Marginal Modeling Approach Research Articles

Early Maternal Depression and Social Skills in Adolescence: A Marginal Structural Modeling Approach

AbstractEarly maternal depression is a risk factor that may have adverse effects on adolescent social skills. Although evidence indicates links between early maternal depression and social outcomes during early childhood, whether an association extends to adolescence needs further examination. We tested the possible long‐term association between early maternal depression and adolescent social skills using a national secondary dataset. A secondary objective was to test if maternal parenting at the transition to adolescence mediated the association, with the notion that adverse outcomes of early maternal depression could be ameliorated by positive parenting practices at an important developmental transition. Data were obtained from the National Institute of Child Health and Human Development Study of Early Child Care and Youth Development. Marginal structural modeling within the context of structural equation modeling revealed a significant association between early maternal depression and adolescent social skills while controlling for maternal depression during pre‐adolescence and adolescence. Maternal parenting skills partially mediated the association between early maternal depression and mother report of adolescent social skills. These findings have important implications for understanding the link between early maternal depression and adolescent social skills, and for informing parenting practices during pre‐adolescence.

A Marginal Structural Modeling Approach with Super Learning for a Study on Oral Bisphosphonate Therapy and Atrial Fibrillation

AbstractPurpose: Observational studies designed to investigate the safety of a drug in a postmarketing setting typically aim to examine rare and non-acute adverse effects in a population that is not restricted to particular patient subgroups for which the therapy, typically a drug, was originally approved. Large healthcare databases and, in particular, rich electronic medical record (EMR) databases, are well suited for the conduct of these safety studies since they can provide detailed longitudinal information on drug exposure, confounders, and outcomes for large and representative samples of patients that are considered for treatment in clinical settings. Analytic efforts for drawing valid causal inferences in such studies are faced with three challenges: (1) the formal definition of relevant effect measures addressing the safety question of interest; (2) the development of analytic protocols to estimate such effects based on causal methodologies that can properly address the problems of time-dependent confounding and selection bias due to informative censoring, and (3) the practical implementation of such protocols in a large clinical/medical database setting. In this article, we describe an effort to specifically address these challenges with marginal structural modeling based on inverse probability weighting with data reduction and super learning.Methods: We describe the principles of, motivation for, and implementation of an analytical protocol applied in a safety study investigating possible effects of exposure to oral bisphosphonate therapy on the risk of non-elective hospitalization for atrial fibrillation or atrial flutter among older women based on EMR data from the Kaiser Permanente Northern California integrated health care delivery system. Adhering to guidelines brought forward by Hernan (Epidemiology 2011;22:290-1), we start by framing the safety research question as one that could be directly addressed by a sequence of ideal randomized experiments before describing the estimation approach that we implemented to emulate inference from such trials using observational data.Results: This report underlines the important computation burden involved in the application of the current R implementation of super learning with large data sets. While computing time and memory requirements did not permit aggressive estimator selection with super learning, this analysis demonstrates the applicability of simplified versions of super learning based on select sets of candidate learners to avoid complete reliance on arbitrary selection of parametric models for confounding and selection bias adjustment. Results do not raise concern over the safety of one-year exposure to BP but may suggest residual bias possibly due to unmeasured confounders or insufficient parametric adjustment for observed confounders with the candidate learners selected.Conclusions: Adjustment for time-dependent confounding and selection bias based on the ad hoc inverse probability weighting approach described in this report may provide a feasible alternative to extended Cox modeling or the point treatment analytic approaches (e.g. based on propensity score matching) that are often adopted in safety research with large data sets. Alternate algorithms are needed to permit the routine and more aggressive application of super learning with large data sets.

Testing hypotheses involving Cronbach's alpha using marginal models

We discuss the statistical testing of three relevant hypotheses involving Cronbach's alpha: one where alpha equals a particular criterion; a second testing the equality of two alpha coefficients for independent samples; and a third testing the equality of two alpha coefficients for dependent samples. For each of these hypotheses, various statistical tests have been proposed. Over the years, these tests have depended on progressively fewer assumptions. We propose a new approach to testing the three hypotheses that relies on even fewer assumptions, is especially suited for discrete item scores, and can be applied easily to tests containing large numbers of items. The new approach uses marginal modelling. We compared the Type I error rate and the power of the marginal modelling approach to several of the available tests in a simulation study using realistic conditions. We found that the marginal modelling approach had the most accurate Type I error rates, whereas the power was similar across the statistical tests.

