Phenotype-based targeted treatment of SGLT2 inhibitors and GLP-1 receptor agonists in type 2 diabetes

AIMS/HYPOTHESIS

A precision medicine approach in type 2 diabetes could enhance targeting specific glucose-lowering therapies to individual patients most likely to benefit. We aimed to use the recently developed Bayesian causal forest (BCF) method to develop and validate an individualised treatment selection algorithm for two major type 2 diabetes drug classes, sodium-glucose cotransporter 2 inhibitors (SGLT2i) and glucagon-like peptide-1 receptor agonists (GLP1-RA).

METHODS

We designed a predictive algorithm using BCF to estimate individual-level conditional average treatment effects for 12-month glycaemic outcome (HbA1c) between SGLT2i and GLP1-RA, based on routine clinical features of 46,394 people with type 2 diabetes in primary care in England (Clinical Practice Research Datalink; 27,319 for model development, 19,075 for hold-out validation), with additional external validation in 2252 people with type 2 diabetes from Scotland (SCI-Diabetes [Tayside & Fife]). Differences in glycaemic outcome with GLP1-RA by sex seen in clinical data were replicated in clinical trial data (HARMONY programme: liraglutide [n=389] and albiglutide [n=1682]). As secondary outcomes, we evaluated the impacts of targeting therapy based on glycaemic response on weight change, tolerability and longer-term risk of new-onset microvascular complications, macrovascular complications and adverse kidney events.

RESULTS

Model development identified marked heterogeneity in glycaemic response, with 4787 (17.5%) of the development cohort having a predicted HbA1c benefit >3 mmol/mol (>0.3%) with SGLT2i over GLP1-RA and 5551 (20.3%) having a predicted HbA1c benefit >3 mmol/mol with GLP1-RA over SGLT2i. Calibration was good in hold-back validation, and external validation in an independent Scottish dataset identified clear differences in glycaemic outcomes between those predicted to benefit from each therapy. Sex, with women markedly more responsive to GLP1-RA, was identified as a major treatment effect modifier in both the UK observational datasets and in clinical trial data: HARMONY-7 liraglutide (GLP1-RA): 4.4 mmol/mol (95% credible interval [95% CrI] 2.2, 6.3) (0.4% [95% CrI 0.2, 0.6]) greater response in women than men. Targeting the two therapies based on predicted glycaemic response was also associated with improvements in short-term tolerability and long-term risk of new-onset microvascular complications.

CONCLUSIONS/INTERPRETATION

Precision medicine approaches can facilitate effective individualised treatment choice between SGLT2i and GLP1-RA therapies, and the use of routinely collected clinical features for treatment selection could support low-cost deployment in many countries.

Comparing type 1 and type 2 error rates of different tests for heterogeneous treatment effects

Psychologists are increasingly interested in whether treatment effects vary in randomized controlled trials. A number of tests have been proposed in the causal inference literature to test for such heterogeneity, which differ in the sample statistic they use (either using the variance terms of the experimental and control group, their empirical distribution functions, or specific quantiles), and in whether they make distributional assumptions or are based on a Fisher randomization procedure. In this manuscript, we present the results of a simulation study in which we examine the performance of the different tests while varying the amount of treatment effect heterogeneity, the type of underlying distribution, the sample size, and whether an additional covariate is considered. Altogether, our results suggest that researchers should use a randomization test to optimally control for type 1 errors. Furthermore, all tests studied are associated with low power in case of small and moderate samples even when the heterogeneity of the treatment effect is substantial. This suggests that current tests for treatment effect heterogeneity require much larger samples than those collected in current research.

