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 The use of propensity score methods has become ubiquitous in causal inference. At the heart of these methods is the positivity assumption. Violation of the positivity assumption leads to the presence of extreme propensity scoreweights when estimating average causal effects, which affects statistical inference. To circumvent this issue, trimming or truncating methods have been widely used. Unfortunately, these methods require that we pre-specify a threshold. There are anumber of alternative methods to deal with the lack of positivity when we estimate the average treatment effect (ATE). However, no other methods exist beyond trimming and truncation to deal with the same issue when the goal is to estimate theaverage treatment effect on the treated (ATT). In this article, we propose a propensity score weight-based alternative for the ATT, called overlap weighted average treatment effect on the treated. The appeal of our proposed method lies in its abilityto obtain similar or even better results than trimming and truncation while relaxing the constraint to choose an a priori threshold (or related measures). The performance of the proposed method is illustrated via a series of Monte Carlo simulationsand a data analysis on racial disparities in health care expenditures.

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Chen and Heitjan (Sensitivity of estimands in clinical trials with imperfect compliance. Int J Biostat. 2023) used linear extrapolation to estimate the population average causal effect (PACE) from the complier average causal effect (CACE) in multiple randomized trials with all-or-none compliance. For extrapolating from CACE to PACE in this setting and in the paired availability design involving different availabilities of treatment among before-and-after studies, we recommend the sensitivity analysis in Baker and Lindeman (J Causal Inference, 2013) because it is not restricted to a linear model, as it involves various random effect and trend models.

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Observational studies are frequently used in clinical research to estimate the effects of treatments or exposures on outcomes. To reduce the effects of confounding when estimating treatment effects, covariate balancing methods are frequently implemented. This study evaluated, using extensive Monte Carlo simulation, several methods of covariate balancing, and two methods for propensity score estimation, for estimating the average treatment effect on the treated using a hazard ratio from a Cox proportional hazards model. With respect to minimizing bias and maximizing accuracy (as measured by the mean square error) of the treatment effect, the average treatment effect on the treated weighting, fine stratification, and optimal full matching with a conventional logistic regression model for the propensity score performed best across all simulated conditions. Other methods performed well in specific circumstances, such as pair matching when sample sizes were large (n = 5000) and the proportion treated was < 0.25. Statistical power was generally higher for weighting methods than matching methods, and Type I error rates were at or below the nominal level for balancing methods with unbiased treatment effect estimates. There was also a decreasing effective sample size with an increasing number of strata, therefore for stratification-based weighting methods, it may be important to consider fewer strata. Generally, we recommend methods that performed well in our simulations, although the identification of methods that performed well is necessarily limited by the specific features of our simulation. The methods are illustrated using a real-world example comparing beta blockers and angiotensin-converting enzyme inhibitors among hypertensive patients at risk for incident stroke.

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Electronic health records and other sources of observational data are increasingly used for drawing causal inferences. The estimation of a causal effect using these data not meant for research purposes is subject to confounding and irregularly-spaced covariate-driven observation times affecting the inference. A doubly-weighted estimator accounting for these features has previously been proposed that relies on the correct specification of two nuisance models used for the weights. In this work, we propose a novel consistent multiply robust estimator and demonstrate analytically and in comprehensive simulation studies that it is more flexible and more efficient than the only alternative estimator proposed for the same setting. It is further applied to data from the Add Health study in the United States to estimate the causal effect of therapy counseling on alcohol consumption in American adolescents.