Investigating the relationship between neighborhood poverty and mortality risk: A marginal structural modeling approach

Extant observational studies generally support the existence of a link between neighborhood context and health. However, estimating the causal impact of neighborhood effects from observational data has proven to be a challenge. Omission of relevant factors may lead to overestimating the effects of neighborhoods on health while inclusion of time-varying confounders that may also be mediators (e.g., income, labor force status) may lead to underestimation. Using longitudinal data from the 1990 to 2007 years of the Panel Study of Income Dynamics, this study investigates the link between neighborhood poverty and overall mortality risk. A marginal structural modeling strategy is employed to appropriately adjust for simultaneous mediating and confounding factors. To address the issue of possible upward bias from the omission of key variables, sensitivity analysis to assess the robustness of results against unobserved confounding is conducted. We examine two continuous measures of neighborhood poverty – single-point and a running average. Both were specified as piece-wise linear splines with a knot at 20 percent. We found no evidence from the traditional naïve strategy that neighborhood context influences mortality risk. In contrast, for both the single-point and running average neighborhood poverty specifications, the marginal structural model estimates indicated a statistically significant increase in mortality risk with increasing neighborhood poverty above the 20 percent threshold. For example, below 20 percent neighborhood poverty, no association was found. However, after the 20 percent poverty threshold is reached, each 10 percentage point increase in running average neighborhood poverty was found to increase the odds for mortality by 89 percent [95% CI = 1.22, 2.91]. Sensitivity analysis indicated that estimates were moderately robust to omitted variable bias.

Alcohol Outlets and Binge Drinking in Urban Neighborhoods: The Implications of Nonlinearity for Intervention and Policy

Alcohol outlet density has long been associated with alcohol-related harms, and policymakers have endorsed alcohol outlet restriction to reduce these harms. However, potential nonlinearity in the relation between outlet density and alcohol consumption has not been rigorously examined. We used data from the New York Social Environment Study (n = 4000) to examine the shape of the relation between neighborhood alcohol outlet density and binge drinking by using a generalized additive model with locally weighted scatterplot smoothing, and applied an imputation-based marginal modeling approach. We found a nonlinear relation between alcohol outlet density and binge drinking; the association was stronger at densities of more than 80 outlets per square mile. Binge drinking prevalence was estimated to be 13% at 130 outlets, 8% at 80 outlets, and 8% at 20 outlets per square mile. This nonlinearity suggests that reductions in alcohol outlet density where density is highest and the association is strongest may have the largest public health impact per unit reduction. Future research should assess the impact of policies and interventions that aim to reduce alcohol outlet density, and consider nonlinearity in effects.

Attributable Mortality of Ventilator-Associated Pneumonia

Measuring the attributable mortality of ventilator-associated pneumonia (VAP) is challenging and prone to different forms of bias. Studies addressing this issue have produced variable and controversial results. We estimate the attributable mortality of VAP in a large multicenter cohort using statistical methods from the field of causal inference. Patients (n = 4,479) from the longitudinal prospective (1997-2008) French multicenter Outcomerea database were included if they stayed in the intensive care unit (ICU) for at least 2 days and received mechanical ventilation (MV) within 48 hours after ICU admission. A competing risk survival analysis, treating ICU discharge as a competing risk for ICU mortality, was conducted using a marginal structural modeling approach to adjust for time-varying confounding by disease severity. Six hundred eighty-five (15.3%) patients acquired at least one episode of VAP. We estimated that 4.4% (95% confidence interval, 1.6-7.0%) of the deaths in the ICU on Day 30 and 5.9% (95% confidence interval, 2.5-9.1%) on Day 60 are attributable to VAP. With an observed ICU mortality of 23.3% on Day 30 and 25.6% on Day 60, this corresponds to an ICU mortality attributable to VAP of about 1% on Day 30 and 1.5% on Day 60. Our study on the attributable mortality of VAP is the first that simultaneously accounts for the time of acquiring VAP, informative loss to follow-up after ICU discharge, and the existence of complex feedback relations between VAP and the evolution of disease severity. In contrast to the majority of previous reports, we detected a relatively limited attributable ICU mortality of VAP.

