Effect Estimation Research Articles

Estimands and Cumulative Incidence Function Regression in Clinical Trials: Some New Results on Interpretability and Robustness.

Regression analyses based on transformations of cumulative incidence functions are often adopted when modeling and testing for treatment effects in clinical trial settings involving competing and semi-competing risks. Common frameworks include the Fine-Gray model and models based on direct binomial regression. Using large sample theory we derive the limiting values of treatment effect estimators based on such models when the data are generated according to multiplicative intensity-based models, and show that the estimand is sensitive to several process features. The rejection rates of hypothesis tests based on cumulative incidence function regression models are also examined for null hypotheses of different types, based on which a robustness property is established. In such settings supportive secondary analyses of treatment effects are essential to ensure a full understanding of the nature of treatment effects. An application to a palliative study of individuals with breast cancer metastatic to bone is provided for illustration.

Inclusion of unexposed clusters improves the precision of fixed effects analysis of stepped-wedge cluster randomized trials with binary and count outcomes

BackgroundThe fixed effects model is a useful alternative to the mixed effects model for analyzing stepped-wedge cluster randomized trials (SW-CRTs). It controls for all time-invariant cluster-level confounders and has proper control of type I error when the number of clusters is small. While all clusters in a SW-CRT are typically designed to crossover from the control to receive the intervention, some trials can end with unexposed clusters (clusters that never receive the intervention), such as when a trial is terminated early due to safety concerns. It was previously unclear whether unexposed clusters would contribute to the estimation of the intervention effect in a fixed effects analysis. However, recent work has demonstrated that including an unexposed cluster can improve the precision of the intervention effect estimator in a fixed effects analysis of SW-CRTs with continuous outcomes. Still, SW-CRTs are commonly designed with binary outcomes and it is unknown if those previous results extend to SW-CRTs with non-continuous outcomes.MethodsIn this article, we mathematically prove that the inclusion of unexposed clusters improves the precision of the fixed effects intervention effect estimator for SW-CRTs with binary and count outcomes. We then explore the benefits of including an unexposed cluster in simulated datasets with binary or count outcomes and a real palliative care data example with binary outcomes.ResultsThe simulations show that including unexposed clusters leads to tangible improvements in the precision, power, and root mean square error of the intervention effect estimator. The inclusion of the unexposed cluster in the SW-CRT of a novel palliative care intervention with binary outcomes yielded smaller standard errors and narrower 95% Wald Confidence Intervals.ConclusionsIn this article, we demonstrate that the inclusion of unexposed clusters in the fixed effects analysis can lead to the improvements in precision, power, and RMSE of the fixed effects intervention effect estimator for SW-CRTs with binary or count outcomes.

Bias analysis on socioeconomic status and lung cancer in a pooled international case-control study

Abstract Background Low socioeconomic status (SES) groups showed increased lung cancer risks even after adjustment for smoking habits and other exposures to lung carcinogens. Although several biases were often indicated and discussed, only few studies quantified the impact of potential biases. Methods We conducted a bias analysis on the association of lung cancer and SES using data from the SYNERGY project, including 12 case-control studies with 18 study centres from Europe and Canada (16,550 cases, 20,147 controls). SES in quartiles was derived from the International Socio-Economic Index of occupational status (ISEI). Odds ratios (OR) with 95% confidence intervals (CI) were estimated by logistic regression adjusting for age, study centre, and smoking. In addition, we estimated natural direct SES effects and natural indirect smoking effects by inverse odds ratio weighting. In a multiple quantitative bias analysis, we considered impacts of misclassification of smoking status, selection bias, and unmeasured mediator-outcome confounding by a protective genetic factor, and created 95% simulation intervals (SI) by bootstrap. All analyses were stratified by sex. Results Adjustment for smoking as well as natural effects estimation showed that nearly half of lung cancer risks of lower SES groups in men and up to one third in women were attributable to smoking. Consideration of all types of bias reduced lung-cancer risks in the fully adjusted logistic regression models, with the strongest impact by selection bias: For the 4th versus 1st (highest) ISEI quartile OR decreased from 1.83 (1.69-1.98 CI) to 1.50 (1.30-1.73 SI) in men, and OR 1.48 (1.27-1.72 CI) to 1.20 (0.96-1.53 SI) in women. Conclusions Smoking is the main target for prevention of lung cancer, along with occupational and environmental exposures, in particular in lower SES groups. This finding remains, though our analysis revealed reduced lung-cancer risks of lower SES groups after multiple bias adjustment. Key messages • Impact of potential biases was quantified in the association of SES and lung cancer. • Lung cancer risks were partially attributable to smoking and multiple biases.

