Average Effect Research Articles

Model Averaging for Estimating Treatment Effects With Binary Responses

ABSTRACTIn this article, we present a novel approach for estimating the conditional average treatment effect in models with binary responses. Our proposed method involves model averaging, and we establish a weight choice criterion based on jackknife model averaging. We analyze the theoretical properties of this approach, including its asymptotic optimality in achieving the lowest possible squared error and the convergence rate of the weights assigned to correctly specified models. Additionally, we introduce a new matching method that combines partition and nearest neighbor pairing, leveraging the strengths of both techniques. To evaluate the performance of our method, we conduct comparisons with existing approaches via a Monte Carlo study and a real data analysis. Overall, our results demonstrate the effectiveness and practicality of our proposed approach for estimating the conditional average treatment effect in binary response models.

On the role of surrogates in the efficient estimation of treatment effects with limited outcome data

Abstract In many experimental and observational studies, the outcome of interest is often difficult or expensive to observe, reducing effective sample sizes for estimating average treatment effects (ATEs) even when identifiable. We study how incorporating data on units for which only surrogate outcomes not of primary interest are observed can increase the precision of ATE estimation. We refrain from imposing stringent surrogacy conditions, which permit surrogates as perfect replacements for the target outcome. Instead, we supplement the available, albeit limited, observations of the target outcome with abundant observations of surrogate outcomes, without any assumptions beyond unconfounded treatment assignment and missingness and corresponding overlap conditions. To quantify the potential gains, we derive the difference in efficiency bounds on ATE estimation with and without surrogates, both when an overwhelming or comparable number of units have missing outcomes. We develop robust ATE estimation and inference methods that realize these efficiency gains. We empirically demonstrate the gains by studying long-term-earning effects of job training.

A Meta-Analytic Evaluation: Investigating Evidence for the Validity of the Cognitive Abilities Test

Cognitive Abilities Test (CogAT) is one of the most frequently used gifted identification tools. In this meta-analytic study, we investigated empirical evidence of the validity of CogAT, in relation to different types of instruments. After reviewing 1,480 studies, a total of 24 with 33 effect sizes were included in the meta-analysis. According to our findings, the average effect size of r was found to be .63 with a 95% confidence interval [.57, .69]. Based on the heterogeneity test, significant variation due to the systematic between-study differences exists among the included correlations. Egger’s test for funnel plot asymmetry also indicates that no obvious publication bias exists in our study pool, which indicates there might not be a serious threat to alter the obtained results with publication bias. The moderator analysis revealed Lohman’s authorship and publication type influenced the effect size differences among studies. CogAT’s overall correlation with other identification tools (.63) might suggest using at least one more identification tool besides CogAT.

Quantitative analysis of human blood glucose by dynamic optical rotation angle of multiple wavelengths based on the polarization camera

Measurement of blood glucose concentration is important in the prevention and treatment of diabetes. To improve the measurement signal-to-noise ratio and accuracy, using a polarization camera as the sensor, this paper proposes a multi-wavelength dynamic optical rotation angle method to quantitatively analyze human blood glucose. First, this paper utilizes a split-time approach to drive nine different wavelengths of light sources to work separately to achieve the collection of multiple different wavelengths of data and increase the amount of information. Second, to capture images with an array sensor such as a camera, using space-for-accuracy, this paper uses the cumulative value of the gray values of all pixel points in the image at each angle as the light intensity value to improve the amplitude (light intensity) resolution. Third, the extraction method of the dynamic optical rotation angle in this paper is to extract the difference between the maximum and minimum values of the optical rotation angle from each cycle of the signal of the continuous cyclic change of the length of the optical path, and the accumulated value of the difference of multiple cycles is recorded as the dynamic optical rotation angle, which not only reduces the errors caused by the individual differences, the external environment and the measuring instrument, but also has the effect of averaging and improves the signal-to-noise ratio of the optical rotation angle. To prove the effectiveness of the proposed methods, human finger real and simulation experiments are carried out, respectively. Firstly, the polarization camera is used to collect the image data of elliptically polarized light of nine different wavelengths of linearly polarized light after passing through the human body’s finger, and obtains the optical rotation angle under each wavelength that changes with the photoplethysmography (PPG) through data processing, and extracts the dynamic optical rotation angles of the nine wavelengths by the extraction method, and the human body’s blood glucose can be quantitatively analyzed. Secondly, this paper builds a simulation model to simulate the blood volume conversion of the human finger, and uses the simulation experimental system to collect the dynamic optical rotation angles of nine wavelengths of a total of 137 human serum samples, and uses partial least squares regression to establish a model between the dynamic optical rotation angles and blood glucose concentration. In the results of predicting all samples using the model, the correlation coefficient and root mean square error were 0.7960 and 2.16 mmol/L, respectively, both of which improved by 137.26 % and decreased by 35.33 %, respectively, compared to the existing method. The experimental results show that the method in this paper has high accuracy in detecting the blood glucose concentration in human beings, which is of great significance in realizing the noninvasive quantitative analysis of human blood glucose components by the polarized light method.

