Event-Based Modeling with High-Dimensional Imaging Biomarkers for Estimating Spatial Progression of Dementia

Event-based models (EBM) are a class of disease progression models that can be used to estimate temporal ordering of neuropathological changes from cross-sectional data. Current EBMs only handle scalar biomarkers, such as regional volumes, as inputs. However, regional aggregates are a crude summary of the underlying high-resolution images, potentially limiting the accuracy of EBM. Therefore, we propose a novel method that exploits high-dimensional voxel-wise imaging biomarkers: n-dimensional discriminative EBM (nDEBM). nDEBM is based on an insight that mixture modeling, which is a key element of conventional EBMs, can be replaced by a more scalable semi-supervised support vector machine (SVM) approach. This SVM is used to estimate the degree of abnormality of each region which is then used to obtain subject-specific disease progression patterns. These patterns are in turn used for estimating the mean ordering by fitting a generalized Mallows model. In order to validate the biomarker ordering obtained using nDEBM, we also present a framework for Simulation of Imaging Biomarkers' Temporal Evolution (SImBioTE) that mimics neurodegeneration in brain regions. SImBioTE trains variational auto-encoders (VAE) in different brain regions independently to simulate images at varying stages of disease progression. We also validate nDEBM clinically using data from the Alzheimer's Disease Neuroimaging Initiative (ADNI). In both experiments, nDEBM using high-dimensional features gave better performance than state-of-the-art EBM methods using regional volume biomarkers. This suggests that nDEBM is a promising approach for disease progression modeling.Comment: IPMI 201

Moment properties of estimators for an exponential regression with type 1 censoring

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Properties of estimators of parameters in logistic regression models

Properties of various types of estimators of the regression coefficients in linear logistic regression models are considered. The estimators include those based on maximum likelihood, minimum chi-square and weighted least squares. Theoretical approximations to the biases of the estimators are developed. The results of a large scale simulation investigation evaluating the moment properties of the estimators are presented for the case of a logistic model with a single explanatory variable

The extreme residuals in logistic regression models

Goodness of fit tests for logistic regression models using extreme residuals are considered. Moment properties of the Pearson residuals are developed and used to define modified residuals, for the cases when the model fit is made by maximum likelihood, minimum chi-square and weighted least squares. Approximations to the critical values of the extreme statistics based on the ordinary and modified Pearson residuals are developed and assessed for the case when the logistic regression model has a single explanatory variable

Null distribution of some goodness of fit statistics for logistic regression

The null distribution moment and percentile properties of several goodness of fit statistics for logistic regression models are considered. Small sample approximations to the critical values of the statistics are evaluated for the case of a single explanatory variable with equally spaced values

Improved estimators for the shape parameter in gamma regression

A regression model is considered in which the response variables have gamma distributions with a common shape parameter. A review is given of existing estimators for the shape parameter. Bias expressions for the maximum likelihood estimates of the regression coe f f i c i ent s and the shape parameter are developed. A new estima t o r f o r t h e shape parameter based on bias correction for the maximum likelihood estimator is shown to have markedly better variance and mean square error properties in small to moderate sized samples. Approximations to the low order moments of the Pearson statistic are derived for gamma regression models with general link functions. These are used for the case of a logarithmic link to develop new estimators for the shape parameter which have better moment properties than the estimators based on the Pearson statistic which have been used previously. Finally, the small sample variance and mean square error efficiencies of the estimators relative to the maximum likelihood estimator are evaluated by simulation for the case of a single explanatory variable and a logarithmic link, for a range of sample sizes less than or equal to 100