GLP1-RA versus DPP4 inhibitors on cardiovascular outcomes: A three-year real-world analysis

Abstract Background Cardiovascular outcome trials of GLP1-RAs have massively impacted the clinical practice in the management of patients with type 2 diabetes. The cardiovascular protective properties of GLP1-RA compared to DPP4 have been demonstrated in an observational setting before, however recent methodological developments have enabled clinically relevant effect estimation. Aim This study aimed to evaluate the real-world cardiovascular outcomes of GLP1-RA versus DPP4 inhibitors in patients with type 2 diabetes and high cardiovascular risk. Methods In this study, we utilized the Danish nationwide registers to identify new users of GLP1-RA or DPP4 therapies from 2012 to 2022. Participants were required to be either at least 50 years of age and have one or more of the following conditions: hypertension, chronic obstructive pulmonary disease, cardiovascular disease, or chronic renal disease or be at least 60 years of age and have hypertension. Additionally, their glycated hemoglobin (HbA1c) levels needed to be 53 mmol/mol or higher within the year preceding their first prescription date for these therapies. The index date was defined as the initial prescription date, and comorbidities and medicine use were evaluated up to 10 years prior to this date. Individuals who had filled prescriptions for SGLT2 inhibitors within six months prior to their index date were excluded from the study. The outcome of interest was a composite of cardiovascular death, nonfatal myocardial infarction, or nonfatal stroke (MACE). Patients were followed for up to three years until MACE, all-cause mortality, emigration, or until the end of follow-up on December 31, 2022. To assess the three-year risk of MACE, the Aalen Johansson estimator was used. A casual inference framework was employed estimating the three-year average treatment effect using g-formula based on Cox regression with competing risk. Results A total of 26,190 individuals were included, with 19,494 initiating DPP4 inhibitor therapy and 6,696 initiating GLP1-RA therapy. The three-year risk of MACE was 8.56% (95% confidence interval [CI]: 8.11 to 9.00) for the DPP4 initiator group, compared to 4.76% (95% CI: 4.08 to 5.43) for the GLP1-RA initiator group. Emulating what would have happened had all included individuals initiated GLP1-RA treatment versus had all initiated treatment with DPP4, accounting for age, sex, income, education, degree of urbanization, diabetes duration, baseline hba1c level, co-medicine, and co-morbidities, we estimated an three-year average treatment effect of -2.05% (95% CI:-2.92;-1.18) , p-value<0.001) for GLP1-RA initiation versus DPP4 initiation for MACE. Conclusion Our findings suggest that GLP1-RA use is associated with a significantly lower risk of MACE compared to DPP4 inhibitors in a real-world population of patients with type 2 diabetes and high cardiovascular risk. This supports the cardiovascular protective role of GLP1-RA in clinical practice.

Mental health impacts of spousal caregiving intensity in the US.