HIGHLY ADAPTIVE LASSO: MACHINE LEARNING THAT PROVIDES VALID NONPARAMETRIC INFERENCE IN REALISTIC MODELS.

Understanding treatment effects on health-related outcomes using real-world data requires defining a causal parameter and imposing relevant identification assumptions to translate it into a statistical estimand. Semiparametric methods, like the targeted maximum likelihood estimator (TMLE), have been developed to construct asymptotically linear estimators of these parameters. To further establish the asymptotic efficiency of these estimators, two conditions must be met: 1) the relevant components of the data likelihood must fall within a Donsker class, and 2) the estimates of nuisance parameters must converge to their true values at a rate faster than . The Highly Adaptive LASSO (HAL) satisfies these criteria by acting as an empirical risk minimizer within a class of càdlàg functions with a bounded sectional variation norm, which is known to be Donsker. HAL achieves the desired rate of convergence, thereby guaranteeing the estimators' asymptotic efficiency. The function class over which HAL minimizes its risk is flexible enough to capture realistic functions while maintaining the conditions for establishing efficiency. Additionally, HAL enables robust inference for non-pathwise differentiable parameters, such as the conditional average treatment effect (CATE) and causal dose-response curve, which are important in precision health. While these parameters are often considered in machine learning literature, these applications typically lack proper statistical inference. HAL addresses this gap by providing reliable statistical uncertainty quantification that is essential for informed decision-making in health research.

Visual SLAM system based on dynamic semantic features

Aiming at the problem that dynamic objects (such as pedestrians, vehicles, and animals) in real scenes affect the positioning and mapping accuracy of visual SLAM (Simultaneous Localization and Mapping), a YOLOv3-ORB-SLAM3 algorithm is proposed based on ORB-SLAM3 (Oriented FAST and Rotated BRIEF-Simultaneous Localization and Mapping 3). The algorithm adds a semantic thread on the basis of ORB-SLAM3, and adopts a dual-thread mechanism for dynamic and static scene feature extraction: the semantic thread uses YOLOv3 to perform semantic recognition target detection on dynamic objects in the scene, and removes outliers from the extracted dynamic area feature points; the tracking thread extracts scene area features through ORB features, and obtains static scene features combined with semantic information and sends them to the backend, thereby eliminating the interference of dynamic scenes on the system and improving the positioning accuracy of the visual SLAM algorithm. Verified using the TUM (Technical University of Munich) dataset, the results show that the ATE (Average Treatment Effect) index of the YOLOv3-ORB-SLAM3 algorithm in the monocular mode is about 30% lower than that of the ORB-SLAM3 algorithm, and the ATE index of the dynamic sequence in the RGB-D (Red, Green and Blue-Depth) mode is reduced 10%, while the static sequence has no significant decrease.

Inference in Experiments with Matched Pairs and Imperfect Compliance

This paper studies inference for the local average treatment effect in randomized controlled trials with imperfect compliance where treatment status is determined according to “matched pairs.” By “matched pairs,” we mean that units are sampled i.i.d. from the population of interest, paired according to observed, baseline covariates and finally, within each pair, one unit is selected at random for treatment. Under weak assumptions governing the quality of the pairings, we first derive the limit distribution of the usual Wald (i.e., two-stage least squares) estimator of the local average treatment effect. We show further that conventional heteroskedasticity-robust estimators of the Wald estimator’s limiting variance are generally conservative, in that their probability limits are (typically strictly) larger than the limiting variance. We therefore provide an alternative estimator of the limiting variance that is consistent. Finally, we consider the use of additional observed, baseline covariates not used in pairing units to increase the precision with which we can estimate the local average treatment effect. To this end, we derive the limiting behavior of a two-stage least squares estimator of the local average treatment effect which includes both the additional covariates in addition to pair fixed effects, and show that its limiting variance is always less than or equal to that of the Wald estimator. To complete our analysis, we provide a consistent estimator of this limiting variance. A simulation study confirms the practical relevance of our theoretical results. Finally, we apply our results to revisit a prominent experiment studying the effect of macroinsurance on microenterprise in Egypt.

