ON THE MERITS OF VOXEL-BASED MORPHOMETRIC PATH-ANALYSIS FOR INVESTIGATING VOLUMETRIC MEDIATION OF A TOXICANT'S INFLUENCE ON COGNITIVE FUNCTION

We previously showed that lifetime cumulative lead dose, measured as lead concentration in the tibia bone by X-ray fluorescence, was associated with persistent and progressive declines in cognitive function and with decreases in MRI-based brain volumes in former lead workers. Moreover, larger region-specific brain volumes were associated with better cognitive function. These findings motivated us to explore a novel application of path analysis to evaluate effect mediation. Voxel-wise path analysis, at face value, represents the natural evolution of voxel-based morphometry methods to answer questions of mediation. Application of these methods to the former lead worker data demonstrated potential limitations in this approach where there was a tendency for results to be strongly biased towards the null hypothesis (lack of mediation). Moreover, a complimentary analysis using anatomically-derived regions of interest volumes yielded opposing results, suggesting evidence of mediation. Specifically, in the ROI-based approach, there was evidence that the association of tibia lead with function in three cognitive domains was mediated through the volumes of total brain, frontal gray matter, and/or possibly cingulate. A simulation study was conducted to investigate whether the voxel-wise results arose from an absence of localized mediation, or more subtle defects in the methodology. The simulation results showed the same null bias evidenced as seen in the lead workers data. Both the lead worker data results and the simulation study suggest that a null-bias in voxel-wise path analysis limits its inferential utility for producing confirmatory results.

A Functional-Based Distribution Diagnostic for a Linear Model with Correlated Outcomes: Technical Report

Despite the widespread popularity of linear models for correlated outcomes (e.g. linear mixed modesl and time series models), distribution diagnostic methodology remains relatively underdeveloped in this context. In this paper we present an easy-to-implement approach that lends itself to graphical displays of model fit. Our approach involves multiplying the estimated marginal residual vector by the Cholesky decomposition of the inverse of the estimated marginal variance matrix. Linear functions or the resulting "rotated" residuals are used to construct an empirical cumulative distribution function (ECDF), whose stochastic limit is characterized. We describe a resampling technique that serves as a computationally efficient parametric bootstrap for generating representatives of the stochastic limit of the ECDF. Through functionals, such representatives are used to construct global tests for the hypothesis of normal margional errors. In addition, we demonstrate that the ECDF of the predicted random effects, as described by Lange and Ryan (1989), can be formulated as a special case of our approach. Thus, our method supports both omnibus and directed tests. Our method works well in a variety of circumstances, including models having independent units of sampling (clustered data) and models for which all observations are correlated (e.g., a single time series).

Estimating Multiple Tumor Transition Rates Based on Data from Survival/Sacrifice Experiments

In this paper, we focus on the model for two types of tumors. Tumor development can be described by four types of death rates and four tumor transition rates. We present a general semi-parametric model to estimate the tumor transition rates based on data from survival/sacrifice experiments. In the model, we make a proportional assumption of tumor transition rates on a common parametric function but no assumption of the death rates from any states. We derived the likelihood function of the data observed in such an experiment, and an EM algorithm that simplified estimating procedures. This article extends work on semi-parametric models for one type of tumor (see Portier and Dinse and Dinse) to two types of tumors.