In the US, spouses are a major source of informal care for older adults and, therefore, key to the US national strategy to provide long-term care to the growing population of older adults. Understanding the mental health impacts of spousal caregiving is therefore critically important. Existing studies on the topic have often been limited by methodological limitations, and most overlook the role of caregiving intensity. In this study, we assess the impact of providing different intensities of caregiving to a spouse on mental health outcomes using data from the Health and Retirement Study. We address the endogeneity of the decision to provide different caregiving intensities using an augmented inverse probability weighted (AIPW) estimator adapted to handle multivalued treatments. We check the robustness of our estimates to the AIPW's identifying assumptions by re-estimating the model using a dynamic fixed effects estimator. We find strong evidence that becoming a caregiver is associated with worsened mental health outcomes for women, while the evidence for men is weaker. When disaggregating by caregiving intensity, we find that transitions into high-intensity caregiving lead to large increases in depression symptoms and the probability of exhibiting major depression for both men and women. The overall mental health impact of transiting into caregiving is driven almost exclusively by the negative impact of high-intensity caregiving, as transitions into low- and moderate-intensity caregiving are not associated with worsening mental health in most specifications. This study provides timely insights that can inform the targeting of long-term care policies and programs aimed at supporting family caregivers of older adults.

Sustainable development goals in emerging markets: Aligning the role of financial inclusion in promoting environmental quality of the Next‐11 economies

AbstractPursuing sustainable development has emerged as a paramount global objective, with the United Nations' Sustainable Development Goals (SDGs) serving as a guiding framework. Increasing environmental degradation is associated with increased greenhouse gas emissions, deforestation, industrial waste, fossil fuel depletion, and loss of biodiversity. This study has analyzed the effect of financial inclusion on ecological sustainability while controlling the effect of financial development, energy consumption, economic growth, urbanization, and trade openness in the Next‐11 economies from 1995 to 2019. The study develops the financial inclusion index through principal components analysis by inculcating three demand‐side and three supply‐side factors of financial inclusion. To analyze the developed model, various first‐generation and second‐generation techniques are applied. The results of Westerlund co‐integration reveal significant long‐run co‐integration among the series. The long‐run elasticities are estimated through dynamic common correlated effect estimation and generalized method of moments where results reveal that FI helps to secure environmental sustainability by reducing the ecological footprint, hence it works on the SDG framework. Economic growth and financial development are found to be the root causes of increasing ecological footprint. So, it is the penetration of excessive credit, not the financial inclusivity which needs to be directed toward sustainability. It is suggested that the governments of Next‐11 countries should steer the capital toward sustainable usage and should continue facilitating financial services to curtail environmental degradation. Our findings have significant repercussions for Next‐11 countries, giving decision makers fresh perceptions of financial inclusion and development implications.

A Unified Framework for Covariate Adjustment Under Stratified Randomisation

ABSTRACTRandomisation, as a key technique in clinical trials, can eliminate sources of bias and produce comparable treatment groups. In randomised experiments, the treatment effect is a parameter of general interest. Researchers have explored the validity of using linear models to estimate the treatment effect and perform covariate adjustment and thus improve the estimation efficiency. However, the relationship between covariates and outcomes is not necessarily linear, and is often intricate. Advances in statistical theory and related computer technology allow us to use nonparametric and machine learning methods to better estimate the relationship between covariates and outcomes and thus obtain further efficiency gains. However, theoretical studies on how to draw valid inferences when using nonparametric and machine learning methods under stratified randomisation are yet to be conducted. In this paper, we discuss a unified framework for covariate adjustment and corresponding statistical inference under stratified randomisation and present a detailed proof of the validity of using local linear kernel‐weighted least squares regression for covariate adjustment in treatment effect estimators as a special case. In the case of high‐dimensional data, we additionally propose an algorithm for statistical inference using machine learning methods under stratified randomisation, which makes use of sample splitting to alleviate the requirements on the asymptotic properties of machine learning methods. Finally, we compare the performances of treatment effect estimators using different machine learning methods by considering various data generation scenarios, to guide practical research.

