Mixture models for eye-tracking data: a case study

Conceptual, Regulatory and Strategic Imperatives in the Early Days of EEG-Based Biomarker Validation for Neurodevelopmental Disabilities

Biological treatment development for syndromal neuropsychiatric conditions such as autism has seen slow progress for decades. Speeding drug discovery may result from the judicious development and application of biomarker measures of brain function to select patients for clinical trials, to confirm target engagement and to optimize drug dose. For neurodevelopmental disorders, electrophysiology (EEG) offers considerable promise because of its ability to monitor brain activity with high temporal resolution and its more ready application for pediatric populations relative to MRI. Here, we discuss conceptual/definitional issues related to biomarker development, discuss practical implementation issues, and suggest preliminary guidelines for validating EEG approaches as biomarkers with a context of use in neurodevelopmental disorder drug development.

Analyzing differences between microbiome communities using mixture distributions

In this paper, we present a method to assess differences between microbiome communities that effectively models sparse count data and accounts for presence-absence bias frequently encountered when zeros are present. We assume that the observed data for each operational taxonomic unit is Poisson generated with the rate for each sample originating from an underlying rate distribution. We propose to model this distribution using a mixture model, specifying the components based on the posterior rate distribution of a count and estimating the optimal weights using a least squares objective function. The distribution incorporates varying resolutions of samples, a point mass for differentiating structural and nonstructural zeros, and a truncation point mass to account for high values that are too sparse to model. As mixture component specification is not always straightforward, a method to estimate a joint model from several mixture distributions using minimum distances of bootstrap iterates is proposed. Once the population rate distribution is approximated, we obtain sample-specific distributions by conditioning on the observed operational taxonomic unit count, resolution, and estimated mixture distribution and then use these to estimate pairwise distances for a permutation test. The method gives an accurate estimate of the true proportion of zeros for presence-absence, effectively models the distribution of low counts using the mixture distribution, and achieves good power for detecting differences in a variety of scenarios. The method is tested using a simulation study and applied to two microbiome datasets. In each case, the results are compared with a number of existing methods.

Eye movement dysfunction in first-degree relatives of patients with schizophrenia: a meta-analytic evaluation of candidate endophenotypes

Several forms of eye movement dysfunction (EMD) are regarded as promising candidate endophenotypes of schizophrenia. Discrepancies in individual study results have led to inconsistent conclusions regarding particular aspects of EMD in relatives of schizophrenia patients. To quantitatively evaluate and compare the candidacy of smooth pursuit, saccade and fixation deficits in first-degree biological relatives, we conducted a set of meta-analytic investigations. Among 18 measures of EMD, memory-guided saccade accuracy and error rate, global smooth pursuit dysfunction, intrusive saccades during fixation, antisaccade error rate and smooth pursuit closed-loop gain emerged as best differentiating relatives from controls (standardized mean differences ranged from .46 to .66), with no significant differences among these measures. Anticipatory saccades, but no other smooth pursuit component measures were also increased in relatives. Visually-guided reflexive saccades were largely normal. Moderator analyses examining design characteristics revealed few variables affecting the magnitude of the meta-analytically observed effects. Moderate effect sizes of relatives v. controls in selective aspects of EMD supports their endophenotype potential. Future work should focus on facilitating endophenotype utility through attention to heterogeneity of EMD performance, relationships among forms of EMD, and application in molecular genetics studies.

Dimensional analyses of taxonic data

Principal component analysis (PCA) and common factor analysis are often used to model latent data structures. Typically, such analyses assume a single population whose correlation or covariance matrix is modelled. However, data may sometimes be unwittingly sampled from mixed populations containing a taxon (nonarbitrary subpopulation) and its complement class. One derives relations between values of PCA parameters within subpopulations and their values in the mixed population. These results are then extended to factor analysis in mixed populations. As relationships between subpopulation and mixed-population principal components and factors sensitively depend on within-subpopulation structures and between-subpopulation differences, naive interpretation of PCA or factor analytic findings can potentially mislead. Several analyses, better suited to the dimensional analysis of admixture data structures, are presented and compared.

On the EM algorithm for overdispersed count data

In this paper, we consider the use of the EM algorithm for the fitting of distributions by maximum likelihood to overdispersed count data. In the course of this, we also provide a review of various approaches that have been proposed for the analysis of such data. As the Poisson and binomial regression models, which are often adopted in the first instance for these analyses, are particular examples of a generalized linear model (GLM), the focus of the account is on the modifications and extensions to GLMs for the handling of overdispersed count data.