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Research Projects

High-Dimensional Data Analysis

As the availability of new data sets with a large number of variables grows, the challenge of analyzing these (ultra) high‐dimensional data sets has emerged as one of the most important and challenging topics in statistics. Given the large number of predictor variables, how to select a subset of predictors from a large pool of candidates for building robust models has been a major problem. Within this approach, my research focuses on development in the penalized variable selection methods. These methods allow automatic selection of the most informative variables from a large pool of candidate variables by adding appropriate penalties on certain parameters to the objective function (e.g., L1 norm penalty on regression coefficients in linear regression). In this context, I have developed computational algorithms for high-dimensional data. Computation is crucial for high-dimensional data because of the problems of non-tractability, non-differentiability, computing capacity and speed with such data. My research on high-dimensional data has been combined with machine learning (e.g. classification), and survival and longitudinal data analyses.

  1. Wu TT, Lange K. Coordinate Descent Algorithms for Lasso Penalized Regression.  Ann Appl Stat. 2008;2:224-244. 
  2. Wu TT, Chen YF, Hastie T, Sobel E, Lange K. Genomewide Association Analysis by Lasso Penalized Logistic Regression. Bioinformatics. 2009;25:714-721. PMCID: PMC2732298
  3. Wu, T.T.$ and Lange, K. (2010) The MM Alternative to EM. Statistical Science, Volume 25, No 4, 492-505.
  4. Wu TT, Lange K. Multicategory Vertex Discriminant Analysis for High-Dimensional Data. Ann Appl Stat 2010;4:1698-1721.
  5. Wu, T.T.$ and He, X. (2012) Coordinate Ascent for Penalized Semiparametric Regression on High-Dimensional Panel Count Data. Computational Statistics and Data Analysis, Volume 56, No 1, 25-33.
  6. Wu, T.T. (2013) Lasso Penalized Semiparametric Regression on High-Dimensional Recurrent Event Data via Coordinate Descent. Journal of Statistical Computation and Simulation, Volume 83, No 6, 1145-1155.
  7. Wu, T.T.$ and Wang, S. (2013) Doubly Regularized Cox Regression for High-dimensional Survival Data with Group Structures. Statistics and Its Interface, Volume 6, No 2, 175-186.
  8. Chen, S., Grant, E.**, Wu, T.T., and Bowman, F. D. (2014) Some Recent Statistical Learning Methods for Longitudinal High-dimensional Data. WIREs Computational Statistics, Volume 6, No 1, 10-18.
  9. Chang, J., Tang, C.Y., and Wu, T.T. (2018) A New Scope of Penalized Empirical Likelihood with High-Dimensional Estimating Equations. Annals of Statistics, Volume 46, 3185--3216.

Empirical Likelihood

I recently gained great interest in empirical likelihood. Empirical likelihood, as the nonparametric counterpart of likelihood method, has desirable merits without requiring parametric model assumptions. However, it encounters substantial difficulties when dealing with high-dimensional statistical problems. My research on empirical likelihood tries to tackle these problems.

  1. Tang, C.Y. and Wu, T.T.$ (2014) Nested Coordinate Descent Algorithms for Empirical Likelihood. Journal of Statistical Computation and Simulation, Volume 84, No 9, 1917-1930.
  2. Wu, T.T.$, Li, G., and Tang, C.Y. (2015) Empirical Likelihood for Censored Linear Regression and Variable Selection. Scandinavian Journal of Statistics, Volume 42, No 3, 798--812.
  3. Chang, J., Tang, C.Y., and Wu, T.T. (2018) A New Scope of Penalized Empirical Likelihood with High-Dimensional Estimating Equations. Annals of Statistics, Volume 46, 3185--3216.
  4. Wang, D., Wu, T.T., and Zhao, Y. (2019) Penalized Empirical Likelihood for the Sparse Cox Regression Model. Journal of Statistical Planning and Inference, Volume 201, 71-85.