Heterogeneous treatment effect estimation for observational data using model-based forests

The estimation of heterogeneous treatment effects has attracted considerable interest in many disciplines, most prominently in medicine and economics. Contemporary research has so far primarily focused on continuous and binary responses where heterogeneous treatment effects are traditionally estimated by a linear model, which allows the estimation of constant or heterogeneous effects even under certain model misspecifications. More complex models for survival, count, or ordinal outcomes require stricter assumptions to reliably estimate the treatment effect. Most importantly, the noncollapsibility issue necessitates the joint estimation of treatment and prognostic effects. Model-based forests allow simultaneous estimation of covariate-dependent treatment and prognostic effects, but only for randomized trials. In this paper, we propose modifications to model-based forests to address the confounding issue in observational data. In particular, we evaluate an orthogonalization strategy originally proposed by Robinson (1988, Econometrica) in the context of model-based forests targeting heterogeneous treatment effect estimation in generalized linear models and transformation models. We found that this strategy reduces confounding effects in a simulated study with various outcome distributions. We demonstrate the practical aspects of heterogeneous treatment effect estimation for survival and ordinal outcomes by an assessment of the potentially heterogeneous effect of Riluzole on the progress of Amyotrophic Lateral Sclerosis.

The Collision of digital and green: Digital transformation and green economic efficiency

Enhancing the green economy efficiency (GEE) is crucial for building a sustainable economy. How can the rapidly advancing digital transformation contribute to this process? The paper empirically examines the direct and spatial spillover effects of digital transformation on cities' GEE in China. This study utilizes the National E-commerce Pilot City (NEPC) policy as a quasi-natural experiment of regional digital transformation and employs the staggered difference-in-differences (DID) method with heterogeneous effects. The findings reveal that (i) implementing the NEPC policy significantly increases urban GEE by 2.6%, corresponding to a 16% increase in the mean of GEE. This effect is particularly pronounced in non-resource-based cities and cities with high Internet penetration. (ii) The mechanism test shows that the pilot policy positively affects GEE by promoting green structural transformation, enhancing green innovation, and strengthening public environmental concerns. (iii) The study highlights a positive spatial spillover effect of the NEPC policy on the GEE of nonpilot cities. (iv) The adoption of the NEPC plays a pivotal role in advancing energy use and carbon emission efficiency. This paper expands the existing knowledge on the green development effects of the digital economy while offering valuable policy insights for building an "Inclusive Green Economy".

Fiscal centralization and urban industrial pollution emissions reduction: Evidence from the vertical reform of environmental administrations in China

The relationship between fiscal regimes and urban industrial pollution emissions is unclear. This paper aims to explore the effects and mechanisms of fiscal centralization on urban industrial pollution emissions and environmental quality. Using the vertical reform of environmental administrations (VREA) in China as a quasi-natural experiment of fiscal centralization, this study applies a staggered difference-in-differences (DID) model to explore the differences in industrial pollution emissions between centralization cities and decentralization cities. The main findings are: (1) VREA significantly inhibits regional industrial pollution emissions, and the reform effect increases over time. This conclusion still holds after considering a series of robustness issues. (2) Industrial sulfur dioxide (SO2) and solid particulate emissions in the fiscal centralization cities have decreased significantly by 0.3281% and 0.2240%, respectively. However, there is no significant change in industrial wastewater discharges. (3) Environmental regulations, environmental expenditures, and pollution control investments of local governments are the main channels through which VREA reduces industrial pollution emissions. (4) The effects of VREA are more significant in central and western cities and small cities. (5) Relative to decentralization cities, centralization cities have improved air and water quality by 0.0825% and 0.1628%, respectively. These findings help to accurately assess the effects of fiscal centralization on regional environmental governance and provide a decision-making reference for further deepening environmental centralization reform in China.

A flexible approach for predictive biomarker discovery

An endeavor central to precision medicine is predictive biomarker discovery; they define patient subpopulations which stand to benefit most, or least, from a given treatment. The identification of these biomarkers is often the byproduct of the related but fundamentally different task of treatment rule estimation. Using treatment rule estimation methods to identify predictive biomarkers in clinical trials where the number of covariates exceeds the number of participants often results in high false discovery rates. The higher than expected number of false positives translates to wasted resources when conducting follow-up experiments for drug target identification and diagnostic assay development. Patient outcomes are in turn negatively affected. We propose a variable importance parameter for directly assessing the importance of potentially predictive biomarkers and develop a flexible nonparametric inference procedure for this estimand. We prove that our estimator is double robust and asymptotically linear under loose conditions in the data-generating process, permitting valid inference about the importance metric. The statistical guarantees of the method are verified in a thorough simulation study representative of randomized control trials with moderate and high-dimensional covariate vectors. Our procedure is then used to discover predictive biomarkers from among the tumor gene expression data of metastatic renal cell carcinoma patients enrolled in recently completed clinical trials. We find that our approach more readily discerns predictive from nonpredictive biomarkers than procedures whose primary purpose is treatment rule estimation. An open-source software implementation of the methodology, the uniCATE R package, is briefly introduced.