Bayesian tests on components of the compound symmetry covariance matrix

Complex dependency structures are often conditionally modeled, where random effects parameters are used to specify the natural heterogeneity in the population. When interest is focused on the dependency structure, inferences can be made from a complex covariance matrix using a marginal modeling approach. In this marginal modeling framework, testing covariance parameters is not a boundary problem. Bayesian tests on covariance parameter(s) of the compound symmetry structure are proposed assuming multivariate normally distributed observations. Innovative proper prior distributions are introduced for the covariance components such that the positive definiteness of the (compound symmetry) covariance matrix is ensured. Furthermore, it is shown that the proposed priors on the covariance parameters lead to a balanced Bayes factor, in case of testing an inequality constrained hypothesis. As an illustration, the proposed Bayes factor is used for testing (non-)invariant intra-class correlations across different group types (public and Catholic schools), using the 1982 High School and Beyond survey data.

Collective Efficacy and Major Depression in Urban Neighborhoods

Depression contributes substantially to the global burden of disease and disability. Population-level factors that shape depression may be efficient targets for intervention to decrease the depression burden. The authors aimed to identify the relation between neighborhood collective efficacy and major depression. Analyses were conducted on data from the New York Social Environment Study (n = 4,000), a representative study of residents of New York, New York, conducted in 2005. Neighborhood collective efficacy was measured as the average neighborhood response on a well-established scale. Major depression was assessed with the Patient Health Questionnaire. A marginal modeling approach was applied to present results on the additive scale relevant to public health and intervention. Analyses were adjusted for demographic and socioeconomic characteristics, recent life events that could contribute to both depression and change in residence, and individual perception of collective efficacy. Collective efficacy was related to major depression among older adults; marginal models estimated a 6.2% (95% confidence interval: 0.1, 17.5) lower prevalence of depression if all older adults (65 years and older) had lived in high versus low collective efficacy neighborhoods. Similar results were suggested among younger adults; however, the confidence interval crossed the null. These and other study findings suggest that community-randomized trials targeting collective efficacy merit consideration.

Semiparametric regression models for repeated measures of mortal cohorts with non‐monotone missing outcomes and time‐dependent covariates

We propose a semiparametric marginal modeling approach for longitudinal analysis of cohorts with data missing due to death and non-response to estimate regression parameters interpreted as conditioned on being alive. Our proposed method accommodates outcomes and time-dependent covariates that are missing not at random with non-monotone missingness patterns via inverse-probability weighting. Missing covariates are replaced by consistent estimates derived from a simultaneously solved inverse-probability-weighted estimating equation. Thus, we utilize data points with the observed outcomes and missing covariates beyond the estimated weights while avoiding numerical methods to integrate over missing covariates. The approach is applied to a cohort of elderly female hip fracture patients to estimate the prevalence of walking disability over time as a function of body composition, inflammation, and age.

Compositional analysis of overdispersed counts using generalized estimating equations

Multivariate abundance data are commonly collected in ecology, and used to explore questions of “community composition”—how relative abundance of different taxa changes with environmental conditions. In this paper, we propose a log-linear marginal modeling approach for analyzing such compositional count data, via generalized estimating equations. This method exploits the multiplicative nature of log-linear models for counts, by reparameterizing models that describe marginal effects on mean abundance. This allows partitioning into “main effects” and compositional effects, which is appealing for interpretation. We apply the proposed approach to reanalyze compositional counts of benthic invertebrates from Delaware Bay, and data of invertebrate communities inhabiting Acacia plants in eastern Australia. In both cases we resort to a resampling approach to make inferences about regression parameters, because the number of clusters was not large compared to cluster size.

