In correlated data settings, analysts typically choose between fitting conditional and marginal models, whose parameters come with distinct interpretations, and as such the choice between the two should be made on scientific grounds. For settings where interest lies in marginal—or population‐averaged—parameters, the question of how best to estimate those parameters is a statistical one, and analysts have at their disposal two distinct modeling frameworks: generalized estimating equations (GEE) and marginalized multilevel models (MMMs). The two have been contrasted theoretically and in large sample settings, but asymptotic theory provides no guarantees in the small sample settings that are commonplace. In a comprehensive series of simulation studies, we shed light on the relative performance of GEE and MMMs in small‐sample settings to help guide analysis decisions in practice. We find that both GEE and MMMs exhibit similar small‐sample bias when the correct correlation structure is adopted (ie, when the random effects distribution is correctly specified or moderately misspecified)—but MMMs can be sensitive to misspecification of the correlation structure. When there are a small number of clusters, MMMs only slightly underestimate standard errors (SEs) for within‐cluster associations but can severely underestimate SEs for between‐cluster associations. By contrast, while GEE severely underestimates SEs, the Mancl and DeRouen correction provides approximately valid inference.
To increase power and minimize bias in statistical analyses, quantitative outcomes are often adjusted for precision and confounding variables using standard regression approaches. The outcome is modeled as a linear function of the precision variables and confounders; however, for many complex phenotypes, the assumptions of the linear regression models are not always met. As an alternative, we used neural networks for the modeling of complex phenotypes and covariate adjustments. We compared the prediction accuracy of the neural network models to that of classical approaches based on linear regression. Using data from the UK Biobank, COPDGene study, and Childhood Asthma Management Program (CAMP), we examined the features of neural networks in this context and compared them with traditional regression approaches for prediction of three outcomes: forced expiratory volume in one second (FEV1), age at smoking cessation, and log transformation of age at smoking cessation (due to age at smoking cessation being right-skewed). We used mean squared error to compare neural network and regression models, and found the models performed similarly unless the observed distribution of the phenotype was skewed, in which case the neural network had smaller mean squared error. Our results suggest neural network models have an advantage over standard regression approaches when the phenotypic distribution is skewed. However, when the distribution is not skewed, the approaches performed similarly. Our findings are relevant to studies that analyze phenotypes that are skewed by nature or where the phenotype of interest is skewed as a result of the ascertainment condition.
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