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BACKGROUND: Two propensity score (PS) based balancing covariate methods, the overlap weighting method (OW) and the fine stratification method (FS), produce superb covariate balance. OW has been compared with various weighting methods while FS has been compared with the traditional stratification method and various matching methods. However, no study has yet compared OW and FS. In addition, OW has not yet been evaluated in large claims data with low prevalence exposure and with low frequency outcomes, a context in which optimal use of balancing methods is critical. In the study, we aimed to compare OW and FS using real-world data and simulations with low prevalence exposure and with low frequency outcomes. METHODS: We used the Texas State Medicaid claims data on adult beneficiaries with diabetes in 2012 as an empirical example (N = 42,628). Based on its real-world research question, we estimated an average treatment effect of health center vs. non-health center attendance in the total population. We also performed simulations to evaluate their relative performance. To preserve associations between covariates, we used the plasmode approach to simulate outcomes and/or exposures with N = 4,000. We simulated both homogeneous and heterogeneous treatment effects with various outcome risks (1-30% or observed: 27.75%) and/or exposure prevalence (2.5-30% or observed:10.55%). We used a weighted generalized linear model to estimate the exposure effect and the cluster-robust standard error (SE) method to estimate its SE. RESULTS: In the empirical example, we found that OW had smaller standardized mean differences in all covariates (range: OW: 0.0-0.02 vs. FS: 0.22-3.26) and Mahalanobis balance distance (MB) (< 0.001 vs. > 0.049) than FS. In simulations, OW also achieved smaller MB (homogeneity: <0.04 vs. > 0.04; heterogeneity: 0.0-0.11 vs. 0.07-0.29), relative bias (homogeneity: 4.04-56.20 vs. 20-61.63; heterogeneity: 7.85-57.6 vs. 15.0-60.4), square root of mean squared error (homogeneity: 0.332-1.308 vs. 0.385-1.365; heterogeneity: 0.263-0.526 vs 0.313-0.620), and coverage probability (homogeneity: 0.0-80.4% vs. 0.0-69.8%; heterogeneity: 0.0-97.6% vs. 0.0-92.8%), than FS, in most cases. CONCLUSIONS: These findings suggest that OW can yield nearly perfect covariate balance and therefore enhance the accuracy of average treatment effect estimation in the total population.

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In this article, we develop CausalEGM, a deep learning framework for nonlinear dimension reduction and generative modeling of the dependency among covariate features affecting treatment and response. CausalEGM can be used for estimating causal effects in both binary and continuous treatment settings. By learning a bidirectional transformation between the high-dimensional covariate space and a low-dimensional latent space and then modeling the dependencies of different subsets of the latent variables on the treatment and response, CausalEGM can extract the latent covariate features that affect both treatment and response. By conditioning on these features, one can mitigate the confounding effect of the high dimensional covariate on the estimation of the causal relation between treatment and response. In a series of experiments, the proposed method is shown to achieve superior performance over existing methods in both binary and continuous treatment settings. The improvement is substantial when the sample size is large and the covariate is of high dimension. Finally, we established excess risk bounds and consistency results for our method, and discuss how our approach is related to and improves upon other dimension reduction approaches in causal inference.

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Background: The coronavirus disease 2019 (COVID-19) outbreak began in China in December 2019, with the World Health Organization declaring a state of emergency in January 2020. Worldwide implementation of lockdown measures to slow the spread of the virus led to reduced physical activity, disrupted eating habits, mental health issues, and sleep disturbances, which increased the risk of lifestyle-related diseases such as metabolic syndrome (MetS). During the COVID-19 pandemic, healthcare workers, especially intensive care workers, experienced longer working hours and burnout, which further increased the risk of lifestyle-related diseases. Accordingly, it is important to identify individuals at a risk of new-onset MetS during a pandemic, which could direct preventive interventions. This study aimed to assess the heterogeneous impact of the COVID-19 pandemic on the incidence of new-onset MetS based on the conditional average treatment effect (CATE) and to identify at-risk populations. Methods: This study analyzed health checkup data obtained from Okayama University Shikata Campus workers using paired baseline and follow-up years. Baseline data encompassed 2017 to 2019, with respective follow-up data from 2018 to 2020. Furthermore, as the COVID-19 pandemic in Japan began in January 2020, workers who underwent follow-up health checkups in 2018 to 2019 and 2020 were considered as "unexposed" and "exposed," respectively. As the Shikata campus has several departments, comparisons among departments were made. The primary outcome was new-onset MetS at follow-up. Predictor variables included baseline health checkup results, sex, age, and department (administrative, research, medical, or intensive care department). X-learner was used to calculate the CATE. Results: This study included 3,572 eligible individuals (unexposed, n = 2,181; exposed, n = 1,391). Among them, 1,544 (70.8%) and 866 (62.3%) participants in the unexposed and exposed groups, respectively, were females. The mean age (±standard deviation) of the unexposed and exposed groups was 48.2 ± 8.2 and 47.8 ± 8.3 years, respectively. The COVID-19 pandemic increased the average probability of new-onset MetS by 4.4% in the overall population. According to the department, the intensive care department showed the highest CATE, with a 15.4% increase. Moreover, there was large heterogeneity according to the department. The high-CATE group was characterized by older age, urinary protein, elevated liver enzymes, higher triglyceride levels, and a history of hyperlipidemia treatment. Conclusions: This study demonstrated that the COVID-19 pandemic increased the incidence of new-onset MetS, with this effect showing heterogeneity at a single Japanese campus. Regarding specific populations, workers in the intensive care department showed an increased risk of new-onset MetS. At-risk populations require specific preventive interventions in case the current COVID-19 pandemic persists or a new pandemic occurs.