Comparison of causal forest and regression-based approaches to evaluate treatment effect heterogeneity: an application for type 2 diabetes precision medicine

OBJECTIVE

Precision medicine requires reliable identification of variation in patient-level outcomes with different available treatments, often termed treatment effect heterogeneity. We aimed to evaluate the comparative utility of individualized treatment selection strategies based on predicted individual-level treatment effects from a causal forest machine learning algorithm and a penalized regression model.

METHODS

Cohort study characterizing individual-level glucose-lowering response (6 month reduction in HbA1c) in people with type 2 diabetes initiating SGLT2-inhibitor or DPP4-inhibitor therapy. Model development set comprised 1,428 participants in the CANTATA-D and CANTATA-D2 randomised clinical trials of SGLT2-inhibitors versus DPP4-inhibitors. For external validation, calibration of observed versus predicted differences in HbA1c in patient strata defined by size of predicted HbA1c benefit was evaluated in 18,741 patients in UK primary care (Clinical Practice Research Datalink).

RESULTS

Heterogeneity in treatment effects was detected in clinical trial participants with both approaches (proportion predicted to have a benefit on SGLT2-inhibitor therapy over DPP4-inhibitor therapy: causal forest: 98.6%; penalized regression: 81.7%). In validation, calibration was good with penalized regression but sub-optimal with causal forest. A strata with an HbA1c benefit > 10 mmol/mol with SGLT2-inhibitors (3.7% of patients, observed benefit 11.0 mmol/mol [95%CI 8.0-14.0]) was identified using penalized regression but not causal forest, and a much larger strata with an HbA1c benefit 5-10 mmol with SGLT2-inhibitors was identified with penalized regression (regression: 20.9% of patients, observed benefit 7.8 mmol/mol (95%CI 6.7-8.9); causal forest 11.6%, observed benefit 8.7 mmol/mol (95%CI 7.4-10.1).

CONCLUSIONS

Consistent with recent results for outcome prediction with clinical data, when evaluating treatment effect heterogeneity researchers should not rely on causal forest or other similar machine learning algorithms alone, and must compare outputs with standard regression, which in this evaluation was superior.

Bayesian Index Models for Heterogeneous Treatment Effects on a Binary Outcome

This paper develops a Bayesian model with a flexible link function connecting a binary treatment response to a linear combination of covariates and a treatment indicator and the interaction between the two. Generalized linear models allowing data-driven link functions are often called "single-index models" and are among popular semi-parametric modeling methods. In this paper, we focus on modeling heterogeneous treatment effects, with the goal of developing a treatment benefit index (TBI) incorporating prior information from historical data. The model makes inference on a composite moderator of treatment effects, summarizing the effect of the predictors within a single variable through a linear projection of the predictors. This treatment benefit index can be useful for stratifying patients according to their predicted treatment benefit levels and can be especially useful for precision health applications. The proposed method is applied to a COVID-19 treatment study.

The effect of COVID-19 on self-reported safety incidents in aviation: An examination of the heterogeneous effects using causal machine learning

INTRODUCTION

Disruptions to aviation operations occur daily on a micro-level with negligible impacts beyond the inconvenience of rebooking and changing aircrew schedules. The unprecedented disruption in global aviation due to COVID-19 highlighted a need to evaluate emergent safety issues rapidly.

METHOD

This paper uses causal machine learning to examine the heterogeneous effects of COVID-19 on reported aircraft incursions/excursions. The analysis utilized self report data from NASA Aviation Safety Reporting System collected from 2018 to 2020. The report attributes include self identified group characteristics and expert categorization of factors and outcomes. The analysis identified attributes and subgroup characteristics that were most sensitive to COVID-19 in inducing incursions/excursions. The method included the generalized random forest and difference-in-difference techniques to explore causal effects.