Do higher public and private debt levels benefit the wealthy? An empirical analysis of top wealth shares in the UK

Purpose Despite the concomitant rise in recent decades in both debt levels (public as well as private) and wealth inequality, empirical evidence on the relationship is absent in existing literature. This is striking especially since recent theoretical contributions point to a link between debt and wealth inequality. We contribute to the debate by investigating empirically whether higher levels of UK public and household debt increase the UK wealth concentration at the top 1 and 10% of the wealth distribution.Design/methodology/approach We employ the Autoregressive Distributed Lag (ARDL) cointegration approach with UK time series data from 1970 to 2019. For robustness, a further analysis using panel data fixed effects estimation on a cross-country sample that also includes France and the USA is undertaken. We also use bootstrapping to conservatively estimate statistical significance.Findings Higher levels of public and household debt are found to increase wealth concentration at the top 1 and 10%. The effect is stronger for household debt. Fixed effects estimation on a cross-country dataset supports the results for the UK.Originality/valueThis study is the first to investigate empirically whether rising levels of UK public and household debt benefit the wealthy and thus widen the gap between the “haves” and “have-nots”.

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.

The impact of corruption and Islamicity on bank stability and profitability: assessing the moderating effect in dual banking systems

Purpose This paper aims to examine the impact of corruption on bank stability and bank profitability separately for Islamic banks as well as conventional banks. Moreover, it also investigates whether the existence of Islamicity and corruption in the environment can moderate the Islamic banks-stability and Islamic banks-profitability relationships. Design/methodology/approach Sample of the study consists 136 banks comprising 70 Islamic and 66 conventional banks over the period 2015–2021 from nine countries with dual banking systems. Panel data fixed effect estimator with year effects is used to estimate the results. Findings Results of the study show that Islamicity is positively and corruption is negatively related to bank stability as well as bank profitability. Further, it is found that the effect of corruption is significantly different between Islamic and conventional banks, wherein conventional banks are more adversely affected than Islamic banks. However, an insignificant difference between Islamic and conventional banks is observed in the case of Islamicity. Practical implications The study provides theoretical and practical implications. On theoretical side, the study presents Islamicity as more reliable measure of religiosity based on Islamic values that can help in control of corruption by moderating corruption-bank stability nexus especially in dual banking economies which have high share of Muslim population. On practical side, the study recommends policy and operational measures for mitigating corruption aiming bank stability. Originality/value The results of this study contribute to the corruption-finance, religion-finance and dual banking literature. This study suggests that regulators and bank management must consider corruption and Islamicity while formulating their policies for better bank performance/stability.

Climate change and economic growth: Evidence for European countries

AbstractClimate change may affect economies and the welfare of people around the world. To design appropriate policy responses, the economic effects of climate change should be known. One strand in the literature empirically estimates the growth effects of climatic variations. However, those studies often neglect economic variables that have proven to be robust in explaining economic growth. Further, often they fail to check for the robustness of their results. The main aim of this study is to detect whether there exists a statistically significant robust relation between climate change and economic growth by estimating different model specifications. To do so panel estimation techniques for 24 European economies for the period from 2002 to 2019 are applied whereby panel fixed effects estimations and dynamic Generalized Methods of Moments estimations are resorted to. No statistically significant robust relationship between the temperature change and economic growth is found just as for precipitation that does not exert a significant effect on growth. As regards the institutional and macroeconomic control variables the rule of law, the fiscal variable, and the output gap are statistically significant and robust. It is argued that far‐reaching policy measures, such as the net zero goal of the European Union, should be given only based on robust results. Otherwise, economic policy may turn out to be inadequate and can lead to welfare losses. Hence, the conclusion is that the net zero goal of the European Green Deal is to be seen skeptical.