Access to credit and scale efficiency: Evidence from family farms in East China

Productivity improvement is an important driving force for developing countries to accelerate the development of agricultural sectors and promote the transformation of economic structures. However, few studies have focused on the impact of credit access on family farms’ scale efficiency, a contributor to productivity changes. We address this gap by using data collected from a survey of 565 family farms in East China. The stochastic frontier input distance function (SFIDF) is utilized to measure the scale efficiency, and the endogenous switching regression model (ESRM) is employed to estimate average treatment effect (ATT) and address the selection bias. The empirical results show that the average scale efficiency is 0.768, with credit users and non-users averaging 0.802 and 0.737, respectively. Most family farms operate below their optimal production scale, and only about 14.5 % of family farms exceed this optimal scale. Access to credit has significantly improved the scale efficiency of family farms and has not contributed to the excessive pursuit of scale expansion for financial subsidies. These findings are validated by robustness checks. The conclusions of our study have important implications for developing countries seeking to increase financial support for agricultural development.

Design-Based Theory for Lasso Adjustment in Randomized Block Experiments and Rerandomized Experiments

Blocking, a special case of rerandomization, is routinely implemented in the design stage of randomized experiments to balance the baseline covariates. This study proposes a regression adjustment method based on the least absolute shrinkage and selection operator (Lasso) to efficiently estimate the average treatment effect in randomized block experiments with high-dimensional covariates. We derive the asymptotic properties of the proposed estimator and outline the conditions under which this estimator is more efficient than the unadjusted one. We provide a conservative variance estimator to facilitate valid inferences. Our framework allows one treated or control unit in some blocks and heterogeneous propensity scores across blocks, thus including paired experiments and finely stratified experiments as special cases. We further accommodate rerandomized experiments and a combination of blocking and rerandomization. Moreover, our analysis allows both the number of blocks and block sizes to tend to infinity, as well as heterogeneous treatment effects across blocks without assuming a true outcome data-generating model. Simulation studies and two real-data analyses demonstrate the advantages of the proposed method.

Uncovering the drivers of food insecurity in Cameroon: insights from a nationwide cross-sectional analysis

BackgroundDespite global efforts to achieve zero hunger, food insecurity remains a critical challenge in several African countries, including Cameroon. This study aims to identify sociodemographic predictors of food insecurity across Cameroon through a comprehensive, nationwide cross-sectional analysis.MethodsData for this study were drawn from the 2018 Cameroon Demographic and Health Survey (CDHS). Food insecurity levels were evaluated using the Food Insecurity Experience Scale (FIES). To estimate the probabilities of moderate and severe food insecurity among different sociodemographic groups, logistic regression models were applied, with results expressed as average marginal effects (AME).ResultsThe findings reveal that approximately 24.86% of participants experienced moderate food insecurity, while 28.96% faced severe food insecurity. Among men, the proportion experiencing severe food insecurity was 38.8%, compared to 24.3% for women. Multivariable regression analysis showed that severe food insecurity was less likely among women [AME = 0.84, 95% CI = 0.83,0.86], Muslims [AME = 0.91, 95%CI = 0.90,0.93], individuals with higher education levels (secondary education: AME = 0.93, 95%CI = 0.90,0.95; higher education: AME = 0.87, 95%CI = 0.85,0.90), those owning land (either alone or jointly) [AME = 0.92, 95%CI = 0.89,0.96], wealthiest households (moderate food insecurity: AME = 0.91, 95%CI = 0.88,0.93; severe food insecurity: AME = 0.73, 95%CI = 0.70,0.75), female-headed households [AME = 0.97, 95%CI = 0.96,0.99], and rural residents [AME = 0.97, 95%CI = 0.95,0.98].ConclusionsThese findings underscore that food insecurity affects a substantial portion of the Cameroonian population, with certain sociodemographic groups more vulnerable than others. This study proposes targeted policy recommendations to address food insecurity in Cameroon, including social assistance programs for at-risk groups, investments in socioeconomic empowerment, improvements in agricultural productivity, and ongoing research to guide evidence-based interventions.

