Novel Statistical Methods for Missing Data and Multiplicity in Alzheimer’s Research

Abstract

The application of statistical procedures to real data sets seldom proceeds as seamlessly as a textbook problem where all assumptions are verified, and sample sizes are adequate. Common issues include lack of adherence to the statistical analysis plan, missing data and in early stage research, small sample sizes and a large number of variables of interest, i.e. multiplicity considerations. We present novel statistical methodologies that have been developed for use in these adverse scenarios with applications to research into Alzheimer's Disease. Specifically, we have developed an approach for the analysis of paired categorical data when the pairing has been lost, in the context of a study examining the effectiveness of a type of therapy on perceptions of Alzheimer's. We used a weighted bootstrap approach to compare the euclidean distance between the pre and post centers of mass the pre and post therapy groups and despite the loss of the pairing, were able to make conclusions about the research hypothesis. In addition, we developed a new global hypothesis test, the Prediction Test, which is intended for use in early stage research when the sample size is small and the number of endpoints of interest is large. We utilize researcher's predictions about the direction different endpoints will move, e.g. increase/decrease, and weight these predictions based on the sample correlation matrix. Using this test, we are able to come to a go/no-go decision concerning the feasibility of continuing to study the current research hypothesis, a common concern in early and exploratory studies. The prediction test had good power properties even for very small sample sizes and a large number of variables of interest, a situation in which most tests fail, while also controlling the Type I error rate. We demonstrate the methodology with a data set consisting of Arterial Spin Labeling (ASL) measures on older adults before and after a 12-week exercise regimen. The research hypothesis for this study was that the exercise intervention would alter the structural/functional aspects of the brain, specifically that ASL would increase in the different regions of the brain. We then provide extensions to the predictions that can be made in the Prediction Test and compare the method to a Linear Mixed Model and a set of t-test on a data set consisting of Diffusion Tensor Imaging (DTI) measures on pre and post kidney transplant patients. The research hypothesis of this study is that kidney transplantation will lead to a normalization of DTI measures, which are emerging bio markers for cognition and Alzheimer's Disease. We also discuss power calculations and conduct a simulation comparison between a set of t-tests and the prediction test.