Survival Analysis

My Ph.D. training on survival analysis focused on two-stage sampling design and nonparametric/semiparametric modeling. With that background, I have combined my research expertise in high-dimensional data analysis to survival analysis and study the identification of important predictors correlated with patient survival.

  1. Li G, Wu, TT. Semiparametric Additive Risks Regression for Two-Stage Design Survival Studies. Stat Sin. 2010;20:1581-1607.  PMCID: PMC3175231
  2. Wu, T.T.$ and He, X. (2012) Coordinate Ascent for Penalized Semiparametric Regression on High-Dimensional Panel Count Data. Computational Statistics and Data Analysis, Volume 56, No 1, 25-33.
  3. Wu, T.T. (2013) Lasso Penalized Semiparametric Regression on High-Dimensional Recurrent Event Data via Coordinate Descent. Journal of Statistical Computation and Simulation, Volume 83, No 6, 1145-1155.
  4. Wu, T.T.$ and Wang, S. (2013) Doubly Regularized Cox Regression for High-dimensional Survival Data with Group Structures. Statistics and Its Interface, Volume 6, No 2, 175-186.
  5. Fang, H.-B., Wu, T.T.$, Rapoport, A.P., and Tan, M. (2014) Survival Analysis with Functional Covariates for Partial Follow-up Studies. Stat Methods Med Res. Volume 25(6), 2405-2419.
  6. Wu, T.T.$, Li, G., and Tang, C.Y. (2015) Empirical Likelihood for Censored Linear Regression and Variable Selection. Scandinavian Journal of Statistics, Volume 42, No 3, 798--812.
  7. Wang, D., Wu, T.T., and Zhao, Y. Penalized Empirical Likelihood for the Sparse Cox Regression Model. Journal of Statistical Planning and Inference, accepted.

Machine Learning

I am also interested in machine learning, in particular, classification and clustering of high-dimensional data.

  1. Lange, K. and Wu, T.T.$ (2008) An MM Algorithm for Multicategory Vertex Discriminant Analysis. Journal of Computational and Graphical Statistics, Volume 17, No 3, 527-544.
  2. Wu, T.T.$ and Lange, K. (2010) Multicategory Vertex Discriminant Analysis for High-Dimensional Data. Annals of Applied Statistics, Volume 4, No 4, 1698-1721.
  3. Wu, T.T.$ and Wu, Y. (2012) Nonlinear Vertex Discriminant Analysis with Reproducing Kernels. Statistical Analysis and Data Mining, Volume 5, No 2, 167-176.
  4. Wu TT, Lange K. Matrix Completion Discriminant Analysis. Computational Statistics and Data Analysis 2015;92:115-125.
  5. Aditya, P., Sen, R., Oh, S.J., Benenson, R., Bhattacharjee, B., Druschel, P., Wu, T.T., Fritz, M., and Schiele, B. (2016) I-Pic: A Platform for Privacy-Compliant Image Capture. ACM MobiSys 2016 TPC, 235--248.

Computational Genetics

My methodology work on high-dimensional data analysis and survival analysis was motivated and has been applied to genetic and biological studies. Applying my analytic tools designed for high-throughput genetic data, I succeeded in identifying genetic signatures of a small number of relevant predictors of diseases from a pool of thousands of genes or millions of single nucleotide polymorphisms (SNPs). With the determination of genetic signatures, the diagnostic procedure will be greatly simplified for clinical applications.

