some study participants becomes informatively truncated (censored, missing, or unobserved) due to death or other forms of dropout, creating a nonignorable missing data problem. In such cases, the use of a composite outcome or imputation methods that fill in unmeasurable QOL values for those who died rely on strong and untestable assumptions and may be conceptually unappealing to certain stakeholders when estimating a treatment effect. The survivor average causal effect (SACE) is an alternative causal estimand that surmounts some of these issues. While principal stratification has been applied to estimate the SACE in individually randomized trials, methods for estimating the SACE in cluster-randomized trials are currently limited. To address this gap, we develop a mixed model approach along with an expectation-maximization algorithm to estimate the SACE in cluster-randomized trials. We model the continuous outcome measure with a random intercept to account for intracluster correlations due to cluster-level randomization, and model the principal strata membership both with and without a random intercept. In simulations, we compare the performance of our approaches with an existing fixed-effects approach to illustrate the importance of accounting for clustering in cluster-randomized trials. The methodology is then illustrated using a cluster-randomized trial of telecare and assistive technology on health-related QOL in the elderly.

Sociodemographic correlates of late HIV diagnosis among men who have sex with men (MSM) in Ghana.

Timely HIV diagnosis and medical engagement are crucial for effective viral load suppression and treatment as prevention. However, significant delays persist, particularly in Africa, including Ghana. This study focused on Ghanaian men whose route of exposure to HIV was through same-gender sexual contact (MSM), a group disproportionately impacted by HIV. Using structured surveys, we investigated the sociodemographic factors associated with late HIV diagnosis, a topic with limited existing research. Results indicate that older age groups were associated with an increased risk of late diagnosis compared to the 18-24 age group. Among the demographic variables studied, only age showed a consistent association with late HIV diagnosis. This study underscores the importance of targeted interventions to address HIV diagnosis disparities among MSM in Ghana, particularly for older age groups. The findings emphasize the need for tailored interventions addressing age-related disparities in timely diagnosis and engagement with medical services among this population. Such interventions can play a crucial role in reducing the burden of HIV within this community and fostering improved public health outcomes.

Hierarchical Bayesian modeling of heterogeneous outcome variance in cluster randomized trials.

BACKGROUND: Heterogeneous outcome correlations across treatment arms and clusters have been increasingly acknowledged in cluster randomized trials with binary endpoints, where analytical methods have been developed to study such heterogeneity. However, cluster-specific outcome variances and correlations have yet to be studied for cluster randomized trials with continuous outcomes. METHODS: This article proposes models fitted in the Bayesian setting with hierarchical variance structure to quantify heterogeneous variances across clusters and explain it with cluster-level covariates when the outcome is continuous. The models can also be extended to analyzing heterogeneous variances in individually randomized group treatment trials, with arm-specific cluster-level covariates, or in partially nested designs. Simulation studies are carried out to validate the performance of the newly introduced models across different settings. RESULTS: Simulations showed that overall the newly introduced models have good performance, reporting low bias and approximately 95% coverage for the intraclass correlation coefficients and regression parameters in the variance model. When variances are heterogeneous, our proposed models had improved model fit over models with homogeneous variances. When used to analyze data from the Kerala Diabetes Prevention Program study, our models identified heterogeneous variances and intraclass correlation coefficients across clusters and examined cluster-level characteristics associated with such heterogeneity. CONCLUSION: We proposed new hierarchical Bayesian variance models to accommodate cluster-specific variances in cluster randomized trials. The newly developed methods inform the understanding of how an intervention strategy is implemented and disseminated differently across clusters and can help improve future trial design.

Adherence to key recommendations for design and analysis of stepped-wedge cluster randomized trials: A review of trials published 2016-2022.