RESULTS

The analysis indicates first officers are more prone to experiencing incursion/excursion events during the pandemic. In addition, events categorized with the human factors confusion, distraction, and the causal factor fatigue increased incursion/excursion events.

PRACTICAL APPLICATIONS

Understanding the attributes associated with the likelihood of incursion/excursion events provides policymakers and aviation organizations insights to improve prevention mechanisms for future pandemics or extended periods of reduced aviation operations.

Refined moderation analysis with binary outcomes in precision medicine research

Moderation analysis for evaluating differential treatment effects serves as the bedrock of precision medicine, which is of growing interest in many fields. In the analysis of data with binary outcomes, we observe an interesting symmetry property concerning the ratio of odds ratios, which suggests that heterogeneous treatment effects could be equivalently estimated via a role exchange between the outcome and treatment variable in logistic regression models. We then obtain refined inference on moderating effects by rearranging data and combining two models into one via a generalized estimating equation approach. The improved efficiency is helpful in addressing the lack-of-power problem that is common in the search for important moderators. We investigate the proposed method by simulation and provide an illustration with data from a randomized trial on wart treatment.

Heterogeneous treatment effects analysis for social scientists: A review

Social scientists have long been interested in the varying responses to a specific intervention, motivating the enterprise of heterogeneous treatment effects (HTE) analysis. Over the past five decades, the rapid development of HTE methods, from conventional multiplicative interactions in linear models to explorations based on machine learning techniques, has been witnessed. This article presents a systematic review of major HTE methods, including multiplicative interaction modeling, generalized additive modeling, propensity-score-based methods, marginal treatment effect, separate LASSO constraints, causal trees, causal forests, Bayesian additive regression trees, and meta-learners (i.e., the S-learner, T-learner, X-learner, and R-learner). These methods, as described roughly in a chronological order to emphasize methodological developments, are addressed to highlight their respective strengths and limitations. Following an illustrative example, this article reflects on future methodological developments.

Estimating heterogeneous treatment effects in road safety analysis using generalized random forests

Numerous evaluation studies have been conducted on a variety of road safety measures. However, the issue of treatment heterogeneity, defined as the variation in treatment effects, has rarely been investigated before. This paper contributes to the literature by introducing generalized random forests (GRF) for estimation of heterogeneous treatment effects (HTEs) in road safety analysis. GRF has high functional flexibility and is able to search for complex treatment heterogeneity. We first perform a series of simulation experiments to compare GRF with three causal methods that have been used in road safety studies, i.e., outcome regression method, propensity score method, and doubly robust estimation method. The simulation results suggest that GRF is superior to these three methods in terms of model specification, especially with the existence of nonlinearity and nonadditivity. On the other hand, a large dataset is required for accurate GRF estimation. Then we conduct a case study on the UK's speed camera program. Our results indicate significant reductions in the number of road accidents at speed camera sites. And the heterogeneity in treatment effects is found to be statistically significant. We further consider the associations between the baseline accident records, traffic volume, local socio-economic characteristics, and the safety effects of speed cameras. In general, the effect of speed cameras is larger at the sites with more baseline accident records, higher traffic volume, and in more densely-populated and deprived areas. Several policy suggestions are provided based on these findings. The evaluation of HTEs likely offers more comprehensive information to local authorities and policy makers, and improves the performance of speed camera programs. Moreover, GRF can be a promising approach for revealing treatment effect heterogeneity in road safety analysis.

Teaching reproducible research for medical students and postgraduate pharmaceutical scientists

In medicine and other academic settings, (doctoral) students often work in interdisciplinary teams together with researchers of pharmaceutical sciences, natural sciences in general, or biostatistics. They should be fundamentally taught good research practices, especially in terms of statistical analysis. This includes reproducibility as a central aspect. Acknowledging that even experienced researchers and supervisors might be unfamiliar with necessary aspects of a perfectly reproducible workflow, a lecture series on reproducible research (RR) was developed for young scientists in clinical pharmacology. The pilot series highlighted definitions of RR, reasons for RR, potential merits of RR, and ways to work accordingly. In trying to actually reproduce a published analysis, several practical obstacles arose. In this article, reproduction of a working example is commented to emphasize the manifold facets of RR, to provide possible explanations for difficulties and solutions, and to argue that harmonized curricula for (quantitative) clinical researchers should include RR principles. These experiences should raise awareness among educators and students, supervisors and young scientists. RR working habits are not only beneficial for ourselves or our students, but also for other researchers within an institution, for scientific partners, for the scientific community, and eventually for the public profiting from research findings.