  1. Wu, T.T.*, Sun, W.*, Yuan, S., Chen, C.-H., and Li, K.-C. (2008) (*: joint first authors) A Method for Analyzing Censored Survival Phenotype with Gene Expression Data. BMC Bioinformatics, Volume 9, 417.
  2. Park CC, Ahn S, Bloom JS, Lin A, Wang RT, Wu TT, Sekar A, Khan AH, Farr CJ, Lusis AJ, Leahy RM, Lange K, Smith DJ. Fine mapping of regulatory loci for mammalian gene expression using radiation hybrids. Nat Genet. 2008;40:421-429.  PMCID: PMC3014048
  3. Wu TT, Gong H, Clarke EM. A Transcriptome Analysis by Lasso Penalized Cox Regression for Pancreatic Cancer Survival. J Bioinform Comput Biol. 2011;9 Suppl 01:63-73. 
  4. Gong H*, Wu TT*, Clarke E. (*: joint first author and corresponding author) Pathway-Gene Identification for Pancreatic Cancer Survival via Doubly Regularized Cox Regression. BMC Systems Biology. 2014;8 Suppl 1:S3.  PMCID: PMC4080266
  5. Costello JC, Heiser LM, Georgii E, Gonen M, Menden MP, Wang NJ, Bansal M, Ammad-ud-din M, Hintsanen P, Khan SA, Mpindi JP, Kallioniemi O, Honkela A, Aittokallio T, Wennerberg K, NCI DREAM Community, Collins JJ, Gallahan D, Singer D, Saez-Roriquez J, Kaski S, Gray JW, Stolovitzky G. (2014) A community effort to assess and improve drug sensitivity prediction algorithms. Nat Biotechnol. 2014;32:1202-1212.  PMCID: PMC4547623

Epidemiology

I have been working with a team of epidemiologists to study the effects of lifestyle intervention and physical activities on health. For example, in the TAAG studies, we have followed up a group of adolescent girls for over 10 years to investigate multi-level factors affecting their physical activities and sedentary behaviors over time.

  1. Young DR, Camhi S, Wu TT, Hagberg J, Stefanick ML. (2013) Relationships Among Changes in C-Reactive Protein and Cardiovascular Disease Risk Factors With Lifestyle Interventions. Nutr Metab Cardiovasc Dis. 2013;23:857-863.  PMCID: PMC3502629
  2. Morrison S, Shenassa E, Mendola P, Wu TT, Schoendorf K. (2013) Allostatic load may not be associated with chronic stress in pregnant women, NHANES 1999-2006. Ann Epidemiology. 2013;23:294-297.  PMCID: PMC4132932
  3. Young DR, Saksvig BI, Wu TT, Zook K, Li X, Champaloux S, Grieser, M, Lee S, Treuth MS. (2014) Multilevel Correlates of Physical Activity For Early, Mid, and Late Adolescent Girls. J Phys Act Health. 2014;11:950-960.
  4. Zook, K.R., Saksvig, B.I.,Wu, T.T.#, and Young, D.R. (2014) Physical Activity Trajectories and Multi-Level Factors among Adolescent Girls. Journal of Adolescent Health, Volume 54, No 1, 74-80.
  5. Grant EM, Young DR*, Wu TT.* (*: joint senior authors) (2015) Predictors for Physical Activity in Adolescent Girls Using Statistical Shrinkage Techniques for Hierarchical Longitudinal Mixed Effects Models. PLoS ONE. 2015;10:e0125431.  PMCID: PMC441601
  6. Meng, Y.**, Groth, S.W., Quinn, J., Bisognano, J.D., and Wu, T.T. (2017) An Exploration of Gene-Gene Interactions and Their Effects on Hypertension. International Journal of Genomics, Volume 2017, Article ID 7208318.
  7. Groth, S.W., LaLonde, A.**, Wu, T.T.#, and Fernandez, I.D. (2018) Obesity candidate genes, gestational weight gain and body weight changes in pregnant women. Nutrition, Volume 48, 61-66.
  8. Young, D.R., Cohen, D., Koebnick, C., Mohan, Y., Saksvig, B.I., Sidell, M., and Wu, T.T.#* (2018) Longitudinal Associations of Physical Activity Among Females from Adolescence to Young Adulthood. Journal of Adolescent Health, Volume 63, 466--473.
  9. Young, D.R., Sidell, M., Koebnick, C., Saksvig, B.I., Mohan, Y., Cohen, D., and Wu, T.T.#* (2019) Longitudinal Sedentary Time among Females from Ages 17 to 23 Years. American Journal of Preventive Medicine, Epub.
  10. Ciminelli, J.T., Love, T., and Wu, T.T. (2019) Social Network Spatial Model. Spatial Statistics, accepted.