BACKGROUND/AIMS: The stepped-wedge cluster randomized trial (SW-CRT), in which clusters are randomized to a time at which they will transition to the intervention condition - rather than a trial arm - is a relatively new design. SW-CRTs have additional design and analytical considerations compared to conventional parallel arm trials. To inform future methodological development, including guidance for trialists and the selection of parameters for statistical simulation studies, we conducted a review of recently published SW-CRTs. Specific objectives were to describe (1) the types of designs used in practice, (2) adherence to key requirements for statistical analysis, and (3) practices around covariate adjustment. We also examined changes in adherence over time and by journal impact factor. METHODS: We used electronic searches to identify primary reports of SW-CRTs published 2016-2022. Two reviewers extracted information from each trial report and its protocol, if available, and resolved disagreements through discussion. RESULTS: We identified 160 eligible trials, randomizing a median (Q1-Q3) of 11 (8-18) clusters to 5 (4-7) sequences. The majority (122, 76%) were cross-sectional (almost all with continuous recruitment), 23 (14%) were closed cohorts and 15 (9%) open cohorts. Many trials had complex design features such as multiple or multivariate primary outcomes (50, 31%) or time-dependent repeated measures (27, 22%). The most common type of primary outcome was binary (51%); continuous outcomes were less common (26%). The most frequently used method of analysis was a generalized linear mixed model (112, 70%); generalized estimating equations were used less frequently (12, 8%). Among 142 trials with fewer than 40 clusters, only 9 (6%) reported using methods appropriate for a small number of clusters. Statistical analyses clearly adjusted for time effects in 119 (74%), for within-cluster correlations in 132 (83%), and for distinct between-period correlations in 13 (8%). Covariates were included in the primary analysis of the primary outcome in 82 (51%) and were most often individual-level covariates; however, clear and complete pre-specification of covariates was uncommon. Adherence to some key methodological requirements (adjusting for time effects, accounting for within-period correlation) was higher among trials published in higher versus lower impact factor journals. Substantial improvements over time were not observed although a slight improvement was observed in the proportion accounting for a distinct between-period correlation. CONCLUSIONS: Future methods development should prioritize methods for SW-CRTs with binary or time-to-event outcomes, small numbers of clusters, continuous recruitment designs, multivariate outcomes, or time-dependent repeated measures. Trialists, journal editors, and peer reviewers should be aware that SW-CRTs have additional methodological requirements over parallel arm designs including the need to account for period effects as well as complex intracluster correlations.

Designing multicenter individually randomized group treatment trials.

In an individually randomized group treatment (IRGT) trial, participant outcomes can be positively correlated due to, for example, shared therapists in treatment delivery. Oftentimes, because of limited treatment resources or participants at one location, an IRGT trial can be carried out across multiple centers. This design can be subject to potential correlations in the participant outcomes between arms within the same center. While the design of a single-center IRGT trial has been studied, little is known about the planning of a multicenter IRGT trial. To address this gap, this paper provides analytical sample size formulas for designing multicenter IRGT trials with a continuous endpoint under the linear mixed model framework. We found that accounting for the additional center-level correlation at the design stage can lead to sample size reduction, and the magnitude of reduction depends on the amount of between-therapist correlation. However, if the variance components of therapist-level random effects are considered as input parameters in the design stage, accounting for the additional center-level variance component has no impact on the sample size estimation. We presented our findings through numeric illustrations and performed simulation studies to validate our sample size procedures under different scenarios. Optimal design configurations under the multicenter IRGT trials have also been discussed, and two real-world trial examples are drawn to illustrate the use of our method.

A Bayesian Approach for Estimating the Survivor Average Causal Effect When Outcomes Are Truncated by Death in Cluster-Randomized Trials.

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

Adult criminal outcomes of juvenile justice involvement.

BACKGROUND: The juvenile justice system in the USA adjudicates over seven hundred thousand youth in the USA annually with significant behavioral offenses. This study aimed to test the effect of juvenile justice involvement on adult criminal outcomes. METHODS: Analyses were based on a prospective, population-based study of 1420 children followed up to eight times during childhood (ages 9-16; 6674 observations) about juvenile justice involvement in the late 1990 and early 2000s. Participants were followed up years later to assess adult criminality, using self-report and official records. A propensity score (i.e. inverse probability) weighting approach was used that approximated an experimental design by balancing potentially confounding characteristics between children with v. without juvenile justice involvement. RESULTS: Between-groups differences on variables that elicit a juvenile justice referral (e.g. violence, property offenses, status offenses, and substance misuse) were attenuated after applying propensity-based inverse probability weights. Participants with a history of juvenile justice involvement were more likely to have later official and violent felony charges, and to self-report police contact and spending time in jail (ORs from 2.5 to 3.3). Residential juvenile justice involvement was associated with the highest risk of both, later official criminal records and self-reported criminality (ORs from 5.1 to 14.5). Sensitivity analyses suggest that our findings are likely robust to potential unobserved confounders. CONCLUSIONS: Juvenile justice involvement was associated with increased risk of adult criminality, with residential services associated with highest risk. Juvenile justice involvement may catalyze rather than deter from adult offending.