The long-run heterogeneous effects of a cholera pandemic on stature: Evidence from industrializing Japan

The recent COVID-19 pandemic poses the general question on how infectious diseases can persistently affect human health. A growing body of literature has found a significant amount of evidence on the long-term adverse effects of infectious diseases, such as influenza, typhoid fever, and yellow fever. However, we must be careful about the fact that little is known about the long-term consequences of the acute diarrheal disease pandemic cholera - Vibrio cholerae bacillus - which still threatens the health of the population in many developing countries. To bridge this gap in the body of knowledge, we utilized unique census-based data on army height at age 20 in early 20th-century Japan, with a difference-in-differences estimation strategy using regional variation in the intensity of cholera pandemics. We found that early-life exposure to a cholera pandemic had heterogeneous stunting effects on the final height of men; the magnitude of the stunting effects increased as the intensity of exposure increased.

Graphing and reporting heterogeneous treatment effects through reference classes

BACKGROUND

Exploration and modelling of heterogeneous treatment effects as a function of baseline covariates is an important aspect of precision medicine in randomised controlled trials (RCTs). Randomisation generally guarantees the internal validity of an RCT, but heterogeneity in treatment effect can reduce external validity. Estimation of heterogeneous treatment effects is usually done via a predictive model for individual outcomes, where one searches for interactions between treatment allocation and important patient baseline covariates. However, such models are prone to overfitting and multiple testing and typically demand a transformation of the outcome measurement, for example, from the absolute risk in the original RCT to log-odds of risk in the predictive model.

METHODS

We show how reference classes derived from baseline covariates can be used to explore heterogeneous treatment effects via a two-stage approach. We first estimate a risk score which captures on a single dimension some of the heterogeneity in outcomes of the trial population. Heterogeneity in the treatment effect can then be explored via reweighting schemes along this axis of variation. This two-stage approach bypasses the search for interactions with multiple covariates, thus protecting against multiple testing. It also allows for exploration of heterogeneous treatment effects on the original outcome scale of the RCT. This approach would typically be applied to multivariable models of baseline risk to assess the stability of average treatment effects with respect to the distribution of risk in the population studied.

CASE STUDY

We illustrate this approach using the single largest randomised treatment trial in severe falciparum malaria and demonstrate how the estimated treatment effect in terms of absolute mortality risk reduction increases considerably in higher risk strata.

CONCLUSIONS

'Local' and 'tilting' reweighting schemes based on ranking patients by baseline risk can be used as a general approach for exploring, graphing and reporting heterogeneity of treatment effect in RCTs.

TRIAL REGISTRATION

ISRCTN clinical trials registry: ISRCTN50258054. Prospectively registered on 22 July 2005.

Identifying treatment effects of an informal caregiver education intervention to increase days in the community and decrease caregiver distress: a machine-learning secondary analysis of subgroup effects in the HI-FIVES randomized clinical trial

BACKGROUND

Informal caregivers report substantial burden and depressive symptoms which predict higher rates of patient institutionalization. While caregiver education interventions may reduce caregiver distress and decrease the use of long-term institutional care, evidence is mixed. Inconsistent findings across studies may be the result of reporting average treatment effects which do not account for how effects differ by participant characteristics. We apply a machine-learning approach to randomized clinical trial (RCT) data of the Helping Invested Family Members Improve Veteran's Experiences Study (HI-FIVES) intervention to explore how intervention effects vary by caregiver and patient characteristics.