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Several epidemiological studies have provided evidence that long-term exposure to fine particulate matter (pm2.5) increases mortality rate. Furthermore, some population characteristics (e.g., age, race, and socioeconomic status) might play a crucial role in understanding vulnerability to air pollution. To inform policy, it is necessary to identify groups of the population that are more or less vulnerable to air pollution. In causal inference literature, the group average treatment effect (GATE) is a distinctive facet of the conditional average treatment effect. This widely employed metric serves to characterize the heterogeneity of a treatment effect based on some population characteristics. In this paper, we introduce a novel Confounder-Dependent Bayesian Mixture Model (CDBMM) to characterize causal effect heterogeneity. More specifically, our method leverages the flexibility of the dependent Dirichlet process to model the distribution of the potential outcomes conditionally to the covariates and the treatment levels, thus enabling us to: (i) identify heterogeneous and mutually exclusive population groups defined by similar GATEs in a data-driven way, and (ii) estimate and characterize the causal effects within each of the identified groups. Through simulations, we demonstrate the effectiveness of our method in uncovering key insights about treatment effects heterogeneity. We apply our method to claims data from Medicare enrollees in Texas. We found six mutually exclusive groups where the causal effects of pm2.5 on mortality rate are heterogeneous.

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The regression discontinuity (RD) design is a widely utilized approach for assessing treatment effects. It involves assigning treatment based on the value of an observed covariate in relation to a fixed threshold. Although the RD design has been widely employed across various problems, its application to specific data types has received limited attention. For instance, there has been little research on utilizing the RD design when the outcome variable exhibits zero-inflation. This study introduces a novel RD estimator using local likelihood, which overcomes the limitations of the local linear regression model, a popular approach for estimating treatment effects in RD design, by considering the data type of the outcome variable. To determine the optimal bandwidth, we propose a modified Ludwig-Miller cross validation method. A set of simulations is carried out, involving binary, count, and zero-inflated outcome variables, to showcase the superior performance of the suggested method over local linear regression models. Subsequently, the proposed local likelihood model is employed on HIV care data, where antiretroviral therapy eligibility is determined by a CD4 count threshold. A comparison is made between the results obtained using the local likelihood model and those obtained using local linear regression.

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【Objective】 To compare the effects of 3 rehydration methods before blood donation on the prevention of on-site and delayed blood donation-related vasovagal response (VVR) . 【Methods】 From January to June 2021, 6 250 whole blood donors in 6 fixed blood donation sites signed informed consent and were divided into 198 clusters according to donor sites and dates, then they were randomly assigned to receive either oral rehydration salts (ORS), sugar water, or water group, and each drank 500 mL of ORS, sugar water or water within 20 minutes before blood donation. The researchers recorded the actual intervention accepted on site, and recorded the immediate VVR and related information. At rest after blood donation, donors submitted an electronic questionnaire containing socio-demographic information. At 48 hours after blood donation, the researchers called back every donor to record delayed VVR and related information. Logistic regression based on intention to treat (ITT) was used to analyze the difference of the incidence of VVR among the three groups, and the average treatment effect on treated (ATT) was calculated. PASS 2021was used to estimate the sample size and R (4.2.0) for statistical analysis. 【Results】 The cumulative incidence of blood donation-related VVR was 2.67% (2.29%-3.11%) among street whole blood donors under the 3 rehydration methods, in which, the incidence of immediate and delayed VVR was 1.02% (0.79%-1.31%) and 1.65% (1.36%-2.01%) respectively. ITT analysis found that ORS were more effective than water in reducing the incidence of delayed VVR【OR=0.59,95% CI[0.37,0.94]】.There was no significant difference in the incidence of immediate VVR between any two groups (P > 0.05), and there was no significant difference in the incidence of delayed VVR in the sugar water group compared with the water group (P > 0.05). There was a difference of -0.013 (【95% CI[-0.022, -0.004]】or -0.008【95% CI[-0.017, -0.000]】in the incidence of delayed VVR in the ORS group compared with water group or sugar water group, the difference was significant (P<0.05). The cumulative VVR of the three groups showed similar results to the delayed VVR. 【Conclusion】 Drinking ORS before blood donation is the most effective rehydration method to prevent delayed VVR. The next step is to establish the predictive model of delayed VVR to screen the susceptible population and provide them with ORS before blood donation, while other population can choose any liquid they like, thus achieving personalized blood donation-related VVR prevention and control.

