Capturing heterogeneous group differences using mixture-of-experts: Application to a study of aging

Abstract

In MRI studies, linear multi-variate methods are often employed to identify regions or connections that are affected due to disease or normal aging. Such linear models inherently assume that there is a single, homogeneous abnormality pattern that is present in all affected individuals. While kernel-based methods can implicitly model a non-linear effect, and therefore the heterogeneity in the affected group, extracting and interpreting information about affected regions is difficult. In this paper, we present a method that explicitly models and captures heterogeneous patterns of change in the affected group relative to a reference group of controls. For this purpose, we use the Mixture-of-Experts (MOE) framework, which combines unsupervised modeling of mixtures of distributions with supervised learning of classifiers. MOE approximates the non-linear boundary between the two groups with a piece-wise linear boundary, thus allowing discovery of multiple patterns of group differences. In the case of patient/control comparisons, each such pattern aims to capture a different dimension of a disease, and hence to identify patient subgroups. We validated our model using multiple simulation scenarios and performance measures. We applied this method to resting state functional MRI data from the Baltimore Longitudinal Study of Aging, to investigate heterogeneous effects of aging on brain function in cognitively normal older adults (>85years) relative to a reference group of normal young to middle-aged adults (<60years). We found strong evidence for the presence of two subgroups of older adults, with similar age distributions in each subgroup, but different connectivity patterns associated with aging. While both older subgroups showed reduced functional connectivity in the Default Mode Network (DMN), increases in functional connectivity within the pre-frontal cortex as well as the bilateral insula were observed only for one of the two subgroups. Interestingly, the subgroup showing this increased connectivity (unlike the other subgroup) was, cognitively similar at baseline to the young and middle-aged subjects in two of seven cognitive domains, and had a faster rate of cognitive decline in one of seven domains. These results suggest that older individuals whose baseline cognitive performance is comparable to that of younger individuals recruit their "cognitive reserve" later in life, to compensate for reduced connectivity in other brain regions.

Keywords: Heterogeneity; Mixture of experts; Support vector machines.