Biomedical Engineering

I have also worked with researchers in the field of bioengineering.

  1. Ramirez, G., Proctor, A.R., Jung, K.W., Wu, T.T.#, Han, S., Adams, R.R., Ren, J., Byun, D.K., Madden, K.S., Brown, E.B., Foster, T.H., Farzam, P., Durduran, T., and Choe, R. (2016) Chemotherapeutic drug-specific alteration of microvascular blood flow in murine breast cancer xenografts as measured by diffuse correlation spectroscopy. Biomedical Optics Express, Volume 7, Issue 9, 3610-3630.
  2. Tang, Q., Wang, J., Frank, A., Lin, J., Li, Z., Chen, C.W., Jin, L., Wu, T.T., Greenwald, B.D., Mashimo, H., and Chen, Y. (2016) Depth-resolved imaging of colon tumor using optical coherence tomography and fluorescence laminar optical tomography. Biomedical Optics Express, Volume 7, 5218-5232.
  3. Wang, B., Wang, H.-W., Guo, H., Anderson, E., Tang, Q., Wu, T.T., Falola, R., Smith, T., Andrews, P.M., and Chen, Y. (2017) Optical Coherence Tomography (OCT) and Computer-Aided Diagnosis (CAD) of a Murine Model of Chronic Kidney Disease (CKD). Journal of Biomedical Optics, Volume 22(12), 1-11.
  4. Konkel, B., Lavin, C., Wu, T.T.#, Anderson, E., Iwamoto, A., Rashid, H., Gaitian, B., Boones, J., Cooper, M., Abrams, P., Gilbert, A., Tang, Q., Levi, M., Fujimoto, J.G., Andrews, P., and Chen, Y. (2019) Fully Automated Analysis of OCT Imaging of Human Kidneys for Prediction of Post-transplant Function. Biomedical Optics Express, Volume 10(4), 1794-1821. .

HIV/AIDS

I worked on HIV/AIDS data when I was a graduate student at UCLA. I re-gained the interest in HIV/AIDS since I joined CFAR (Center for AIDS Research) at UofR. I welcome collaborations in the related areas.

  1. Liu H, Miller LG, Hays RD, Golin CE, Wu TT, Wenger NS, Kaplan AH (2006) Repeated Measures Longitudinal Analyses of HIV Virologic Response as A Function of Percent Adherence, Dose Timing, Genotypic Sensitivity, and Other Factors. J Acquir Immune Defic Syndr. 2006;41:315-322.  PMID: 16540932
  2. Liu, H., Miller, L.G., Golin, C.E., Hays, R.D., Wu, T.T., Wenger, N.S., and Kaplan, A.H. (2007) Repeated Measures Analyses of Dose Timing of Antiretroviral Medication and its Relationship to HIV Virologic Outcomes. Statistics in Medicine, Volume 26, No 5, 991-1007.
  3. Jaworski, J.P., Bryk, P., Brower, Z., Zheng, B., Hessell, A.J., Rosenberg, A.F., Wu, T.T., Sanz, I., Keefer, M.C., Haigwood, N.L., and Kobie, J.J. (2017) Pre-Existing Neutralizing Antibody Mitigates B cell Dysregulation and Enhances the Env-Specific Antibody Response  in SHIV-Infected Rhesus Macaques. PLoS One, 12(2):e0172524.

Medicine and Dentistry

I have also worked with researchers in various health-related fields, such as cancer, pain, dentistry, etc.