Causal relationship between IgA nephropathy and common neuropsychiatric disorders: A two-sample Mendelian randomization analysis

ObjectiveUtilizing two-sample Mendelian randomization (TSMR), this study seeks to determine the causal relationship between IgA nephropathy and five prevalent neuropsychiatric disorders. By exploring the genetic associations between IgA nephropathy and neuropsychiatric disorders, this research aims to contribute to the prevention of neuropsychiatric disorders in patients with IgA nephropathy. MethodsPublic genome-wide association study databases were searched, with IgA nephropathy as the exposure factor, including 15,587 patients with IgA nephropathy and 462,197 healthy controls. The outcome factors were five common neuropsychiatric disorders (bipolar disorder, depressive disorder, schizophrenia, anorexia nervosa, and Alzheimer's disease), with outcome data drawn from five datasets in the PGC and GWAScatalog databases. Inverse-variance weighting served as the primary method for causal effect estimation, supplemented by MR-Egger, weighted median, weighted mode, and simple mode methods. Heterogeneity was tested using Cochran's Q test, and sensitivity analysis was conducted using MR-Egger and MR-presso. ResultsMR analysis indicated a positive causal relationship between IgA nephropathy and depressive disorder (OR = 1.010, 95%CI: 1.003–1.017, P = 3.27 × 10−3), and a potential positive causal relationship between IgA nephropathy and anorexia nervosa (OR = 1.165, 95%CI: 1.030–1.319, P = 0.015). ConclusionThere is a positive causal relationship between IgA nephropathy and depressive disorder, and a potential positive causal relationship with anorexia nervosa. No causal relationship was found with schizophrenia, bipolar disorder, or Alzheimer's disease.

The moderation effect of institutional quality on the nexus between migrant remittance and financial inclusion in West Africa

BACKGROUND: Migrants' remittances are critical in financing the economies of Africa and the West African region, in addition to FDI and ODA. It is also a significant driver of financial inclusion. OBJECTIVE: This paper assessed the moderating role of institutional quality on migrants' remittances and financial inclusion in West Africa during 2004–2023. METHODS: Secondary data was used for this study, sourced from the World Bank’s World Development Indicators (WDI), the World Governance Indicator (WGI), and the IMF’s Financial Access Survey (FAS), 2023. This study employed the Panel Fixed Effects (PFE) estimation technique, which accounts for Driscoll and Kraay's (1998) standard error. To ensure the robustness of the findings, the analysis was augmented with the utilisation of feasible generalised least squares (FGLS). RESULTS: There was an overall positive impact of institutional quality on financial inclusion (FI), at a significant rate of 120.8%, accounting for deposit-taking microfinance institutions, thereby highlighting that institutions play a crucial part in improving financial inclusion in West Africa. Also, the moderating effect of institutional quality had a more positive impact on microfinance institutions than commercial banks, at a significant rate of 16.2%. CONCLUSION: In summary, attention should be given to establishing more microfinance institutions as they serve as a better remittance distribution channel when compared to commercial banks, emphasising enhancing quality in financial services delivery. This also encourages more people to be financially included, thereby making better economic use of the remittance received in West Africa.

On approximate equality of Z-values of the statistical tests for win statistics (win ratio, win odds, and net benefit)

ABSTRACT Dong et al. (2023) showed that the win statistics (win ratio, win odds, and net benefit) can complement each another to demonstrate the strength of treatment effects in randomized trials with prioritized multiple outcomes. This result was built on the connections among the point and variance estimates of the three statistics, and the approximate equality of Z-values in their statistical tests. However, the impact of this approximation was not clear. This Discussion refines this approach and shows that the approximate equality of Z-values for the win statistics holds more generally. Thus, the three win statistics consistently yield closely similar p-values. In addition, our simulations show an example that the naive approach without adjustment for censoring bias may produce a completely opposite conclusion from the true results, whereas the IPCW (inverse-probability-of-censoring weighting) approach can effectively adjust the win statistics to the corresponding true values (i.e. IPCW-adjusted win statistics are unbiased estimators of treatment effect).

Comparison of random forest methods for conditional average treatment effect estimation with a continuous treatment.

