Bayesian Models for Multiple Outcomes in Domains with Application to the Seychelles Child Development Study

Discovering structure in multiple outcomes models for tests of childhood neurodevelopment

Bayesian model-based clustering provides a powerful and flexible tool that can be incorporated into regression models to better understand the grouping of observations. Using data from the Seychelles Child Development Study, we explore the effect of prenatal methylmercury exposure on 20 neurodevelopmental outcomes measured in 9-year-old children. Rather than cluster individual subjects, we cluster the outcomes within a multiple outcomes model. By using information in the data to nest the outcomes into groups called domains, the model more accurately reflects the shared characteristics of neurodevelopmental domains and improves estimation of the overall and outcome-specific exposure effects by shrinking effects within and between domains selected by the data. The Bayesian paradigm allows for sampling from the posterior distribution of the grouping parameters; thus, inference can be made about group membership and their defining characteristics. We avoid the often difficult and highly subjective requirement of a priori identification of the total number of groups by incorporating a Dirichlet process prior to form a fully Bayesian multiple outcomes model.

USING THE SEYCHELLES CHILD DEVELOPMENT STUDY TO CLUSTER MULTIPLE OUTCOMES INTO DOMAINS TO IMPROVE ESTIMATION OF THE OVERALL EFFECT OF MERCURY ON NEURODEVELOPMENT

Environmental exposure effects on human development can be small and difficult to detect due to the nature of observational data. In the Seychelles Child Development Study, researchers examined the effect of prenatal methylmercury exposure using a battery of tests measuring aspects of child development [23, 25]. We build a multiple outcomes model similar to that of the previous analyses (see [23, 25]); however, our multiple outcomes model makes no assumptions of relationships between the testing outcomes. Instead, the nesting of outcomes into domains is a clustering problem we address with a Dirichlet process mixture model implemented through a Bayesian MCMC approach [16]. This model provides inference for the methylmercury exposure effect as well as greater insight into the similarities and differences across the outcomes.

Early ART Results in Greater Immune Reconstitution Benefits in HIV-Infected Infants: Working with Data Missingness in a Longitudinal Dataset

Background

Early initiation of anti-retroviral treatment (ART) decreases mortality as compared to deferred treatment, but whether it preserves immune cells from early loss or promotes their recovery remains undefined. Determination of complex immunological endpoints in infants is often marred by missing data due to missed visits and/or inadequate sampling. Specialized methods are required to address missingness and facilitate data analysis.

Methods

We characterized the changes in cellular and humoral immune parameters over the first year of life in 66 HIV-infected infants (0–1 year of age) enrolled in the CHER study starting therapy within 12 weeks of birth (n = 42) or upon disease progression (n = 24). A convenience cohort of 23 uninfected infants aged 0–6 months born to mothers with HIV-1 infection was used as controls. Flow cytometry and ELISA were used to evaluate changes in natural killer (NK) cells, plasmacytoid dendritic cells (pDC), and CD4⁺ or CD8⁺ T-cell frequencies. Data missingness was assessed using Little's test. Complete datasets for analysis were created using Multiple Imputation (MI) or Bayesian modeling and multivariate analysis was conducted on the imputed datasets.

Results

HIV-1-infected infants had greater frequency of CD4⁺ T cells with naïve phenotype, as well as higher serum IL-7 levels than HIV exposed/uninfected infants. The elevated data missingness was completely at random, allowing the use of both MI and Bayesian modeling. Both methods indicate that early ART initiation results in higher CD4⁺ T cell frequency, lower expression of CD95 in CD8⁺ T cell, and preservation of naïve T cell subsets. In contrast, innate immune effectors appeared to be similar independently of the timing of ART initiation.

Conclusions

Early ART initiation in infants with perinatal HIV infection reduces immune activation and preserves an early expansion of naïve T-cells with undiminished innate cell numbers, giving greater immune reconstitution than achieved with deferred ART. Both statistical approaches concurred in this finding.

Hierarchical regression for analyses of multiple outcomes

In cohort mortality studies, there often is interest in associations between an exposure of primary interest and mortality due to a range of different causes. A standard approach to such analyses involves fitting a separate regression model for each type of outcome. However, the statistical precision of some estimated associations may be poor because of sparse data. In this paper, we describe a hierarchical regression model for estimation of parameters describing outcome-specific relative rate functions and associated credible intervals. The proposed model uses background stratification to provide flexible control for the outcome-specific associations of potential confounders, and it employs a hierarchical "shrinkage" approach to stabilize estimates of an exposure's associations with mortality due to different causes of death. The approach is illustrated in analyses of cancer mortality in 2 cohorts: a cohort of dioxin-exposed US chemical workers and a cohort of radiation-exposed Japanese atomic bomb survivors. Compared with standard regression estimates of associations, hierarchical regression yielded estimates with improved precision that tended to have less extreme values. The hierarchical regression approach also allowed the fitting of models with effect-measure modification. The proposed hierarchical approach can yield estimates of association that are more precise than conventional estimates when one wishes to estimate associations with multiple outcomes.