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INTRODUCTION: The hijra and transgender (H/TG) population in India is vulnerable to HIV/AIDS. India had instituted a targeted intervention (TI) program to reduce this vulnerability. We aimed to measure the effectiveness of the TI program for H/TG. MATERIALS AND METHODS: The National Integrated Behavioral and Biological Survey (IBBS) was carried out in 2014-15. H/TG data from IBBS was analyzed. Bivariate and multivariate logistic regression were used to calculate the unadjusted and adjusted odds ratios with 95% confidence interval. Condom use during the last sexual intercourse, and the consistent condom use in the last one month were considered as indicators of program effectiveness. The Propensity Score Matching (PSM) method was used to assess the effectiveness. RESULTS: We found that the participants who had received condoms from peer educator/outreach worker were 1.74 and 1.40 times more likely to use condoms in the last sexual intercourse (aOR: 1.74, CI: 1.35 - 2.26) and consistent condom use in the last one month (aOR: 1.40, CI: 1.12 - 1.74) respectively compared to the participants who did not receive the condom. The matched-samples estimate (i.e., average treatment effect on treated) for the condom use during the last sexual intercourse increased by 13.0%, i.e., 0.13 (CI; 0.08 - 0.18) and consistent condom use in the last one month increased by 5.0%, i.e., 0.05 (CI; 0.00 - 0.10) among those who had received condoms from the peer educator/outreach worker compared with those who had not received condom, respectively. CONCLUSIONS: The TI program intervention for H/TG was effective in reducing HIV risk behavior as evidenced by increase in use of condom during last sexual intercourse, and consistent condom use in the last one month.

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BACKGROUND: Across studies of average treatment effects, some population subgroups consistently have lower representation than others which can lead to discrepancies in how well results generalize. METHODS: We develop a framework for quantifying inequity due to systemic disparities in sample representation and a method for mitigation during data analysis. Assuming subgroup treatment effects are exchangeable, an unbiased sample average treatment effect estimator will have lower mean-squared error, on average across studies, for subgroups with less representation when treatment effects vary. We present a method for estimating average treatment effects in representation-adjusted samples which enables subgroups to optimally leverage information from the full sample rather than only their own subgroup's data. Two approaches for specifying representation adjustment are offered-one minimizes average mean-squared error for each subgroup separately and the other balances minimization of mean-squared error and equal representation. We conduct simulation studies to compare the performance of the proposed estimators to several subgroup-specific estimators. RESULTS: We find that the proposed estimators generally provide lower mean squared error, particularly for smaller subgroups, relative to the other estimators. As a case study, we apply this method to a subgroup analysis from a published study. CONCLUSIONS: We recommend the use of the proposed estimators to mitigate the impact of disparities in representation, though structural change is ultimately needed.

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Purpose: To demonstrate that using an instrumental variable (IV) with monotonicity reduces the accuracy of propensity score (PS) weighted estimators for the average treatment effect (ATE). Methods: Monotonicity in the relationship between a binary IV and a binary treatment variable is an important assumption to identify the ATE for compliers who would only take treatment when encouraged by the IV. We perform theoretical and numerical investigations to study the impact of using the IV that satisfies monotonicity on the PS of treatment in terms of the positivity assumption, which requires that the PS be strictly between 0 and 1, and the accuracy of PS weighted estimators. Two versions of monotonicity that result in one-sided or two-sided noncompliance are considered. Results: The PS adjusting for the IV always violates the positivity assumption when noncompliance occurs in one direction (one-sided noncompliance) and is more extreme than without the IV under two-sided noncompliance. These results are valid if the probability of being encouraged to get treatment and the compliance score, the probability of being a complier, are strictly between 0 and 1. Conclusion: Using a binary IV with monotonicity as a covariate for the PS model makes the estimated PSs unnecessarily extreme, reducing the accuracy of the PS weighted estimators.

