MATH 5P99 Project Presentations

10:00-10:40am:

Approximate Sampling Distributions of the Parameter Estimators in the AR(1)-model

Clarence Deladem Kalitsi

Abstract: We consider the first-order autoregressive model defined by X_(i+1) = pX_(i) + e_(i+1).
Based on a fully analytical approach, we demonstrate how to obtain the first four moments of some well-known estimators of . This enables us to utilize the Edgeworth expansion series to approximate the corresponding sampling distributions, which vastly improves that of the central limit theorem. More importantly, the resulting approximate sampling distributions perform very well even when the sample size is relatively small. In the case of the maximum likelihood estimator of , we further show how this technique can be extended to higher order autoregressive models.

Supervisors: Jan Vrbik and Wai Kong Yuen

11:00 - 11:40 am:

Joint Models on the Impact of Lipids Change over Time on the Risk of Coronary Heart Disease

Beili Zheng

Abstract: Coronary heart disease (CHD) is the leading cause of death for both men and women in the world. Non-high-density lipoprotein (non-HDL) is proved to be a strong risk predictor of CHD in short-term clinical trials. In this project, we use statistical models to measure associations between non-HDL cholesterol and the risk of CHD in a long-term period. To analyze the clinical trials data from Framingham Offspring Study, we perform longitudinal data analysis and survival analysis under the joint modeling frameworks, an approach that uses latent variables to find the associations between longitudinal and event time outcomes. We review the maximum likelihood method and the EM algorithm used in this analysis. Furthermore, we study the association between time-dependent slope and time to event. Under the joint model, we can dynamically predict the risk of getting disease according to historical biomarker records and baseline covariates using Monte Carlo simulation. Our results are good complement of those from many clinical trials that suggest lowering non-HDL cholesterol may reduce CHD mortality among patients with high risk for CHD in the short-term.

Supervisor: Wai Kong Yuen