Cultural contributions to adults' self-rated mental health problems and strengths: 7 culture clusters, 28 societies, 16 906 adults.

BACKGROUND: It is unknown how much variation in adult mental health problems is associated with differences between societal/cultural groups, over and above differences between individuals. METHODS: To test these relative contributions, a consortium of indigenous researchers collected Adult Self-Report (ASR) ratings from 16 906 18- to 59-year-olds in 28 societies that represented seven culture clusters identified in the Global Leadership and Organizational Behavioral Effectiveness study (e.g. Confucian, Anglo). The ASR is scored on 17 problem scales, plus a personal strengths scale. Hierarchical linear modeling estimated variance accounted for by individual differences (including measurement error), society, and culture cluster. Multi-level analyses of covariance tested age and gender effects. RESULTS: Across the 17 problem scales, the variance accounted for by individual differences ranged from 80.3% for DSM-oriented anxiety problems to 95.2% for DSM-oriented avoidant personality (mean = 90.7%); by society: 3.2% for DSM-oriented somatic problems to 8.0% for DSM-oriented anxiety problems (mean = 6.3%); and by culture cluster: 0.0% for DSM-oriented avoidant personality to 11.6% for DSM-oriented anxiety problems (mean = 3.0%). For strengths, individual differences accounted for 80.8% of variance, societal differences 10.5%, and cultural differences 8.7%. Age and gender had very small effects. CONCLUSIONS: Overall, adults' self-ratings of mental health problems and strengths were associated much more with individual differences than societal/cultural differences, although this varied across scales. These findings support cross-cultural use of standardized measures to assess mental health problems, but urge caution in assessment of personal strengths.

Sample size considerations for assessing treatment effect heterogeneity in randomized trials with heterogeneous intracluster correlations and variances.

An important consideration in the design and analysis of randomized trials is the need to account for outcome observations being positively correlated within groups or clusters. Two notable types of designs with this consideration are individually randomized group treatment trials and cluster randomized trials. While sample size methods for testing the average treatment effect are available for both types of designs, methods for detecting treatment effect modification are relatively limited. In this article, we present new sample size formulas for testing treatment effect modification based on either a univariate or multivariate effect modifier in both individually randomized group treatment and cluster randomized trials with a continuous outcome but any types of effect modifier, while accounting for differences across study arms in the outcome variance, outcome intracluster correlation coefficient (ICC) and the cluster size. We consider cases where the effect modifier can be measured at either the individual level or cluster level, and with a univariate effect modifier, our closed-form sample size expressions provide insights into the optimal allocation of groups or clusters to maximize design efficiency. Overall, our results show that the required sample size for testing treatment effect heterogeneity with an individual-level effect modifier can be affected by unequal ICCs and variances between arms, and accounting for such between-arm heterogeneity can lead to more accurate sample size determination. We use simulations to validate our sample size formulas and illustrate their application in the context of two real trials: an individually randomized group treatment trial (the AWARE study) and a cluster randomized trial (the K-DPP study).

Accounting for expected attrition in the planning of cluster randomized trials for assessing treatment effect heterogeneity.

BACKGROUND: Detecting treatment effect heterogeneity is an important objective in cluster randomized trials and implementation research. While sample size procedures for testing the average treatment effect accounting for participant attrition assuming missing completely at random or missing at random have been previously developed, the impact of attrition on the power for detecting heterogeneous treatment effects in cluster randomized trials remains unknown. METHODS: We provide a sample size formula for testing for a heterogeneous treatment effect assuming the outcome is missing completely at random. We also propose an efficient Monte Carlo sample size procedure for assessing heterogeneous treatment effect assuming covariate-dependent outcome missingness (missing at random). We compare our sample size methods with the direct inflation method that divides the estimated sample size by the mean follow-up rate. We also evaluate our methods through simulation studies and illustrate them with a real-world example. RESULTS: Simulation results show that our proposed sample size methods under both missing completely at random and missing at random provide sufficient power for assessing heterogeneous treatment effect. The proposed sample size methods lead to more accurate sample size estimates than the direct inflation method when the missingness rate is high (e.g., ≥ 30%). Moreover, sample size estimation under both missing completely at random and missing at random is sensitive to the missingness rate, but not sensitive to the intracluster correlation coefficient among the missingness indicators. CONCLUSION: Our new sample size methods can assist in planning cluster randomized trials that plan to assess a heterogeneous treatment effect and participant attrition is expected to occur.

