Sensitivity Analysis of the No-Omitted Confounder Assumption in Latent Growth Curve Mediation Models

Public health spending in Sub-Saharan Africa: exploring transmission mechanisms using the latent growth curve mediation model

In response to the imperatives of universal health coverage, structural factors that may hinder the effectiveness of increased spending in sub-Saharan Africa (SSA) need attention. This study assessed the mediating role of these factors in domestic general government health expenditure (DGGHE) effects to propose solutions for improving population health outcomes (PHO). The analysis used the Latent Growth Curve Mediation Model (LGCMM) approach within the structural equation model (SEM) framework for panel data from 42 SSA countries from 2015 to 2018. The findings were that malaria and female education formed a channel through which DGGHE imparted its effects on DALY in SSA, and these effects were achieved via the specific path from the DGGHE slope to the DALY slope, via malaria and female education slopes. However, the paper found no evidence of immunization coverage mediating the relationship between DGGHE and DALY in SSA. The paper concludes that structural factors affect the effectiveness of DGGHE on PHO, implying that governments should emphasize existing programs to fight against malaria and increase immunization coverage.

The impact of omitting confounders in parallel process latent growth curve mediation models: Three sensitivity analysis approaches

Parallel process latent growth curve mediation models (PP-LGCMMs) are frequently used to longitudinally investigate the mediation effects of treatment on the level and change of outcome through the level and change of mediator. An important but often violated assumption in empirical PP-LGCMM analysis is the absence of omitted confounders of the relationships among treatment, mediator, and outcome. In this study, we analytically examined how omitting pretreatment confounders impacts the inference of mediation from the PP-LGCMM. Using the analytical results, we developed three sensitivity analysis approaches for the PP-LGCMM, including the frequentist, Bayesian, and Monte Carlo approaches. The three approaches help investigate different questions regarding the robustness of mediation results from the PP-LGCMM, and handle the uncertainty in the sensitivity parameters differently. Applications of the three sensitivity analyses are illustrated using a real-data example. A user-friendly Shiny web application is developed to conduct the sensitivity analyses.

Teacher's Corner: An R Shiny App for Sensitivity Analysis for Latent Growth Curve Mediation

Mechanisms of behavior change are the processes through which interventions are hypothesized to cause changes in outcomes. Latent growth curve mediation models (LGCMM) are recommended for investigating the mechanisms of behavior change because LGCMM models establish temporal precedence of change from the mediator to the outcome variable. The Correlated Augmented Mediation Sensitivity Analyses (CAMSA) App implements sensitivity analysis for LGCMM models to evaluate if a mediating path (mechanism) is robust to potential confounding variables. The CAMSA approach is described and applied to simulated data, and data from a research study exploring a mechanism of change in the treatment of substance use disorder.

Mechanisms of Behavior Change in Substance Use Disorder With and Without Formal Treatment

This article provides a narrative review of studies that examined mechanisms of behavior change in substance use disorder. Several mechanisms have some support, including self-efficacy, craving, protective behavioral strategies, and increasing substance-free rewards, whereas others have minimal support (e.g., motivation, identity). The review provides recommendations for expanding the research agenda for studying mechanisms of change, including designs to manipulate putative change mechanisms, measurement approaches that expand the temporal units of analysis during change efforts, more studies of change outside of treatment, and analytic approaches that move beyond mediation tests. The dominant causal inference approach that focuses on treatment and individuals as change agents could be expanded to include a molar behavioral approach that focuses on patterns of behavior in temporally extended environmental contexts. Molar behavioral approaches may advance understanding of how recovery from substance use disorder is influenced by broader contextual features, community-level variables, and social determinants of health. Expected final online publication date for the Annual Review of Clinical Psychology, Volume 18 is May 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Sensitivity Analysis in Nonrandomized Longitudinal Mediation Analysis

Mediation analysis relies on an untestable assumption of the no omitted confounders, which posits that an omitted variable that confounds the relationships between the antecedent, mediator, and outcome variables cannot exist. One common model in alcohol addiction studies is a nonrandomized latent growth curve mediation model (LGCMM), where the antecedent variable is not randomized, the two covarying mediators are latent intercept and slope modeling longitudinal effect of the repeated measures mediator, and an outcome variable that measures alcohol use. An important gap in the literature is lack of sensitivity analysis techniques to assess the effect of the violation of the no omitted confounder assumption in a nonrandomized LGCMM. We extend a sensitivity analysis technique, termed correlated augmented mediation sensitivity analysis (CAMSA), to a nonrandomized LGCMM. We address several unresolved issues in conducting CAMSA for the nonrandomized LGCMM and present: (a) analytical results showing how confounder correlations model a confounding bias, (b) algorithms to address admissible values for confounder correlations, (c) accessible R code within an SEM framework to conduct our proposed sensitivity analysis, and (d) an empirical example. We conclude that conducting sensitivity analysis to ascertain robustness of the mediation analysis is critical.