  1. Hamza, M., Wang, X.M., Wu, T.T.#, Jaber, L., Brahim, J.S., Rowan, J.S., and Dionne, R.A. (2010) Nitric Oxide is Negatively Correlated to Pain During Acute Inflammation. Molecular Pain, Volume 6, No 55.
  2. Saligan, L.N., Levy-Clarke, G., Wu, T.T.#, Faia, L.J., Wroblewski, K., Yeh, S., Nussenblatt, R.B., and Sen, H.N. (2010) Quality of Life in Sarcoidosis: Comparing the Impact of Ocular and Non-Ocular Involvement of the Disease. Ophthalmic Epidemiology, Volume 17, No 4, 217-224.
  3. Huber, A.R., Tan, D., Sun, J., Dean, D., Wu, T.T.#, and Zhou, Z. (2015) High expression of carbonic anhydrase IX is significantly associated with glandular lesions in gastroesophageal junction and with tumorigenesis markers BMI1, MCM4 and MCM7. BMC Gastroenterology, 15:80.
  4. Choy, B., Lalonde, A.**, Taboada, S., Wu, T.T.#, and Zhou, Z. (2016) MCM4 and MCM7, Potential Novel Proliferation Markers, Significantly Correlated with Ki67, Bmi1, and Cyclin E Expression in Esophageal Adenocarcinoma, Squamous Cell Carcinoma, and Precancerous Lesions. Human Pathology, Volume 57, 126-135.
  5. Pang, C., Lalonde, A.**, Godfrey, T.E., Que, J., Da, J., Sun, J., Wu, T.T.#, and Zhou, Z. (2017) Bile salt receptor TGR5 is highly expressed in esophageal adenocarcinoma and precancerous lesions with significantly worse overall survival and gender differences. Clinical and Experimental Gastroenterology, Volume 10, 29-37.
  6. Abu-Farsakh, S., Wu, T.T.#, Lalonde, A.**, Sun, J., and Zhou, Z. (2017) High expression of the Claudin-2 in esophageal carcinoma and precancerous lesions is significantly associated with the bile salt receptors VDR and TGR5. BMC Gastroenterology, 17:33.
  7. Xiao, J., Huang, X., Alkhers, N., Alzamil, H., Alzoubi, S., Wu, T.T.#, Castillo, D., Campbell, F., Harokopakis-Hajishengallis, E., Koo, H. (2018) Candida albicans and Early Childhood Caries: A Systematic Review and Meta-analysis. Caries Research, Volume 52(1-2), 102-112.
  8. Chen, W.**, Anokhina, V., Miller, B., Dieudonne, G., Abramowitz, M.K., Kashyap, R., Yan, C., Wu, T.T.#, Bentley, K., and Bushinsky, D.A. (2018) Patients with Advanced Chronic Kidney Disease and Vascular Calcification Have a Large Hydrodynamic Radius of Secondary Calciprotein Particles. Nephrology Dialysis Transplantation, 1-9.
  9. Lee, C.Y., Robinson, D.A., Johnson, C.A., Zhang, Y.**, Wong, J., Joshi, D.J., Wu, T.T.#, and Knight, P.A. (2019) A Randomized Controlled Trial of Liposomal Bupivacaine Parasternal Intercostal Block for Sternotomy. Annals of Thoracic Surgery, Volume 107(1), 128-134.
  10. Xiao, J., Alkhers, N., Kopycka-Kedzierawski, D.T., Billings, R., Wu, T.T.#, Castillo, D., Rasubala, L., Malmstrom, H., Ren, Y., and Eliav, E. (2019) Prenatal Oral Health Care and Early Childhood Caries Prevention: A Systematic Review and Meta-analysis. Caries Research, accepted.
  11. Chen, W., Fitzpatrick, J., Monroy-Trujillo, J., Sozio, S., Jaar, B., Estrella, M., Wu, T.T.#, Melamed, M., Parekh, R., and Bushinsky, D.A. Diabetes Mellitus Modifies the Associations of Serum Magnesium Concentration with Arterial Calcification and Stiffness in Incident Hemodialysis Patients. Kidney International Reports, accepted.
  12. Krieger, N.S., Asplin, J., Granja, I., Ramos, F.M., Flotteron, C., Chen, L., Wu, T.T.#, Grynpas, M., and Bushinsky, D.A. Chlorthalidone is Superior to Potassium Citrate in Reducing Calcium Phosphate Stones and Increasing Bone Quality in Hypercalciuric Stone-Forming Rats. Journal of the American Society of Nephrology, accepted.