Measuring overlap in binary regression

Variations in structural MRI quality significantly impact commonly used measures of brain anatomy

Subject motion can introduce noise into neuroimaging data and result in biased estimations of brain structure. In-scanner motion can compromise data quality in a number of ways and varies widely across developmental and clinical populations. However, quantification of structural image quality is often limited to proxy or indirect measures gathered from functional scans; this may be missing true differences related to these potential artifacts. In this study, we take advantage of novel informatic tools, the CAT12 toolbox, to more directly measure image quality from T1-weighted images to understand if these measures of image quality: (1) relate to rigorous quality-control checks visually completed by human raters; (2) are associated with sociodemographic variables of interest; (3) influence regional estimates of cortical surface area, cortical thickness, and subcortical volumes from the commonly used Freesurfer tool suite. We leverage public-access data that includes a community-based sample of children and adolescents, spanning a large age-range (N = 388; ages 5-21). Interestingly, even after visually inspecting our data, we find image quality significantly impacts derived cortical surface area, cortical thickness, and subcortical volumes from multiple regions across the brain (~ 23.4% of all areas investigated). We believe these results are important for research groups completing structural MRI studies using Freesurfer or other morphometric tools. As such, future studies should consider using measures of image quality to minimize the influence of this potential confound in group comparisons or studies focused on individual differences.

Default Priors for the Intercept Parameter in Logistic Regressions

In logistic regression, separation occurs when a linear combination of predictors perfectly discriminates the binary outcome. Because finite-valued maximum likelihood parameter estimates do not exist under separation, Bayesian regressions with informative shrinkage of the regression coefficients offer a suitable alternative. Classical studies of separation imply that efficiency in estimating regression coefficients may also depend upon the choice of intercept prior, yet relatively little focus has been given on whether and how to shrink the intercept parameter. Alternative prior distributions for the intercept are proposed that downweight implausibly extreme regions of the parameter space, rendering regression estimates that are less sensitive to separation. Through simulation and the analysis of exemplar datasets, differences across priors stratified by established statistics measuring the degree of separation are quantified. Relative to diffuse priors, these proposed priors generally yield more efficient estimation of the regression coefficients themselves when the data are nearly separated. They are equally efficient in non-separated datasets, making them suitable for default use. Modest differences were observed with respect to out-of-sample discrimination. These numerical studies also highlight the interplay between priors for the intercept and the regression coefficients: findings are more sensitive to the choice of intercept prior when using a weakly informative prior on the regression coefficients than an informative shrinkage prior.

A solution to separation for clustered binary data

The presence of one or more covariates that perfectly or almost perfectly predict the outcome of interest (which is referred to as complete or quasi-complete separation, the latter denoting the case when such perfect prediction occurs only for a subset of observations in the data) has been extensively studied in the last four decades. Since 1984, when Albert and Anderson (1984) differentiated between complete and quasi-complete separation, several authors have studied this phenomenon and tried to provide answers or ways of identifying the problem (Lesaffre and Albert, 1989; Firth, 1993; Christmann and Rousseeuw, 2001; Rousseeuw and Christmann, 2003; Allison, 2004; Zorn, 2005; Heinze, 2006). From an estimation perspective, separation leads to infinite coefficients and standard errors, which makes the algorithm collapse or give inappropriate results. As a practical matter, separation forces the analyst to choose from a number of problematic alternatives for dealing with the problem, and in the past the elimination of such problematic variables were common practice to deal with such situations. In the last decade, solutions using penalized likelihood have been proposed, but always dealing with independent binary data. Here we will propose a Bayesian solution to the problem when we deal with clustered binary data using informative priors that are supported by the data and compare it with an alternative procedure proposed by Gelman et al. (2008).

Between-breed variability of stillbirth and its relationship with sow and piglet characteristics

Litter characteristics at birth were recorded in 4 genetic types of sows with differing maternal abilities. Eighty-two litters from F(1) Duroc x Large White sows, 651 litters from Large White sows, 63 litters from Meishan sows, and 173 litters from Laconie sows were considered. Statistical models included random effects of sow, litter, or both; fixed effects of sow genetic type, parity, birth assistance, and piglet sex, as well as gestation length, farrowing duration, piglet birth weight, and litter size as linear covariates. The quadratic components of the last 2 factors were also considered. For statistical analyses, GLM were first considered, assuming a binomial distribution of stillbirth. Hierarchical models were also fitted to the data to take into account correlations among piglets from the same litter. Model selection was performed based on deviance and deviance information criterion. Finally, standard and robust generalized estimating equations (GEE) procedures were applied to quantify the importance of each effect on a piglet's probability of stillbirth. The 5 most important factors involved were, in decreasing order (contribution of each effect to variance reduction): difference between piglet birth weight and the litter mean (2.36%), individual birth weight (2.25%), piglet sex (1.01%), farrowing duration (0.99%), and sow genetic type (0.94%). Probability of stillbirth was greater for lighter piglets, for male piglets, and for piglets from small or very large litters. Probability of stillbirth increased with sow parity number and with farrowing duration. Piglets born from Meishan sows had a lower risk of stillbirth (P < 0.0001) and were little affected by the sources of variation mentioned above compared with the 3 other sow genetic types. Standard and robust GEE approaches gave similar results despite some disequilibrium in the data set structure highlighted with the robust GEE approach.

Bagging tree classifiers for laser scanning images: a data- and simulation-based strategy

Diagnosis based on medical image data is common in medical decision making and clinical routine. We discuss a strategy to derive a classifier with good performance on clinical image data and to justify the properties of the classifier by an adapted simulation model of image data. We focus on the problem of classifying eyes as normal or glaucomatous based on 62 routine explanatory variables derived from laser scanning images of the optic nerve head. As learning sample we use a case-control study of 98 normal and 98 glaucomatous subjects matched by age and sex. Aggregating multiple unstable classifiers allows substantial reduction of misclassification error in many applications and bench mark problems. We investigate the performance of various classifiers for the clinical learning sample as well as for a simulation model of eye morphologies. Bagged classification trees (bagged-CTREE) are compared to single classification trees and linear discriminant analysis (LDA). We additionally compare three estimators of misclassification error: 10-fold cross-validation, the 0.632+ bootstrap and the out-of-bag estimate. In summary, the application of our strategy of a knowledge-based decision support shows that bagged classification trees perform best for glaucoma classification.