Ambient Ozone Concentrations and Cardiac Mortality in Southern California 1983-2000: Application of a New Marginal Structural Model Approach

The authors evaluated the association between ambient ozone levels and cardiac mortality in California's South Coast Air Basin during the period 1983-2000 and compared inferences from several types of marginal structural model (MSM) estimators. The authors undertook an ecologic study during the high-ozone seasons among persons over age 55 years. In contrast to conditional regression analysis and MSMs based on G-computation and simple inverse probability-of-treatment weighting (IPTW), an MSM that protected against violation of the experimental treatment assignment (ETA) assumption and considered only those areas that could have experienced both high and low ozone concentrations during 1983-2000 found no consistent evidence that reductions in quarterly 1-hour maximum ozone concentrations from levels above any of the regulatory standards to levels below those standards led to decreases in cardiac mortality; however, it did find evidence of decreases related to a decrease in 8-hour maximum concentrations. The G-computation estimator and simple IPTW estimators were biased because of serious violation of the ETA assumption. These analyses highlight the importance of nonviolation of the ETA assumption for valid inference and the failure of conditional regression to provide marginal estimates in the presence of interactions. Noncausal models also consistently inferred larger associations, which may have been due to bias violation of the ETA assumption on which these models rely.

A Marginal Structural Modeling Approach to Assess the Cumulative Effect of Drug Treatment on Later Drug Use Abstinence

In this article, we applied a marginal structural model (MSM) to estimate the effect on later drug use of drug treatments occurring over 10 years following first use of the primary drug. The study was based on the longitudinal data that were collected in three projects among 421 subjects and covered 15 years since first use of their primary drug. The cumulative treatment effect was estimated by the inverse-probability of treatment weighted estimators of MSM as well as the traditional regression analysis. Contrary to the traditional regression analysis, results of the MSM showed that the cumulative treatment occurring over the 10 years significantly increased the likelihood of drug use abstinence in the subsequent 5-year period. From both the statistical and empirical point of view, MSM is a better approach to assessing cumulative treatment effects, considering its advantage of controlling for self-selection bias over time.

Optimal combination of estimating equations in the analysis of multilevel nested correlated data

Multilevel nested, correlated data often arise in biomedical research. Examples include teeth nested within quadrants in a mouth or students nested within classrooms in schools. In some settings, cluster sizes may be large relative to the number of independent clusters and the degree of correlation may vary across clusters. When cluster sizes are large, fitting marginal regression models using Generalized Estimating Equations with flexible correlation structures that reflect the nested structure may fail to converge and result in unstable covariance estimates. Also, the use of patterned, nested working correlation structures may not be efficient when correlation varies across clusters. This paper describes a flexible marginal regression modeling approach based on an optimal combination of estimating equations. Particular within-cluster and between-cluster data contrasts are used without specification of the working covariance structure and without estimation of covariance parameters. The method involves estimation of the covariance matrix only for the vector of component estimating equations (which is typically of small dimension) rather than the covariance matrix of the observations within a cluster (which may be of large dimension). In settings where the number of clusters is large relative to the cluster size, the method is stable and is highly efficient, while maintaining appropriate coverage levels. Performance of the method is investigated with simulation studies and an application to a periodontal study.

Regression analysis of multivariate recurrent event data with time-varying covariate effects

Recurrent event data occur in many fields and many approaches have been proposed for their analyses (Andersen et al. (1993) [1]; Cook and Lawless (2007) [3]). However, most of the available methods allow only time-independent covariate effects, and sometimes this may not be true. In this paper, we consider regression analysis of multivariate recurrent event data in which some covariate effects may be time-dependent. For the problem, we employ the marginal modeling approach and, especially, estimating equation-based inference procedures are developed. Both asymptotic and finite-sample properties of the proposed estimates are established and an illustrative example is provided.

Marginal Hazards Regression for Retrospective Studies within Cohort with Possibly Correlated Failure Time Data

A retrospective dental study was conducted to evaluate the degree to which pulpal involvement affects tooth survival. Due to the clustering of teeth, the survival times within each subject could be correlated and thus the conventional method for the case-control studies cannot be directly applied. In this article, we propose a marginal model approach for this type of correlated case-control within cohort data. Weighted estimating equations are proposed for the estimation of the regression parameters. Different types of weights are also considered for improving the efficiency. Asymptotic properties of the proposed estimators are investigated and their finite sample properties are assessed via simulations studies. The proposed method is applied to the aforementioned dental study.