Trusted residents and housing assistance to decrease violence exposure in New Haven (TRUE HAVEN): a strengths-based and community-driven stepped-wedge intervention to reduce gun violence.

BACKGROUND: We describe the rationale and study design for "TRUsted rEsidents and Housing Assistance to decrease Violence Exposure in New Haven (TRUE HAVEN)," a prospective type 1 hybrid effectiveness/implementation study of a multi-level intervention using a stepped wedge design. TRUE HAVEN aims to lower rates of community gun violence by fostering the stability, wealth, and well-being of individuals and families directly impacted by incarceration through the provision of stable housing and by breaking the cycle of trauma. DESIGN: TRUE HAVEN is an ongoing, multi-level intervention with three primary components: financial education paired with housing support (individual level), trauma-informed counseling (neighborhood level), and policy changes to address structural racism (city/state level). Six neighborhoods with among the highest rates of gun violence in New Haven, Connecticut, will receive the individual and neighborhood level intervention components sequentially beginning at staggered 6-month steps. Residents of these neighborhoods will be eligible to participate in the housing stability and financial education component if they were recently incarcerated or are family members of currently incarcerated people; participants will receive intense financial education and follow-up for six months and be eligible for special down payment and rental assistance programs. In addition, trusted community members and organization leaders within each target neighborhood will participate in trauma-informed care training sessions to then be able to recognize when their peers are suffering from trauma symptoms, to support these affected peers, and to destigmatize accessing professional mental health services and connect them to these services when needed. Finally, a multi-stakeholder coalition will be convened to address policies that act as barriers to housing stability or accessing mental healthcare. Interventions will be delivered through existing partnerships with community-based organizations and networks. The primary outcome is neighborhood rate of incident gun violence. To inform future implementation and optimize the intervention package as the study progresses, we will use the Learn As You Go approach to optimize and assess the effectiveness of the intervention package on the primary study outcome. DISCUSSION: Results from this protocol will yield novel evidence for whether and how addressing structural racism citywide leads to a reduction in gun violence. TRIAL REGISTRATION: ClinicalTrials.gov Identifier: NCT05723614. Registration date: February 01, 2023. Please refer to https://clinicaltrials.gov/ct2/show/NCT05723614 for public and scientific inquiries.

Accounting for unequal cluster sizes in designing cluster randomized trials to detect treatment effect heterogeneity.

Unequal cluster sizes are common in cluster randomized trials (CRTs). While there are a number of previous investigations studying the impact of unequal cluster sizes on the power for testing the average treatment effect in CRTs, little is known about the impact of unequal cluster sizes on the power for testing the heterogeneous treatment effect (HTE) in CRTs. In this work, we expand the sample size procedures for studying HTE in CRTs to accommodate cluster size variation under the linear mixed model framework. Through analytical derivation and graphical exploration, we show that the sample size for the HTE with an individual-level effect modifier is less affected by unequal cluster sizes than with a cluster-level effect modifier. The impact of cluster size variability jointly depends on the mean and coefficient of variation of cluster sizes, covariate intraclass correlation coefficient (ICC) and the conditional outcome ICC. In addition, we demonstrate that the HTE-motivated analysis of covariance framework can be used for analyzing the average treatment effect, and offer a more efficient sample size procedure for studying the average treatment effect adjusting for the effect modifier. We use simulations to confirm the accuracy of the proposed sample size procedures for both the average treatment effect and HTE in CRTs. Extensions to multivariate effect modifiers are provided and our procedure is illustrated in the context of the Strategies to Reduce Injuries and Develop Confidence in Elders trial.

Sample size calculation in hierarchical 2×2 factorial trials with unequal cluster sizes.