Does Employing Skilled Immigrants Enhance Competitive Performance? Evidence from European Football Clubs

We investigate the effect of employing skilled immigrants on the competitive performance of organizations by studying European football (soccer) clubs in Germany, Italy, France, England, and Spain from 1990 to 2020. Microdata from this setting offers unusual transparency about players’ birthplaces and their contributions to organizational performance. Further, country-level rules govern how many immigrant players clubs can deploy. Using changes to these rules as the basis for instrumental variables, we find that the number of immigrant players in the club’s starting lineup has a positive local average treatment effect on the club’s performance. We show that this occurs for two related reasons. First, immigrants exhibit higher individual talent. Second, immigrants play a coordinating role that enables the organization to broaden the variety of on-field strategies and actions it uses to outperform rivals. The latter mechanism is novel to the literature. This paper was accepted by Olav Sorenson, organizations. Funding: F. Morales acknowledges research funding from Agencia Nacional de Investigación y Desarrollo, Chile (Fondecyt de Iniciación) [Grant 11200342]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2021.03356 .

International spillovers of unconventional monetary policy: A meta-analysis

AbstractThe impacts of the unconventional monetary policy measures adopted by central banks after the 2007 financial crisis have been the focus of an increasing number of empirical studies. While some studies have focused on the impacts on the domestic economy, others have examined the international spillover effects of the policies adopted by the major central banks. The latter studies have, however, reported heterogeneous results. In this paper, we develop a meta-analysis of the empirical literature that examines the spillover effects of unconventional monetary policy on international capital flows. We find that, while the global average effect is not statistically different from zero, there are specific effects that vary significantly according to the development level of the destination country, the nature of the capital flow, the Central Bank that adopts the UMP, and the type and year of implementation of the UMP measure.

Nonseparable panel models with index structure and correlated random effects

. To facilitate semiparametric estimation of general discrete-choice, censored, sample selection, and other complex panel data models, we study identification and estimation of nonseparable multiple-index models in panel data with correlated random effects and a fixed number of time periods. The parameter vectors of interest are shown to be identified up to multiplicative constants and the average marginal effects are identified under the assumption that the distribution of individual effects depends on the explanatory variables only through their averages across time. Under this assumption, we propose to estimate the unknown parameters by the generalized method of moments based on the average and outer product of the difference of derivatives of the regression function. The rate of convergence and asymptotic distribution is established both for the proposed parameter estimates and the average marginal effects. We conduct Monte Carlo simulation studies to assess finite-sample performance of the proposed estimator. We also use it to model dynamic earnings of women, and using our general identification results, we find a negative effect of the number of children not only on the selection into employment as usual, but also on the average earnings.

Variability in Causal Effects and Noncompliance in a Multisite Trial: A Bivariate Hierarchical Generalized Random Coefficients Model for a Binary Outcome.

Within each of 170 physicians, patients were randomized to access e-assist, an online program that aimed to increase colorectal cancer screening (CRCS), or control. Compliance was partial: of the experimental patients accessed e-assist while no controls were provided the access. Of interest are the average causal effect of assignment to treatment and the complier average causal effect as well as the variation of these causal effects across physicians. Each physician generates probabilities of screening for experimental compliers (experimental patients who accessed e-assist), control compliers (controls who would have accessed e-assist had they been assigned to e-assist), and never takers (patients who would have avoided e-assist no matter what). Estimating physician-specific probabilities jointly over physicians poses novel challenges. We address these challenges by maximum likelihood, factoring a "complete-data likelihood" uniquely into the conditional distribution of screening and partially observed compliance given random effects and the distribution of random effects. We marginalize this likelihood using adaptive Gauss-Hermite quadrature. The approach is doubly iterative in that the conditional distribution defies analytic evaluation. Because the small sample size per physician constrains estimability of multiple random effects, we reduce their dimensionality using a shared random effects model having a factor analytic structure. We assess estimators and recommend sample sizes to produce reasonably accurate and precise estimates by simulation, and analyze data from a trial of a CRCS intervention.