We are addressing the problem of estimating conditional average treatment effects with a continuous treatment and a continuous response, using random forests. We explore two general approaches: building trees with a split rule that seeks to increase the heterogeneity of the treatment effect estimation and building trees to predict as a proxy target variable. We conduct a simulation study to investigate several aspects including the presence or absence of confounding and colliding effects and the merits of locally centering the treatment and/or the response. Our study incorporates both existing and new implementations of random forests. The results indicate that locally centering both the response and treatment variables is generally the best strategy, and both general approaches are viable. Additionally, we provide an illustration using data from the 1987 National Medical Expenditure Survey.

Association of crop commercialization and rural households' multidimensional poverty using targeted maximum likelihood estimation

Recent evidence shows the highest prevalence of multidimensional poverty in the world. To alleviate poverty, Ethiopia is investing in stimulating agricultural commercialization for poverty reduction, driving sustainable economic growth, and creating jobs. Therefore, this study investigated the causal relationship between crop commercialization and multidimensional poverty across Ethiopian rural households using the Ethiopia Socioeconomic Survey 2018/19 data, which included 1129 crop commercialized and 1585 completely subsistence rural households. Moreover, this study also examined the causal effect of crop commercialization on the multidimensional poverty mediated by mobile phone ownership status. The study used the double robust method of the augmented inverse probability of treatment weighted (AIPTW) and targeted maximum likelihood estimation (TMLE) methods. The result showed that crop commercialization has an association with multidimensional poverty. Specifically, the TMLE with a default super learner model estimates were the most precise and suggest that the prevalence of risk of being multidimensionally poor among rural households who were crop commercialized is 12.2 % lower than for those who were completely subsistence households. Thus, it is important to have more robust policies like crop commercialization to target rural multidimensional poverty reduction. Moreover, the controlled direct effect estimation analyses showed that crop-commercialized rural households reduced the adjusted risk of multidimensional poverty by; 12 % for those who owned mobile phones and 7.8 % for those who did not. To ensure sustainable livelihoods for rural multidimensional poor households, it is necessary to have a multidisciplinary policy intervention to promote crop commercialization through the spread of mobile phones in rural areas.

Causal Inference Over a Subpopulation: The Effect of Malaria Vaccine in Women During Pregnancy.

Preventing malaria during pregnancy is of critical importance, yet there are no approved malaria vaccines for pregnant women due to lack of efficacy results within this population. Conducting a randomized trial in pregnant women throughout the entire duration of pregnancy is impractical. Instead, a randomized trial was conducted among women of childbearing potential (WOCBP), and some participants became pregnant during the 2-year study. We explore a statistical method for estimating vaccine effect within the target subpopulation-women who can naturally become pregnant, namely, women who can become pregnant under a placebo condition-within the causal inference framework. Two vaccine effect estimators are employed to effectively utilize baseline characteristics and account for the fact that certain baseline characteristics were only available from pregnant participants. The first estimator considers all participants but can only utilize baseline variables collected from the entire participant pool. In contrast, the second estimator, which includes only pregnant participants, utilizes all available baseline information. Both estimators are evaluated numerically through simulation studies and applied to the WOCBP trial to assess vaccine effect against pregnancy malaria.

Using double-debiased machine learning to estimate the impact of Covid-19 vaccination on mortality and staff absences in elderly care homes.

Machine learning approaches provide an alternative to traditional fixed effects estimators in causal inference. In particular, double-debiased machine learning (DDML) can control for confounders without making subjective judgements about appropriate functional forms. In this paper, we use DDML to examine the impact of differential Covid-19 vaccination rates on care home mortality and other outcomes. Our approach accommodates fixed effects to account for unobserved heterogeneity. In contrast to standard fixed effects estimates, the DDML results provide some evidence that higher vaccination take-up amongst residents, but not staff, reduced Covid mortality in elderly care homes. However, this effect was relatively small, is not robust to alternative measures of mortality and was restricted to the initial vaccination roll-out period.

Multimedia: Multimodal Mediation Analysis of Microbiome Data.