Motivated by a suicide prevention trial with hierarchical treatment allocation (cluster-level and individual-level treatments), we address the sample size requirements for testing the treatment effects as well as their interaction. We assume a linear mixed model, within which two types of treatment effect estimands (controlled effect and marginal effect) are defined. For each null hypothesis corresponding to an estimand, we derive sample size formulas based on large-sample z-approximation, and provide finite-sample modifications based on a t-approximation. We relax the equal cluster size assumption and express the sample size formulas as functions of the mean and coefficient of variation of cluster sizes. We show that the sample size requirement for testing the controlled effect of the cluster-level treatment is more sensitive to cluster size variability than that for testing the controlled effect of the individual-level treatment; the same observation holds for testing the marginal effects. In addition, we show that the sample size for testing the interaction effect is proportional to that for testing the controlled or the marginal effect of the individual-level treatment. We conduct extensive simulations to validate the proposed sample size formulas, and find the empirical power agrees well with the predicted power for each test. Furthermore, the t-approximations often provide better control of type I error rate with a small number of clusters. Finally, we illustrate our sample size formulas to design the motivating suicide prevention factorial trial. The proposed methods are implemented in the R package H2x2Factorial.

Gun violence among young adults with a juvenile crime record in North Carolina: Implications for firearm restrictions based on age and risk.

Youth who acquire a juvenile crime record may be at increased risk of perpetrating gun violence as adults. North Carolina and 22 other states permit young adults who were adjudicated by a juvenile court - even for some felony-equivalent offenses - to legally access firearms. Effectiveness of gun restrictions for adults with juvenile crime histories has not been systematically studied. This article reports findings from a longitudinal study of arrests and convictions for gun-involved and other offenses in 51,059 young adults in North Carolina, comparing those with gun-disqualifying and not-disqualifying juvenile records. The annualized rate of arrest for gun-involved crime in those with a felony-level juvenile record was 9 times higher than the rate of reported comparable offenses in the same age group in the North Carolina general population (3349 vs. 376 per 100,000). Among those with a felony-equivalent juvenile delinquency adjudication who became legally eligible to possess firearms at age 18, 61.8% were later arrested for any criminal offense, 14.3% for a firearm-involved offense. Crimes with guns were most likely to occur among young adults who had committed more serious (felony or equivalent) offenses before age 18; had been adjudicated at younger ages; acquired a felony conviction as a youth; and spent time in prison. The prevalence of arrests for crimes involving guns among young adults in North Carolina with a gun-disqualifying felony record acquired before age 18 suggests that the federal gun prohibitor conferred by a felony record is not highly effective as currently implemented in this population. From a risk-based perspective, these restrictions appear to be justified; better implementation and enforcement may improve their effectiveness. Gun crime prevention policies and interventions should focus on these populations and on limiting illegal access to firearms.

Impact of complex, partially nested clustering in a three-arm individually randomized group treatment trial: A case study with the wHOPE trial.

BACKGROUND/AIMS: When participants in individually randomized group treatment trials are treated by multiple clinicians or in multiple group treatment sessions throughout the trial, this induces partially nested clusters which can affect the power of a trial. We investigate this issue in the Whole Health Options and Pain Education trial, a three-arm pragmatic, individually randomized clinical trial. We evaluate whether partial clusters due to multiple visits delivered by different clinicians in the Whole Health Team arm and dynamic participant groups due to changing group leaders and/or participants across treatment sessions during treatment delivery in the Primary Care Group Education arm may impact the power of the trial. We also present a Bayesian approach to estimate the intraclass correlation coefficients. METHODS: We present statistical models for each treatment arm of Whole Health Options and Pain Education trial in which power is estimated under different intraclass correlation coefficients and mapping matrices between participants and clinicians or treatment sessions. Power calculations are based on pairwise comparisons. In practice, sample size calculations depend on estimates of the intraclass correlation coefficients at the treatment sessions and clinician levels. To accommodate such complexities, we present a Bayesian framework for the estimation of intraclass correlation coefficients under different participant-to-session and participant-to-clinician mapping scenarios. We simulated continuous outcome data based on various clinical scenarios in Whole Health Options and Pain Education trial using a range of intraclass correlation coefficients and mapping matrices and used Gibbs samplers with conjugate priors to obtain posteriors of the intraclass correlation coefficients under those different scenarios. Posterior means and medians and their biases are calculated for the intraclass correlation coefficients to evaluate the operating characteristics of the Bayesian intraclass correlation coefficient estimators. RESULTS: Power for Whole Health Team versus Primary Care Group Education is sensitive to the intraclass correlation coefficient in the Whole Health Team arm. In these two arms, an increased number of clinicians, more evenly distributed workload of clinicians, or more homogeneous treatment group sizes leads to increased power. Our simulation study for the intraclass correlation coefficient estimation indicates that the posterior mean intraclass correlation coefficient estimator has less bias when the true intraclass correlation coefficients are large (i.e. 0.10), but when the intraclass correlation coefficient is small (i.e. 0.01), the posterior median intraclass correlation coefficient estimator is less biased. CONCLUSION: Knowledge of intraclass correlation coefficients and the structure of clustering are critical to the design of individually randomized group treatment trials with partially nested clusters. We demonstrate that the intraclass correlation coefficient of the Whole Health Team arm can affect power in the Whole Health Options and Pain Education trial. A Bayesian approach provides a flexible procedure for estimating the intraclass correlation coefficients under complex scenarios. More work is needed to educate the research community about the individually randomized group treatment design and encourage publication of intraclass correlation coefficients to help inform future trial designs.