Preparing efficient self-healing polyimide coating for enhancing stability of electromagnetic interference shielding film

Electromagnetic interference (EMI) shielding films were widely utilized in various electronic devices, but they were prone to damage and performance degradation in harsh environments. Therefore, it was urgent to maintain stable performance of EMI shielding films. In this work, we adopt the reactions between aldehyde-modified diamine monomers and dianhydride monomers with dynamic imine bond to successfully prepare a self-healing PI (SHPI) film. Benefit from dynamic imine and imide bond, the SHPI film possessed excellent thermal stability (T5 %=527.7°C), tensile strength (72 MPa) and self-healing efficiency (94.4 %). As protecting coating layer, the SHPI film was able to maintain the commercial aluminized polyimide (PI/Al) film with good EMI shielding performance in acid environment. The electromagnetic shielding film with self-healing coating still had average EMI shielding effectiveness value of 44.5 dB after exposed to 10 % concentration nitric acid solution for 30 min. It is noteworthy that when damaged by external forces, the electromagnetic shielding film with self-healing coating could achieve rapid healing, while the tensile strength was up to 87 MPa and the self-healing efficiency reached 92.5 %. This work provided an effective self-healing protective layer for EMI shielding material against corrosion in acidic environments and damage from external pressures.

Racial and ethnic disparities in COVID-19 hospital cost of care.

Although studies have evaluated the hospital cost of care associated with treating patients with COVID-19, there are no studies that compare the hospital cost of care among racial and ethnic groups based on detailed cost accounting data. The aims of this study were to provide a detailed description of the hospital costs of COVID-19 based on individual resources during the hospital stay and standardized costs that do not rely on inflation adjustment and evaluate the extent to which hospital total cost of care for patients with COVID-19 differs by race and ethnicity. This study used electronic medical record data from an urban academic medical center in Chicago, Illinois USA. Hospital cost of care was calculated using accounting data representing the cost of the resources used to the hospital (i.e., cost to the hospital, not payments). A multivariable generalized linear model with a log link function and inverse gaussian distribution family was used to calculate the average marginal effect (AME) for Black, White, and Hispanic patients. A second regression model further compared Hispanic patients by preferred language (English versus Spanish). In our sample of 1,853 patients, the average adjusted cost of care was significantly lower for Black compared to White patients (AME = -$5,606; 95% confidence interval (CI), -$10,711 to -$501), and Hispanic patients had higher cost of care compared to White patients (AME = $8,539, 95% CI, $3,963 to $13,115). In addition, Hispanic patients who preferred Spanish had significantly higher cost than Hispanic patients who preferred English (AME = $11,866; 95% CI $5,302 to $18,431). Total cost of care takes into account both the intensity of the treatment as well as the duration of the hospital stay. Thus, policy makers and health systems can use cost of care as a proxy for severity, especially when looking at the disparities among different race and ethnicity groups.

Comparative analysis of income level in matched small farms with and without eucalyptus plantations in Senan, Ethiopia

The cultivation of eucalyptus trees is a widely practiced economic activity in the highlands of the Amhara region, Ethiopia. This study investigates the causal impact of eucalyptus plantation ownership on household income within the Senan District of Ethiopia. Using cross-sectional data from 332 rural households, comprising 166 households with eucalyptus plantations and 166 without, the study employed a two-sample t-test comparison to compare the income level of households in the two groups. To identify the key factors influencing household income, the study conducted a Principal Component Analysis (PCA) and Propensity Score Matching (PSM) to isolate the causal impact of eucalyptus plantations on household income. This involved estimating propensity scores using a binary logistic regression model. The Average Treatment Effect on the Treated (ATT) analysis revealed that households that plant eucalyptus trees had 40.2 % higher total household income than those that did not participate in such activities. Therefore, considering potential demand and market fluctuations, eucalyptus tree growers need to diversify their livelihood strategies by utilizing the income generated from their plantations.

Considerations for using tree-based machine learning to assess causation between demographic and environmental risk factors and health outcomes.