METHODS

We used model-based recursive partitioning models. Caregivers of community-residing older adult US veterans with functional or cognitive impairment at a single VA Medical Center site were randomized to receive HI-FIVES (n = 118) vs. usual care (n = 123). The outcomes included cumulative days not in the community and caregiver depressive symptoms assessed at 12 months post intervention. Potential moderating characteristics were: veteran age, caregiver age, caregiver ethnicity and race, relationship satisfaction, caregiver burden, perceived financial strain, caregiver depressive symptoms, and patient risk score.

RESULTS

The effect of HI-FIVES on days not at home was moderated by caregiver burden (p < 0.001); treatment effects were higher for caregivers with a Zarit Burden Scale score ≤ 28. Caregivers with lower baseline Center for Epidemiologic Studies Depression Scale (CESD-10) scores (≤ 8) had slightly lower CESD-10 scores at follow-up (p < 0.001).

CONCLUSIONS

Family caregiver education interventions may be less beneficial for highly burdened and distressed caregivers; these caregivers may require a more tailored approach that involves assessing caregiver needs and developing personalized approaches.

TRIAL REGISTRATION

ClinicalTrials.gov, ID:NCT01777490. Registered on 28 January 2013.

Machine learning analysis plans for randomised controlled trials: detecting treatment effect heterogeneity with strict control of type I error

BACKGROUND

Retrospective exploratory analyses of randomised controlled trials (RCTs) seeking to identify treatment effect heterogeneity (TEH) are prone to bias and false positives. Yet the desire to learn all we can from exhaustive data measurements on trial participants motivates the inclusion of such analyses within RCTs. Moreover, widespread advances in machine learning (ML) methods hold potential to utilise such data to identify subjects exhibiting heterogeneous treatment response.

METHODS

We present a novel analysis strategy for detecting TEH in randomised data using ML methods, whilst ensuring proper control of the false positive discovery rate. Our approach uses random data partitioning with statistical or ML-based prediction on held-out data. This method can test for both crossover TEH (switch in optimal treatment) and non-crossover TEH (systematic variation in benefit across patients). The former is done via a two-sample hypothesis test measuring overall predictive performance. The latter is done via 'stacking' the ML predictors alongside a classical statistical model to formally test the added benefit of the ML algorithm. An adaptation of recent statistical theory allows for the construction of a valid aggregate p value. This testing strategy is independent of the choice of ML method.

RESULTS

We demonstrate our approach with a re-analysis of the SEAQUAMAT trial, which compared quinine to artesunate for the treatment of severe malaria in Asian adults. We find no evidence for any subgroup who would benefit from a change in treatment from the current standard of care, artesunate, but strong evidence for significant TEH within the artesunate treatment group. In particular, we find that artesunate provides a differential benefit to patients with high numbers of circulating ring stage parasites.

CONCLUSIONS

ML analysis plans using computational notebooks (documents linked to a programming language that capture the model parameter settings, data processing choices, and evaluation criteria) along with version control can improve the robustness and transparency of RCT exploratory analyses. A data-partitioning algorithm allows researchers to apply the latest ML techniques safe in the knowledge that any declared associations are statistically significant at a user-defined level.

Nonparametric Bayesian Instrumental Variable Analysis: Evaluating Heterogeneous Effects of Coronary Arterial Access Site Strategies

Percutaneous coronary interventions (PCIs) are nonsurgical procedures to open blocked blood vessels to the heart, frequently using a catheter to place a stent. The catheter can be inserted into the blood vessels using an artery in the groin or an artery in the wrist. Because clinical trials have indicated that access via the wrist may result in fewer post procedure complications, shortening the length of stay, and ultimately cost less than groin access, adoption of access via the wrist has been encouraged. However, patients treated in usual care are likely to differ from those participating in clinical trials, and there is reason to believe that the effectiveness of wrist access may differ between males and females. Moreover, the choice of artery access strategy is likely to be influenced by patient or physician unmeasured factors. To study the effectiveness of the two artery access site strategies on hospitalization charges, we use data from a state-mandated clinical registry including 7,963 patients undergoing PCI. A hierarchical Bayesian likelihood-based instrumental variable analysis under a latent index modeling framework is introduced to jointly model outcomes and treatment status. Our approach accounts for unobserved heterogeneity via a latent factor structure, and permits nonparametric error distributions with Dirichlet process mixture models. Our results demonstrate that artery access in the wrist reduces hospitalization charges compared to access in the groin, with a higher mean reduction for male patients.

