Evaluating differential effects using regression interactions and regression mixture models

Evidence Clearinghouses as Tools to Advance Health Equity: What We Know from a Systematic Scan

Evidence clearinghouses evaluate and summarize literature to help decision-makers prioritize and invest in evidence-informed interventions. Clearinghouses and related practice-oriented tools are continuously evolving; however, it is unclear the extent to which these tools assess and summarize evidence describing an intervention's impact on health equity. We conducted a systematic scan to explore how clearinghouses communicated an intervention's equity impact and reviewed their underlying methods and how they defined and operationalized health equity. In 2021, we identified 18 clearinghouses that were US-focused, web-based registries of interventions that assigned an intervention effectiveness rating for improving community health and the social determinants of health. We reviewed each clearinghouse's website and collected publicly available information about their health equity impact review, review methods, and health equity definitions and values. We conducted a comparative analysis among select clearinghouses using qualitative methods. Among the 18 clearinghouses, fewer than half (only seven) summarized an intervention's potential impact on health equity. Overall, those seven clearinghouses defined and operationalized equity differently, and most lacked transparency in their review methods. Clearinghouses used one or more approaches to communicate findings from their review: summarize study findings on differential impact for subpopulations, curate interventions that reduce health disparities, and/or assign a disparity/equity rating to each intervention. Evidence clearinghouses can enhance equity-focused methods and be transparent in their underlying values to better support the uptake and implementation of evidence-informed interventions to advance health equity. However, clearinghouses are unable to do so without underlying equity-focused empirical evidence.

Semiparametric finite mixture of regression models with Bayesian P-splines

Mixture models provide a useful tool to account for unobserved heterogeneity and are at the basis of many model-based clustering methods. To gain additional flexibility, some model parameters can be expressed as functions of concomitant covariates. In this Paper, a semiparametric finite mixture of regression models is defined, with concomitant information assumed to influence both the component weights and the conditional means. In particular, linear predictors are replaced with smooth functions of the covariate considered by resorting to cubic splines. An estimation procedure within the Bayesian paradigm is suggested, where smoothness of the covariate effects is controlled by suitable choices for the prior distributions of the spline coefficients. A data augmentation scheme based on difference random utility models is exploited to describe the mixture weights as functions of the covariate. The performance of the proposed methodology is investigated via simulation experiments and two real-world datasets, one about baseball salaries and the other concerning nitrogen oxide in engine exhaust.

Seemingly unrelated clusterwise linear regression for contaminated data

Clusterwise regression is an approach to regression analysis based on finite mixtures which is generally employed when sample observations come from a population composed of several unknown sub-populations. Whenever the response is continuous, Gaussian clusterwise linear regression models are usually employed. Such models have been recently robustified with respect to the possible presence of mild outliers in the sub-populations. However, in some fields of research, especially in the modelling of multivariate economic data or data from the social sciences, there may be prior information on the specific covariates to be considered in the linear term employed in the prediction of a certain response. As a consequence, covariates may not be the same for all responses. Thus, a novel class of multivariate Gaussian linear clusterwise regression models is proposed. This class provides an extension to mixture-based regression analysis for modelling multivariate and correlated responses in the presence of mild outliers that let the researcher free to use a different vector of covariates for each response. Details about the model identification and maximum likelihood estimation via an expectation-conditional maximisation algorithm are given. The performance of the new models is studied by simulation in comparison with other clusterwise linear regression models. A comparative evaluation of their effectiveness and usefulness is provided through the analysis of a real dataset.

The Impact of Imposing Equality Constraints on Residual Variances Across Classes in Regression Mixture Models

The purpose of this study is to explore the impact of constraining class-specific residual variances to be equal by examining and comparing the parameter estimation of a free model and a constrained model under various conditions. A Monte Carlo simulation study was conducted under several conditions, including the number of predictors, class-specific intercepts, sample size, class-specific regression weights, and class proportion to evaluate the results for parameter estimation of the free model and the restricted model. The free model yielded a more accurate estimation than the restricted model for most of the conditions, but the accuracy of the free model estimation was impacted by the number of predictors, sample size, the disparity in the magnitude of class-specific slopes and intercepts, and class proportion. When equality constraints were imposed in residual variance discrepant conditions, the parameter estimates showed substantial inaccuracy for slopes, intercepts, and residual variances, especially for those in Class 2 (with a lower class-specific slope). When the residual variances were equal between the classes, the restricted model showed better performance under some conditions.