Mediation analysis has emerged as a versatile tool for answering mechanistic questions in microbiome research because it provides a statistical framework for attributing treatment effects to alternative causal pathways. Using a series of linked regressions, this analysis quantifies how complementary data relate to one another and respond to treatments. Despite these advances, existing software's rigid assumptions often result in users viewing mediation analysis as a black box. We designed the multimedia R package to make advanced mediation analysis techniques accessible, ensuring that statistical components are interpretable and adaptable. The package provides a uniform interface to direct and indirect effect estimation, synthetic null hypothesis testing, bootstrap confidence interval construction, and sensitivity analysis, enabling experimentation with various mediator and outcome models while maintaining a simple overall workflow. The software includes modules for regularized linear, compositional, random forest, hierarchical, and hurdle modeling, making it well-suited to microbiome data. We illustrate the package through two case studies. The first re-analyzes a study of the microbiome and metabolome of Inflammatory Bowel Disease patients, uncovering potential mechanistic interactions between the microbiome and disease-associated metabolites, not found in the original study. The second analyzes new data about the influence of mindfulness practice on the microbiome. The mediation analysis highlights shifts in taxa previously associated with depression that cannot be explained indirectly by diet or sleep behaviors alone. A gallery of examples and further documentation can be found at https://go.wisc.edu/830110.

Prognostic score-based model averaging approach for propensity score estimation

BackgroundPropensity scores (PS) are typically evaluated using balance metrics that focus on covariate balance, often without considering their predictive power for the outcome. This approach may not always result in optimal bias reduction in the treatment effect estimate. To address this issue, evaluating covariate balance through prognostic scores, which account for the relationship between covariates and the outcome, has been proposed. Similarly, using a typical model averaging approach for PS estimation that minimizes prediction error for treatment status and covariate imbalance does not necessarily optimize PS-based confounding adjustment. As an alternative approach, using the averaged PS model that minimizes inter-group differences in the prognostic score may further reduce bias in the treatment effect estimate. Moreover, since the prognostic score is also an estimated quantity, model averaging in the prognostic scores can help identify a better prognostic score model. Utilizing the model-averaged prognostic scores as the balance metric for constructing the averaged PS model can contribute to further decreasing bias in treatment effect estimates. This paper demonstrates the effectiveness of the PS model averaging approach based on prognostic score balance and proposes a method that uses the model-averaged prognostic score as a balance metric, evaluating its performance through simulations and empirical analysis.MethodsWe conduct a series of simulations alongside an analysis of empirical observational data to compare the performances of weighted treatment effect estimates using the proposed and existing approaches. In our examination, we separately provid four candidate estimates for the PS and prognostic score models using traditional regression and machine learning methods. The model averaging of PS based on these candidate estimators is performed to either maximize the prediction accuracy of the treatment or to minimize intergroup differences in covariate distributions or prognostic scores. We also utilize not only the prognostic scores from each candidate model but also an averaged score that best predicted the outcome, for the balance assessment.ResultsThe simulation and empirical data analysis reveal that our proposed model-averaging approaches for PS estimation consistently yield lower bias and less variability in treatment effect estimates across various scenarios compared to existing methods. Specifically, using the optimally averaged prognostic scores as a balance metric significantly improves the robustness of the weighted treatment effect estimates.DiscussionThe prognostic score-based model averaging approach for estimating PS can outperform existing model averaging methods. In particular, the estimator using the model averaging prognostic score as a balance metric can produce more robust estimates. Since our results are obtained under relatively simple conditions, applying them to real data analysis requires adjustments to obtain accurate estimates according to the complexity and dimensionality of the data.ConclusionsUsing the prognostic score as the balance metric for the PS model averaging enhances the performance of the treatment effect estimator, which can be recommended for a wide variety of situations. When applying the proposed method to real-world data, it is important to use it in conjunction with techniques that mitigate issues arising from the complexity and high dimensionality of the data.