The impact of measurement error and omitting confounders on statistical inference of mediation effects and tools for sensitivity analysis

To make valid statistical inferences from mediation analysis, a number of assumptions need to be assessed. Among the assumptions, 2 frequently discussed ones are (a) the independent variable, mediator, and outcome variables are measured without error; and (b) no confounders of the effects in the mediation model are omitted. The impact of violating either assumption alone on statistical inference of mediation has been discussed in previous literature. In practice, violations of the 2 assumptions often co-occur. In this study, we analytically investigated the effects of measurement error and omitting confounders on statistical inference of mediation effects, including both point estimation and significance testing. Based on the analytical results, we proposed sensitivity analysis techniques for assessing the robustness of mediation inference to the violation of the 2 assumptions. To implement the techniques, we developed R functions and a user-friendly web tool. Simulated-data and real-data examples were provided for illustrations. We hope the developed tools will help researchers conduct sensitivity analyses of mediation inference more conveniently. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Income disparity in school readiness and the mediating role of perinatal maternal mental health: a longitudinal birth cohort study

AIMS

There is compelling evidence for gradient effects of household income on school readiness. Potential mechanisms are described, yet the growth curve trajectory of maternal mental health in a child's early life has not been thoroughly investigated. We aimed to examine the relationships between household incomes, maternal mental health trajectories from antenatal to the postnatal period, and school readiness.

METHODS

Prospective data from 505 mother-child dyads in a birth cohort in Singapore were used, including household income, repeated measures of maternal mental health from pregnancy to 2-years postpartum, and a range of child behavioural, socio-emotional and cognitive outcomes from 2 to 6 years of age. Antenatal mental health and its trajectory were tested as mediators in the latent growth curve models.

RESULTS

Household income was a robust predictor of antenatal maternal mental health and all child outcomes. Between children from the bottom and top household income quartiles, four dimensions of school readiness skills differed by a range of 0.52 (95% Cl: 0.23, 0.67) to 1.21 s.d. (95% CI: 1.02, 1.40). Thirty-eight percent of pregnant mothers in this cohort were found to have perinatal depressive and anxiety symptoms in the subclinical and clinical ranges. Poorer school readiness skills were found in children of these mothers when compared to those of mothers with little or no symptoms. After adjustment of unmeasured confounding on the indirect effect, antenatal maternal mental health provided a robust mediating path between household income and multiple school readiness outcomes (χ2 126.05, df 63, p < 0.001; RMSEA = 0.031, CFI = 0.980, SRMR = 0.034).

CONCLUSIONS

Pregnant mothers with mental health symptoms, particularly those from economically-challenged households, are potential targets for intervention to level the playing field of their children.

Improved inference in mediation analysis: Introducing the model-based constrained optimization procedure

Mediation analysis is an important approach for investigating causal pathways. One approach used in mediation analysis is the test of an indirect effect, which seeks to measure how the effect of an independent variable impacts an outcome variable through 1 or more mediators. However, in many situations the proposed tests of indirect effects, including popular confidence interval-based methods, tend to produce poor Type I error rates when mediation does not occur and, more generally, only allow dichotomous decisions of "not significant" or "significant" with regards to the statistical conclusion. To remedy these issues, we propose a new method, a likelihood ratio test (LRT), that uses nonlinear constraints in what we term the model-based constrained optimization (MBCO) procedure. The MBCO procedure (a) offers a more robust Type I error rate than existing methods; (b) provides a p value, which serves as a continuous measure of compatibility of data with the hypothesized null model (not just a dichotomous reject or fail-to-reject decision rule); (c) allows simple and complex hypotheses about mediation (i.e., 1 or more mediators; different mediational pathways); and (d) allows the mediation model to use observed or latent variables. The MBCO procedure is based on a structural equation modeling framework (even if latent variables are not specified) with specialized fitting routines, namely with the use of nonlinear constraints. We advocate using the MBCO procedure to test hypotheses about an indirect effect in addition to reporting a confidence interval to capture uncertainty about the indirect effect because this combination transcends existing methods. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

Indirect Effects in Sequential Mediation Models: Evaluating Methods for Hypothesis Testing and Confidence Interval Formation

Complex mediation models, such as a two-mediator sequential model, have become more prevalent in the literature. To test an indirect effect in a two-mediator model, we conducted a large-scale Monte Carlo simulation study of the Type I error, statistical power, and confidence interval coverage rates of 10 frequentist and Bayesian confidence/credible intervals (CIs) for normally and nonnormally distributed data. The simulation included never-studied methods and conditions (e.g., Bayesian CI with flat and weakly informative prior methods, two model-based bootstrap methods, and two nonnormality conditions) as well as understudied methods (e.g., profile-likelihood, Monte Carlo with maximum likelihood standard error [MC-ML] and robust standard error [MC-Robust]). The popular BC bootstrap showed inflated Type I error rates and CI under-coverage. We recommend different methods depending on the purpose of the analysis. For testing the null hypothesis of no mediation, we recommend MC-ML, profile-likelihood, and two Bayesian methods. To report a CI, if data has a multivariate normal distribution, we recommend MC-ML, profile-likelihood, and the two Bayesian methods; otherwise, for multivariate nonnormal data we recommend the percentile bootstrap. We argue that the best method for testing hypotheses is not necessarily the best method for CI construction, which is consistent with the findings we present.

Bootstrap Model-Based Constrained Optimization Tests of Indirect Effects

In mediation analysis, conditions necessary for commonly recommended tests, including the confidence interval (CI)-based tests, to produce an accurate Type I error, do not generally hold for finite sample sizes and non-normally distributed model residuals. This is typically the case because of the complexity of testing a null hypothesis about indirect effects. To remedy these issues, we propose two extensions of the recently developed asymptotic Model-based Constrained Optimization (MBCO) likelihood ratio test (LRT), a promising new model comparison method for testing a general function of indirect effects. The proposed tests, semi-parametric and parametric bootstrap MBCO LRT are shown to yield a more accurate Type I error rate in smaller sample sizes and under various degrees of non-normality of the model residuals compared to the asymptotic MBCO LRT and the CI-based methods. We provide R script in the Supplemental Materials to perform all three MBCO LRTs.