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BACKGROUND: In observational studies, double robust or multiply robust (MR) approaches provide more protection from model misspecification than the inverse probability weighting and g-computation for estimating the average treatment effect (ATE). However, the approaches are based on parametric models, leading to biased estimates when all models are incorrectly specified. Nonparametric methods, such as machine learning or nonparametric double robust approaches, are robust to model misspecification, but the efficiency of nonparametric methods is low. METHOD: In the study, we proposed an improved MR method combining parametric and nonparametric models based on the previous MR method (Han, JASA 109(507):1159-73, 2014) to improve the robustness to model misspecification and the efficiency. We performed comprehensive simulations to evaluate the performance of the proposed method. RESULTS: Our simulation study showed that the MR estimators with only outcome regression (OR) models, where one of the models was a nonparametric model, were the most recommended because of the robustness to model misspecification and the lowest root mean square error (RMSE) when including a correct parametric OR model. And the performance of the recommended estimators was comparative, even if all parametric models were misspecified. As an application, the proposed method was used to estimate the effect of social activity on depression levels in the China Health and Retirement Longitudinal Study dataset. CONCLUSIONS: The proposed estimator with nonparametric and parametric models is more robust to model misspecification.

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BACKGROUND: Right-sided ligamentum teres (RSLT) is often associated with portal venous anomalies (PVA) and is regarded as a concerning feature for hepatobiliary intervention. Most studies consider RSLT to be one of the causes of left-sided gallbladder (LGB), leading to the hypothesis that LGB must always be present with RSLT. However, some cases have shown that right-sided gallbladder (RGB) can also be present in livers with RSLT. AIM: To highlight the rare variation that RSLT may not come with LGB and to determine whether ligamentum teres (LT) or gallbladder location is reliable to predict PVA. METHODS: This study retrospectively assessed 8552 contrast-enhanced abdominal computed tomography examinations from 2018 to 2021 [4483 men, 4069 women; mean age, 59.5 ± 16.2 (SD) years]. We defined the surrogate outcome as major PVAs. The cases were divided into 4 subgroups according to gallbladder and LT locations. On one hand, we analyzed PVA prevalence by LT locations using gallbladder location as a controlled variable (n = 36). On the other hand, we controlled LT location and computed PVA prevalence by gallbladder locations (n = 34). Finally, we investigated LT location as an independent factor of PVA by using propensity score matching (PSM) and inverse probability of treatment weighting (IPTW). RESULTS: We found 9 cases of RSLT present with RGB. Among the LGB cases, RSLT is associated with significantly higher PVA prevalence than typical LT [80.0% vs 18.2%, P = 0.001; OR = 18, 95% confidence interval (CI): 2.92-110.96]. When RSLT is present, we found no statistically significant difference in PVA prevalence for RGB and LGB cases (88.9 % vs 80.0%, P > 0.99). Both PSM and IPTW yielded balanced cohorts in demographics and gallbladder locations. The RSLT group had a significantly higher PVA prevalence after adjusted by PSM (77.3% vs 4.5%, P < 0.001; OR = 16.27, 95%CI: 2.25-117.53) and IPTW (82.5% vs 4.7%, P < 0.001). CONCLUSION: RSLT doesn't consistently coexist with LGB. RSLT can predict PVA independently while the gallbladder location does not serve as a sufficient predictor.

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BACKGROUND: Creating activity-friendly communities (AFCs) is an important strategy to increase physical activity (PA). While cross-sectional links between community environments and PA are well documented, their causal relationships remain insufficiently explored. METHODS: Using the accelerometer and survey data collected from adults who moved to an AFC (cases) and similar non-AFC-residing adults who did not move (comparisons), this pre-post, case-comparison study examines if moving to an AFC increases PA. Data came from 115 participants (cases = 37, comparisons = 78) from Austin, Texas, who completed 2 waves of 1-weeklong data collection. Difference-in-difference analyses and fixed-effect models were used to test the significance of the pre-post differences in moderate-to-vigorous PA (MVPA) between cases and comparisons, for the full sample and the subsample of 37 pairs matched in key covariates using the Propensity Score Matching method. RESULTS: Average treatment effect generated based on Propensity Score Matching and difference-in-difference showed that moving to this AFC led to an average of 10.88 additional minutes of daily MVPA (76.16 weekly minutes, P = .015). Fixed-effect models echoed the result with an increase of 10.39 minutes of daily MVPA after moving to the AFC. We also found that case participants who were less active at baseline and had higher income increased their MVPA more than their counterparts. CONCLUSIONS: This study showed that, among our study sample, moving to an AFC increased residents' PA significantly when compared to their premove level and the comparison group. This causal evidence suggests the potential of AFCs as sustainable interventions for PA promotion.