Meta-Analysis in Sociological Research: Power and Heterogeneity.

Meta-analysis is a statistical method that combines quantitative findings from previous studies. It has been increasingly used to obtain more credible results in a wide range of scientific fields. Combining the results of relevant studies allows researchers to leverage study similarities while modeling potential sources of between-study heterogeneity. This paper provides a review of the core methodologies of meta-analysis that we consider most relevant to sociological research. After developing the foundation of the fixed-effects and random-effects models of meta-analysis, this paper illustrates the utility of the method with regression coefficients reported from two sets of social science studies. We explain the various steps of the process including constructing the meta-sample from primary studies; estimating the fixed- and random-effects models; analyzing the source of heterogeneity across studies; assessing publication bias. We conclude with a discussion of steps that could be taken to strengthen the development of meta-analysis in sociological research, which will eventually increase the credibility of sociological inquiry via a knowledge-cumulative process.

Sample size and power considerations for cluster randomized trials with count outcomes subject to right truncation.

Cluster randomized trials (CRTs) are widely used in epidemiological and public health studies assessing population-level effect of group-based interventions. One important application of CRTs is the control of vector-borne disease, such as malaria. However, a particular challenge for designing these trials is that the primary outcome involves counts of episodes that are subject to right truncation. While sample size formulas have been developed for CRTs with clustered counts, they are not directly applicable when the counts are right truncated. To address this limitation, we discuss two marginal modeling approaches for the analysis of CRTs with truncated counts and develop two corresponding closed-form sample size formulas to facilitate the design of such trials. The proposed sample size formulas allow investigators to explore the power under a large number of scenarios without computationally intensive simulations. The proposed formulas are validated in extensive simulations. We further explore the implication of right truncation on power and apply the proposed formulas to illustrate the power calculation for a malaria control CRT where the primary outcome is subject to right truncation.

A BAYESIAN MACHINE LEARNING APPROACH FOR ESTIMATING HETEROGENEOUS SURVIVOR CAUSAL EFFECTS: APPLICATIONS TO A CRITICAL CARE TRIAL.

Assessing heterogeneity in the effects of treatments has become increasingly popular in the field of causal inference and carries important implications for clinical decision-making. While extensive literature exists for studying treatment effect heterogeneity when outcomes are fully observed, there has been limited development in tools for estimating heterogeneous causal effects when patient-centered outcomes are truncated by a terminal event, such as death. Due to mortality occurring during study follow-up, the outcomes of interest are unobservable, undefined, or not fully observed for many participants in which case principal stratification is an appealing framework to draw valid causal conclusions. Motivated by the Acute Respiratory Distress Syndrome Network (ARDSNetwork) ARDS respiratory management (ARMA) trial, we developed a flexible Bayesian machine learning approach to estimate the average causal effect and heterogeneous causal effects among the always-survivors stratum when clinical outcomes are subject to truncation. We adopted Bayesian additive regression trees (BART) to flexibly specify separate mean models for the potential outcomes and latent stratum membership. In the analysis of the ARMA trial, we found that the low tidal volume treatment had an overall benefit for participants sustaining acute lung injuries on the outcome of time to returning home but substantial heterogeneity in treatment effects among the always-survivors, driven most strongly by biologic sex and the alveolar-arterial oxygen gradient at baseline (a physiologic measure of lung function and degree of hypoxemia). These findings illustrate how the proposed methodology could guide the prognostic enrichment of future trials in the field.

Correction: Parental supervision positively impacts children's economic prospects two decades later: A prospective longitudinal study.

[This corrects the article DOI: 10.1371/journal.pone.0286218.].