The 41.5 Alberta Statistics Meeting

Abstracts

Peng Yu, Joint modeling approach for Matrix-variate CSD-EEG and antidepressant Treatment outcome via mixtures: a Bayesian approach

Recent studies have shown the existence of latent classes in electroencephalography (EEG) and Current Source Density transformed electroencephalography (CSD-EEG). However, statisticians seldom involve the latent class information when studying the correlation between EEG based biomarkers and clinical treatment responses. In this talk, we consider a joint modeling approach via mixtures to study the association between pre-treatment matrix-variate CSD-EEG covariates and binary antidepression treatment response. In our approach, the latent class structure in CSD-EEG is extracted through a special designed model called mixture of probabilistic multilinear principle component analysis (MPCA) with common loading. In the meantime, the extracted latent class information is involved as the predictor through a Probit regression when analyzing the antidepression treatment response. Finally, the approach returns a promising result in that four CSD-EEG latent classes with different signal patterns were found and the correlation between these latent classes and the antidepression treatment response is not only clear but also consistent with previous neuroscience studies. (Joint work with Linglong Kong and Bei Jiang)

Madeline Ward, Computationally Efficient Parameter Estimation for Spatial Individual-Level Models of Infectious Disease Transmission

Infectious disease transmission dynamics can vary from individual to individual based on spatial location, susceptibility risk factors, and other individual-level factors. Individual-level models have been developed to account for this complexity, however model-fitting can quickly become prohibitively computationally intensive as population size or number of parameters increase. This talk proposes a new method to reduce the computational burden for parameterizing individual-level models wherein parameters are estimated from a spatially aggregated data set and subsequently used to disaggregate aggregate-level estimates of epidemic statistics back to the individual level. We compare the performance of this “cluster-disaggregation” method to that of the traditional method of individual-level model parameter estimation, Metropolis-Hastings Markov chain Monte Carlo. The performance of these methods is illustrated with both a simulation study and a data set from a 2001 U.K. foot and mouth disease outbreak amongst livestock.

Tiantian Ma, Functional linear mixed effects models for cytotoxicity assessment and clustering

A multitude of natural and synthetic chemicals are present in our environment. Through the study of a compound’s cytotoxicity, researchers can carefully set regulations regarding how much of a certain chemical in the ambient environment is tolerable. In the past, research has focused on point measurements such as the LD50. In this article, we consider entire cellular growth and death curves through the use of functional mixed effects models. The data was provided by the Alberta Center for Toxicology Cytotoxicity Profiling Project. We identify differences in such curves corresponding to the chemical’s mode of action—i.e. how the compound attacks human cells. Through such analysis, we identify curve features to be used for cluster analysis via application of both k-means and self organizing maps. The data is analyzed by making use of functional principal components as a data driven basis and separately by considering B-splines for identifying local-time features. Our analysis can be used to drastically speed up future cytotoxicity research.

Michael John Ilagan, A goodness-of-fit test for the necessary-but-not-sufficient hypothesis

In the social sciences, theory often casts bivariate relationships in terms of logical asymmetries. For example, in psychology, one theory is that intelligence is necessary but not sufficient for creativity: unintelligent people are only uncreative (necessity); but intelligent people may be creative or uncreative (insufficiency). While statistical methods conventional among social scientists are linear, such asymmetries are not. Consequently, when dealing with such asymmetries, a mismatch between theory and method persisted in the literature for decades. Towards remedying this mismatch, recent methodological work proposed the Linear Ceiling and Floor Probability Region (LCFPR) model, which analyzes bivariate relationships in terms of necessity and sufficiency. In this work, I propose a goodness-of-fit test for LCFPR. Simulation studies show acceptable power and size for such a test. The test is then used to reanalyze a real dataset on intelligence and creativity. (Joint work with Alexander de Leon, Karen Kopciuk, and Welfredo Patungan.)

Meichen Liu, Reproducing kernel based functional partial linear expectile regression

In this paper, we develop a smoothness regularization method for combining functional as well as nonfunctional random variables in expectile regression which we often encounter simultaneously in neuroimaging data analysis or economic systems. Existing work on functional expectile regression mostly focuses on the means of functional principal component analysis. However, by developing a tool based on a reproducing kernel Hilbert space framework, we establish theoretical results on the minimax rates of convergence and show that smoothness regularized estimators achieve the optimal rates of convergence. Meanwhile, the easily implementable and powerful ADMM algorithm is introduced in simulation studies and real data analysis to validate our methodology and to demonstrate the numerical performance. (Joint work with Matthew Pietrosanu, Bei Jiang and Linglong Kong)