Research:
Current Research:
Small sample behavior of resampling methods:
This research topic is motivated by one project I did for a
biology professor in the Department of Horticulture and Crop Science at the
Ohio State University. They tried to find some differentially expressed genes
between different developmental stages of tomato plants (flower vs. fruit)
using microarray technique. However, they only have three replicates for each
stage due to the funding limit and time constraint, which is common in most
biology fields. With such small sample size, we tried the resampling
techniques commonly used in microarray data analysis. For the same data set, no
significant differentially expressed genes was found
by permutation method. However, a lot of significant differentially expressed
genes were found using post-pivot resampling method
proposed by K.Pollard and M. van der
Laan (2003) and pre-pivot resampling
method proposed by Efron (1979) even after
multiplicity adjustment. This phenomenon caused my great interest. I began to
study the reason for this contradiction. I explored the discreteness of the
test statistics by the maximum number of unique test statistic values in small
sample case, and derived the conditions for getting 0 adjusted P-values for
post-pivot and pre-pivot resampling methods. Now, I
am extending the two sample comparison to fixed effects and mixed effects
general linear model situations.
Partitioning
to Uncover Conditions for Permutation Tests and Bootstrap Tests to Control
Multiple Testing Error Rates:
As first pointed out by
Huang, Xu, Calian, and Hsu (2006), permutation method
concernes testing whether the joint distribution of
two groups are identical in the two sample comparison situation, while the
multiple testing will make inference on those marginal distributions.
Therefore, permutation method only gives correct estimation of the joint test
statistics distributions under certain conditions. By using the partitioning
principle to partition the parameter spaces into disjoint subspaces, we found
the conditions for permutation tests to control multiple testing error rates in
the fixed effects general linear model setting in the quantitative trait loci
(QTL) study. The results have been submitted to the Biometrical Journal. Now, I
am working on conditions for bootstrap tests (pre-pivot resampling
method and post-pivot resampling method) to
asymptotically control multiple testing error rates using partitioning
principle, and corresponding short-cuts of partitioning tests using resampling techniques.
Publications:
Violeta Calian, Dongmei Li, and Jason C. Hsu (2007). Partitioning to Uncover Conditions for Permutation Tests to Control Multiple Testing Error Rates. Biometrical Journal.(Submitted).
Dongmei Li and Jason C. Hsu (2007). Small Sample Behavior of Resampling methods (In preparation).
L Norris, A Collene, M Asp, LF Liu J Hsu, D Li, K Osei, R Jackson, MA Belury (2007). Conjugated Linoleic Acid Reduces Body Weight and Body Fat in Women with Type 2 Diabetes. Experimental Biology. (Submitted).
L Norris, A Collene, M Asp, LF Liu J Hsu, D Li, K Osei, R Jackson, MA Belury (2007). Comparative Effects of Dietary Oils on Markers of Insulin Sensitivity in Women with Type 2 Diabetes. Experimental Biology. (Submitted).
Z Xie, JR Lucas, K
Morohashi, E Lee, D Li, FD Sack, E Grotewold (2007). The MYB Factor FLP
Links Cell Cycle Control and Stomatal Specification.
(In preparation for Cell ).
Yuwen Li and Dongmei Li (2000). Promoting creativity in primary mathematics education. ICME9 conference paper.
Guizhi Yan and Dongmei Li (1996). Specific Property of Function (ax+b)/(cx-a). Journal of Shandong Normal University.
Conference Presentations:
"Small Sample
Behavior of Resampling Methods". The
Joint Statistical Meeting,
"Small Sample Behavior of Resampling
Methods". The 30th Annual Midwest Biopharmaceutical Statistics
Workshop,
"Differential Gene Expression:
Ischemic vs. Nonischemic". The
Mathematical Biology Institute Workshop,