Assessing Differential Effects of Somatic Amplification to Positive Affect in Midlife and Late Adulthood-A Regression Mixture Approach

This study aims to provide an empirical demonstration of a novel method, regression mixture model, by examining differential effects of somatic amplification to positive affect and identifying the predictors that contribute to the differential effects. Data derived from the second wave of Midlife in the United States. The analytic sample consisted of 1,766 adults aged from 33 to 84 years. Regression mixture models were fitted using Mplus 7.4, and a two-step model-building approach was adopted. Three latent groups were identified consisting of a maladaptive (32.1%), a vulnerable (62.5%), and a resilient (5.4%) group. Six covariates (i.e., age, education level, positive relations with others, purpose in life, depressive symptoms, and physical health) significantly predicted the latent class membership in the regression mixture model. The study demonstrated the regression mixture model to be a flexible and efficient statistical tool in assessing individual differences in response to adversity and identifying resilience factors, which contributes to aging research.

Using baseline target moderation to guide decisions on adapting prevention programs

Tom Dishion, a pioneer in prevention science, was one of the first to recognize the importance of adapting interventions to the needs of individual families. Building towards this goal, we suggest that prevention trials be used to assess baseline target moderated mediation (BTMM), where preventive intervention effects are mediated through change in specific targets, and the resulting effect varies across baseline levels of the target. Four forms of BTMM found in recent trials are discussed including compensatory, rich-get-richer, crossover, and differential iatrogenic effects. A strategy for evaluating meaningful preventive effects is presented based on preventive thresholds for diagnostic conditions, midpoint targets and proximal risk or protective mechanisms. Methods are described for using the results from BTMM analyses of these thresholds to estimate indices of intervention risk reduction or increase as they vary over baseline target levels, and potential cut points are presented for identifying subgroups that would benefit from program adaptation because of weak or potentially iatrogenic program effects. Simulated data are used to illustrate curves for the four forms of BTMM effects and how implications for adaptation change when untreated control group outcomes also vary over baseline target levels.

Repeated measures regression mixture models

Regression mixture models are one increasingly utilized approach for developing theories about and exploring the heterogeneity of effects. In this study we aimed to extend the current use of regression mixtures to a repeated regression mixture method when repeated measures, such as diary-type and experience-sampling method, data are available. We hypothesized that additional information borrowed from the repeated measures would improve the model performance, in terms of class enumeration and accuracy of the parameter estimates. We specifically compared three types of model specifications in regression mixtures: (a) traditional single-outcome model; (b) repeated measures models with three, five, and seven measures; and (c) a single-outcome model with the average of seven repeated measures. The results showed that the repeated measures regression mixture models substantially outperformed the traditional and average single-outcome models in class enumeration, with less bias in the parameter estimates. For sample size, whereas prior recommendations have suggested that regression mixtures require samples of well over 1,000 participants, even for classes at a large distance from each other (classes with regression weights of .20 vs. .70), the present repeated measures regression mixture models allow for samples as low as 200 participants with an increased number (i.e., seven) of repeated measures. We also demonstrate an application of the proposed repeated measures approach using data from the Sleep Research Project. Implications and limitations of the study are discussed.

The Effects of Sample Size on the Estimation of Regression Mixture Models

Regression mixture models are a statistical approach used for estimating heterogeneity in effects. This study investigates the impact of sample size on regression mixture's ability to produce "stable" results. Monte Carlo simulations and analysis of resamples from an application data set were used to illustrate the types of problems that may occur with small samples in real data sets. The results suggest that (a) when class separation is low, very large sample sizes may be needed to obtain stable results; (b) it may often be necessary to consider a preponderance of evidence in latent class enumeration; (c) regression mixtures with ordinal outcomes result in even more instability; and (d) with small samples, it is possible to obtain spurious results without any clear indication of there being a problem.

Extensions of Auxiliary Variable Approaches for the Investigation of Mediation, Moderation, and Conditional Effects in Mixture Models

Person-centered analyses and mixture models, such as latent profile analyses (LPA), are becoming increasingly common in the organizational literature. However, common usage of LPA rarely extends to the estimation of moderation, conditional effects, and mediation within a single model. This can affect the accuracy of parameter estimates, and it interferes with development and investigation of complex theories. The current study provides an overview of systematic approaches that allows researchers to investigate models involving moderation, conditional effects on outcomes, and mediation. Using M plus, we offer an accessible method of testing complex statistical models that are auxiliary to the focal mixture model. We provide syntax for typical moderation, conditional effects, and mediation hypotheses, and we provide a detailed explanation of the procedures. We demonstrate these procedures with applications involving the five-factor model (FFM) of personality and several additional variables that comprise complex auxiliary statistical models. The pedagogical approach offered by this research will facilitate future theoretical developments and empirical advancements in the use of person-centered analyses.