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BACKGROUND: Recent work has shown that cluster-randomised trials can estimate two distinct estimands: the participant-average and cluster-average treatment effects. These can differ when participant outcomes or the treatment effect depends on the cluster size (termed informative cluster size). In this case, estimators that target one estimand (such as the analysis of unweighted cluster-level summaries, which targets the cluster-average effect) may be biased for the other. Furthermore, commonly used estimators such as mixed-effects models or generalised estimating equations with an exchangeable correlation structure can be biased for both estimands. However, there has been little empirical research into whether informative cluster size is likely to occur in practice. METHOD: We re-analysed a cluster-randomised trial comparing two different thresholds for red blood cell transfusion in patients with acute upper gastrointestinal bleeding to explore whether estimates for the participant- and cluster-average effects differed, to provide empirical evidence for whether informative cluster size may be present. For each outcome, we first estimated a participant-average effect using independence estimating equations, which are unbiased under informative cluster size. We then compared this to two further methods: (1) a cluster-average effect estimated using either weighted independence estimating equations or unweighted cluster-level summaries, and (2) estimates from a mixed-effects model or generalised estimating equations with an exchangeable correlation structure. We then performed a small simulation study to evaluate whether observed differences between cluster- and participant-average estimates were likely to occur even if no informative cluster size was present. RESULTS: For most outcomes, treatment effect estimates from different methods were similar. However, differences of >10% occurred between participant- and cluster-average estimates for 5 of 17 outcomes (29%). We also observed several notable differences between estimates from mixed-effects models or generalised estimating equations with an exchangeable correlation structure and those based on independence estimating equations. For example, for the EQ-5D VAS score, the independence estimating equation estimate of the participant-average difference was 4.15 (95% confidence interval: -3.37 to 11.66), compared with 2.84 (95% confidence interval: -7.37 to 13.04) for the cluster-average independence estimating equation estimate, and 3.23 (95% confidence interval: -6.70 to 13.16) from a mixed-effects model. Similarly, for thromboembolic/ischaemic events, the independence estimating equation estimate for the participant-average odds ratio was 0.43 (95% confidence interval: 0.07 to 2.48), compared with 0.33 (95% confidence interval: 0.06 to 1.77) from the cluster-average estimator. CONCLUSION: In this re-analysis, we found that estimates from the various approaches could differ, which may be due to the presence of informative cluster size. Careful consideration of the estimand and the plausibility of assumptions underpinning each estimator can help ensure an appropriate analysis methods are used. Independence estimating equations and the analysis of cluster-level summaries (with appropriate weighting for each to correspond to either the participant-average or cluster-average treatment effect) are a desirable choice when informative cluster size is deemed possible, due to their unbiasedness in this setting.

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Cluster randomized trials (CRTs) are studies where treatment is randomized at the cluster level but outcomes are typically collected at the individual level. When CRTs are employed in pragmatic settings, baseline population characteristics may moderate treatment effects, leading to what is known as heterogeneous treatment effects (HTEs). Pre-specified, hypothesis-driven HTE analyses in CRTs can enable an understanding of how interventions may impact subpopulation outcomes. While closed-form sample size formulas have recently been proposed, assuming known intracluster correlation coefficients (ICCs) for both the covariate and outcome, guidance on optimal cluster randomized designs to ensure maximum power with pre-specified HTE analyses has not yet been developed. We derive new design formulas to determine the cluster size and number of clusters to achieve the locally optimal design (LOD) that minimizes variance for estimating the HTE parameter given a budget constraint. Given the LODs are based on covariate and outcome-ICC values that are usually unknown, we further develop the maximin design for assessing HTE, identifying the combination of design resources that maximize the relative efficiency of the HTE analysis in the worst case scenario. In addition, given the analysis of the average treatment effect is often of primary interest, we also establish optimal designs to accommodate multiple objectives by combining considerations for studying both the average and heterogeneous treatment effects. We illustrate our methods using the context of the Kerala Diabetes Prevention Program CRT, and provide an R Shiny app to facilitate calculation of optimal designs under a wide range of design parameters.

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