A comparison between the design-based and model-based approaches using longitudinal survey data

Survey data analysis using complex sampling designs ought to account for clustering, stratification and unequal probability of selection. Design-based and model-based methods are two commonly used routes taken to account for such survey designs. Several studies of cross-sectional survey designs have shown that these two approaches provide similar results when the model fits the data well. The present paper aims at comparing these two approaches for longitudinal survey design using the National Population Health Survey (NPHS) dataset. A marginal modeling approach proposed by Rao and modified bootstrap method for longitudinal data were used by way of a design-based method. The Generalized Estimating Equation (GEE) method, proposed by Liang and Zeger was used as a typical model-based approach. The parameter estimates obtained using the design-based and model-based methods were similar. However, the standard errors and the 95% confidence interval were different. Rao's method produced the most conservative standard errors. In conclusion, design-based methods should be preferred over model-based methods, as this method provides reliable results.

Analysis of marginally specified semi‐nonparametric models for clustered binary data

Generalized linear mixed models are widely used for analyzing clustered data. If the primary interest is in regression parameters, one can proceed alternatively, through the marginal mean model approach. In the present study, a joint model consisting of a marginal mean model and a cluster‐specific conditional mean model is considered. This model is useful when both time‐independent and time‐dependent covariates are available. Furthermore our model is semi‐parametric, as we assume a flexible, smooth semi‐nonparametric density of the cluster‐specific effects. This semi‐nonparametric density‐based approach outperforms the approach based on normality assumption with respect to some important features of ‘between‐cluster variation’. We employ a full likelihood‐based approach and apply the Monte Carlo EM algorithm to analyze the model. A simulation study is carried out to demonstrate the consistency of the approach. Finally, we apply this to a study of long‐term illness data.

Weighted estimating equations for longitudinal studies with death and non‐monotone missing time‐dependent covariates and outcomes

We propose a marginal modeling approach to estimate the association between a time-dependent covariate and an outcome in longitudinal studies where some study participants die during follow-up and both variables have non-monotone response patterns. The proposed method is an extension of weighted estimating equations that allows the outcome and covariate to have different missing-data patterns. We present methods for both random and non-random missing-data mechanisms. A study of functional recovery in a cohort of elderly female hip-fracture patients motivates the approach.

A Goodness‐of‐fit Test for the Marginal Cox Model for Correlated Interval‐censored Failure Time Data

The marginal Cox model approach is perhaps the most commonly used method in the analysis of correlated failure time data (Cai, 1999; Cai and Prentice, 1995; Lin, 1994; Wei, Lin and Weissfeld, 1989). It assumes that the marginal distributions for the correlated failure times can be described by the Cox model and leaves the dependence structure completely unspecified. This paper discusses the assessment of the marginal Cox model for correlated interval-censored data and a goodness-of-fit test is presented for the problem. The method is applied to a set of correlated interval-censored data arising from an AIDS clinical trial.

Causal effects in longitudinal studies: Definition and maximum likelihood estimation

Recently, a nonparametric marginal structural model (NPMSM) approach to Causal Inference has been proposed [Neugebauer, R., van der Laan, M., 2006. Nonparametric causal effects based on marginal structural models. J. Statist. Plann. Inference (in press), 〈 www http://www.sciencedirect.com/science/journal/03783758 〉 .] as an appealing practical alternative to the original parametric MSM (PMSM) approach introduced by Robins [Robins, J., 1998a. Marginal structural models. In: 1997 Proceedings of the American Statistical Association, American Statistical Association, Alexandria, VA, pp. 1–10]. The new MSM-based causal inference methodology generalizes the concept of causal effects: the proposed nonparametric causal effects are interpreted as summary measures of the causal effects defined with PMSMs. In addition, causal inference with NPMSM does not rely on the assumed correct specification of a parametric MSM but instead defines causal effects based on a user-specified working causal model which can be willingly misspecified. The NPMSM approach was developed for studies with point treatment data or with longitudinal data where the outcome is not time-dependent (typically collected at the end of data collection). In this paper, we generalize this approach to longitudinal studies where the outcome is time-dependent, i.e. collected throughout the span of the studies, and address the subsequent estimation inconsistency which could easily arise from a hasty generalization of the algorithm for maximum likelihood estimation. More generally, we provide an overview of the multiple causal effect representations which have been developed based on MSMs in longitudinal studies.