Foundations for screening adverse childhood experiences: Exploring patterns of exposure through infancy and toddlerhood

Adverse childhood experiences (ACEs) have lifetime consequences for health and development. Identification of ACEs early in childhood provides the potential to intervene before health and development are impaired. This study examined the timing and duration of exposure to ACEs experienced by children from low-income families from ages one to three years to identify whether there were patterns of exposure when infants and toddlers were most vulnerable. We were able to confirm the early negative consequences on cognitive, health, and behavior outcomes previously reported in young children using a national, longitudinal data set of parents and children from low-income households (N=2250). Using Finite Mixture Models, five classes of exposure were identified for children, Consistently Low (63.8%), Decreasing (10.3%), High at Age 2 (11.4%), Increasing (10.4%), and Consistently High (4%). The Consistently Low and Consistently High classes had the most and least optimal development across all domains, respectively. When examining child development outcomes among children with variable exposures to adversities, we found that for cognitive, language, and physical development, the most proximal ACEs were more robust for predicting child outcomes. For socioemotional health, exposure at any time from one to three to ACEs had negative consequences. As a whole, findings from this study highlight the need to consider ACEs screening tools that are both time-sensitive and permit a lifetime report.

An evaluation of the bootstrap for model validation in mixture models

Bootstrapping has been used as a diagnostic tool for validating model results for a wide array of statistical models. Here we evaluate the use of the non-parametric bootstrap for model validation in mixture models. We show that the bootstrap is problematic for validating the results of class enumeration and demonstrating the stability of parameter estimates in both finite mixture and regression mixture models. In only 44% of simulations did bootstrapping detect the correct number of classes in at least 90% of the bootstrap samples for a finite mixture model without any model violations. For regression mixture models and cases with violated model assumptions, the performance was even worse. Consequently, we cannot recommend the non-parametric bootstrap for validating mixture models. The cause of the problem is that when resampling is used influential individual observations have a high likelihood of being sampled many times. The presence of multiple replications of even moderately extreme observations is shown to lead to additional latent classes being extracted. To verify that these replications cause the problems we show that leave-k-out cross-validation where sub-samples taken without replacement does not suffer from the same problem.

Multidisciplinary design and analytic approaches to advance prospective research on the multilevel determinants of child health

PURPOSE

Characterizing the determinants of child health and development over time, and identifying the mechanisms by which these determinants operate, is a research priority. The growth of precision medicine has increased awareness and refinement of conceptual frameworks, data management systems, and analytic methods for multilevel data. This article reviews key methodological challenges in cohort studies designed to investigate multilevel influences on child health and strategies to address them.

METHODS

We review and summarize methodological challenges that could undermine prospective studies of the multilevel determinants of child health and ways to address them, borrowing approaches from the social and behavioral sciences.

RESULTS

Nested data, variation in intervals of data collection and assessment, missing data, construct measurement across development and reporters, and unobserved population heterogeneity pose challenges in prospective multilevel cohort studies with children. We discuss innovations in missing data, innovations in person-oriented analyses, and innovations in multilevel modeling to address these challenges.

CONCLUSIONS

Study design and analytic approaches that facilitate the integration across multiple levels, and that account for changes in people and the multiple, dynamic, nested systems in which they participate over time, are crucial to fully realize the promise of precision medicine for children and adolescents.

Children exposed to intimate partner violence: Identifying differential effects of family environment on children's trauma and psychopathology symptoms through regression mixture models

The majority of analytic approaches aimed at understanding the influence of environmental context on children's socioemotional adjustment assume comparable effects of contextual risk and protective factors for all children. Using self-reported data from 289 maternal caregiver-child dyads, we examined the degree to which there are differential effects of severity of intimate partner violence (IPV) exposure, yearly household income, and number of children in the family on posttraumatic stress symptoms (PTS) and psychopathology symptoms (i.e., internalizing and externalizing problems) among school-age children between the ages of 7-12 years. A regression mixture model identified three latent classes that were primarily distinguished by differential effects of IPV exposure severity on PTS and psychopathology symptoms: (1) asymptomatic with low sensitivity to environmental factors (66% of children), (2) maladjusted with moderate sensitivity (24%), and (3) highly maladjusted with high sensitivity (10%). Children with mothers who had higher levels of education were more likely to be in the maladjusted with moderate sensitivity group than the asymptomatic with low sensitivity group. Latino children were less likely to be in both maladjusted groups compared to the asymptomatic group. Overall, the findings suggest differential effects of family environmental factors on PTS and psychopathology symptoms among children exposed to IPV. Implications for research and practice are discussed.