Evaluation of the heterogeneous treatment effect (HTE) allows for the assessment of the causal effect of a therapy or intervention while considering heterogeneity in individual factors within a population. Machine learning (ML) methods have previously been employed for HTE evaluation, addressing the limitations associated with modelling complex systems. In this work, three tree-based ML algorithms, causal random forest (CRF), causal Bayesian additive regression trees (CBART), and causal rule ensemble (CRE), are used to analyze the potential causation of benzene exposure to cause childhood acute myeloid leukemia (AML). Data for this analysis is generated by drawing samples from a previously developed model that estimates AML probability given as input demographic information and benzene exposure. Comparison is drawn between the three tree-based algorithms in terms of the predicted average treatment effect (ATE), the regression coefficient of determination, and the computational time of each algorithm. Minimal difference is reported between the three tree-based algorithms in terms of the ATE, as well as the regression coefficient of determination. However, CRF outperforms CBART in terms of algorithm computational time. Moreover, CRF allows for both continuous and binary treatment variables, as opposed to CBART and CRE, making it better suited to environmental health studies, where exposure levels of pollutants shall be considered continuous. Following the comparison of all three algorithms, the influence of adding Gaussian noise to the treatment and outcome variables, as well as outliers, is investigated using CRF. A set of considerations is drawn to guide researchers in using these algorithms. These considerations detail the simulation settings, applications, and results interpretation and aim to provide prompt information in decision-making surrounding the establishment of pollutant exposure thresholds in environmental risk assessments.

Mutation potentiates migration swamping in polygenic local adaptation.

Locally adapted traits can exhibit a wide range of genetic architectures, from pronounced divergence at a few loci to small frequency divergence at many loci. The type of architecture that evolves depends strongly on the migration rate, as weakly selected loci experience swamping and do not make lasting contributions to divergence. Simulations from previous studies showed that even when mutations are strongly selected and should resist migration swamping, the architecture of adaptation can collapse and become transient at high mutation rates. Here, we use an analytical two-population model to study how this transition in genetic architecture depends upon population size, strength of selection, and parameters describing the mutation process. To do this, we develop a mathematical theory based on the diffusion approximation to predict the threshold mutation rate above which the transition occurs. We find that this performs well across a wide range of parameter space, based on comparisons with individual-based simulations. The threshold mutation rate depends most strongly on the average effect size of mutations, weakly on the strength of selection, and marginally on the population size. Across a wide range of the parameter space, we observe that the transition to a transient architecture occurs when the trait-wide mutation rate is 10-3-10-2, suggesting that this phenomenon is potentially relevant to complex traits with a large mutational target. On the other hand, based on the apparent stability of genetic architecture in many classic examples of local adaptation, our theory suggests that per-trait mutation rates are often relatively low.

Medicaid managed care restrictions on medications for the treatment of opioid use disorder.

To examine whether Medicaid managed care plan (MCP) utilization management policies for buprenorphine-naloxone and injectable naltrexone are related to key state Medicaid program policy decisions. We abstracted data on state Medicaid regulatory and policy information from publicly available sources and publicly available insurance benefit documentation from all 241 Medicaid MCPs operating in 2021. In this cross-sectional study, we used bivariate and multivariate analyses to examine whether Medicaid MCP prior authorization and quantity limits on receipt of buprenorphine and injectable naltrexone were associated with key state Medicaid choices to leverage federal funds to expand coverage and eligibility (Medicaid expansion, 1115 waivers) and to regulate Medicaid MCPs (uniform preferred drug lists, medical loss ratio remittance). Models were adjusted for MCP characteristics, including profit status, behavioral health contracting arrangement, National Committee for Quality Assurance accreditation, size, market share, and state opioid overdose death rates. Average marginal effects (AME) were reported. Utilization management was common among MCPs, and restrictions were more commonly applied to buprenorphine than injectable naltrexone, despite its higher cost. States that required MCPs to comply with utilization management policies stipulated in a uniform preferred drug list were more likely to require prior authorization for buprenorphine (AME: 0.29, 95% CI: 0.15-0.42) and injectable naltrexone (AME: 0.25, 95% CI: 0.12-0.38). MCPs in states that required plans to pay back earnings above a certain threshold were less likely to require prior authorization for buprenorphine (AME: -0.30, 95% CI: -0.43 to -0.18). Restrictions on medications for opioid use disorder are widespread among MCPs and vary by medication. State Medicaid regulatory and policy characteristics were strongly linked to MCPs' utilization management approaches. State Medicaid policy and contracting approaches may be levers to eliminate utilization management restrictions on medications for opioid use disorder.