Preventing false discovery of heterogeneous treatment effect subgroups in randomized trials

Background

Heterogeneous treatment effects (HTEs), or systematic differences in treatment effectiveness among participants with different observable features, may be important when applying trial results to clinical practice. Current methods suffer from a potential for false detection of HTEs due to imbalances in covariates between candidate subgroups.

Methods

We introduce a new method, matching plus classification and regression trees (mCART), that yields balance in covariates in identified HTE subgroups. We compared mCART to a classical method (logistic regression [LR] with backwards covariate selection using the Akaike information criterion ) and two machine-learning approaches increasingly applied to HTE detection (random forest [RF] and gradient RF) in simulations with a binary outcome with known HTE subgroups. We considered an N = 200 phase II oncology trial where there were either no HTEs (1A) or two HTE subgroups (1B) and an N = 6000 phase III cardiovascular disease trial where there were either no HTEs (2A) or four HTE subgroups (2B). Additionally, we considered an N = 6000 phase III cardiovascular disease trial where there was no average treatment effect but there were four HTE subgroups (2C).

Results

In simulations 1A and 2A (no HTEs), mCART did not identify any HTE subgroups, whereas LR found 2 and 448, RF 5 and 2, and gradient RF 5 and 24, respectively (all false positives). In simulation 1B, mCART failed to identify the two true HTE subgroups whereas LR found 4, RF 6, and gradient RF 10 (half or more of which were false positives). In simulations 2B and 2C, mCART captured the four true HTE subgroups, whereas the other methods found only false positives.

All HTE subgroups identified by mCART had acceptable treated vs. control covariate balance with absolute standardized differences less than 0.2, whereas the absolute standardized differences for the other methods typically exceeded 0.2. The imbalance in covariates in identified subgroups for LR, RF, and gradient RF indicates the false HTE detection may have been due to confounding.

Conclusions

Covariate imbalances may be producing false positives in subgroup analyses. mCART could be a useful tool to help prevent the false discovery of HTE subgroups in secondary analyses of randomized trial data.

The Unequal Consequences of Mass Incarceration for Children

A growing literature has documented the mostly deleterious intergenerational consequences of paternal incarceration, but less research has considered heterogeneity in these relationships. In this article, I use data from the Fragile Families and Child Wellbeing Study (N = 3,065) to estimate the heterogeneous relationship between paternal incarceration and children's problem behaviors (internalizing behaviors, externalizing behaviors, and early juvenile delinquency) and cognitive skills (reading comprehension, math comprehension, and verbal ability) in middle childhood. Taking into account children's risk of experiencing paternal incarceration, measured by the social contexts in which children are embedded (e.g., father's residential status, poverty, neighborhood disadvantage) reveals that the consequences-across all outcomes except early juvenile delinquency-are more deleterious for children with relatively low risks of exposure to paternal incarceration than for children with relatively high risks of exposure to paternal incarceration. These findings suggest that the intergenerational consequences of paternal incarceration are more complicated than documented in previous research and, more generally, suggest that research on family inequality consider both differential selection into treatments and differential responses to treatments.

Local Control Strategy: Simple Analyses of Air Pollution Data Can Reveal Heterogeneity in Longevity Outcomes

Claims from observational studies that use traditional model specification searches often fail to replicate, partially because the available data tend to be biased. There is an urgent need for an alternative statistical analysis strategy, that is not only simple and easily understood but also is more likely to give reliable insights when the available data have not been designed and balanced. The alternative strategy known as local control first generates local, nonparametric effect-size estimates (fair treatment comparisons) and only then asks whether the observed variation in these local estimates can be predicted from potential confounding factors. Here, we illustrate application of local control to a historical air pollution data set describing a "natural experiment" initiated by the federal Clean Air Act Amendments of 1970. Our reanalysis reveals subgroup heterogeneity in the effects of air quality regulation on elderly longevity (one size does not fit all), and we show that this heterogeneity is largely explained by socioeconomic and environmental confounders other than air quality.