α1/2w
,
which follows a MLG(c, α1/2V, α1, α1). It follows from Theorem 5.1.8 of Lehmann [23] that q converges in distribution to a multivariate normal distribution with mean c and covariance matrix VV0 as α goes to infinity.
A.5 Proof in Section 2.4
Proof of (2.7) - (2.9) (Bradley et al. [5])
Let c = (c1, c2), where c1 is the first g-dimensional components of c, and c2 is the remaining (m − g)-dimensional components. The joint distribution of (q1, q2) is given by
f (q1, q2|c, V, α, κ)
Office of the Vice President for Research Human Subjects Committee
Tallahassee, Florida 32306-2742 (850) 644-8673 · FAX (850) 644-4392 APPROVAL MEMORANDUM Date: 03/29/2019
To: Pengpeng Wang
Address: 214 Rogers Building (OSB), 117 N. Woodward Ave., Tallahassee, Florida 32306 Dept.: STATISTICS DEPARTMENT
From: Thomas L. Jacobson, Chair Re: Use of Human Subjects in Research
A Bayesian Semiparametric Joint Model for Longitudinal and Survival Data (Grant Title: Smart Early Screening for Autism and Communication Disorders in Primary Care)
The application that you submitted to this office in regard to the use of human subjects in the proposal referenced above have been reviewed by the Secretary, the Chair, and two members of the Human Subjects Committee. Your project is determined to be Expedited per 45 CFR § 46.110(6) and has been approved by an expedited review process.
The Human Subjects Committee has not evaluated your proposal for scientific merit, except to weigh the risk to the human participants and the aspects of the proposal related to potential risk and benefit. This approval does not replace any departmental or other approvals, which may be required.
If you submitted a proposed consent form with your application, the approved stamped consent form is attached to this approval notice. Only the stamped version of the consent form may be used in recruiting research subjects.
If the project has not been completed by 03/27/2020 you must request a renewal of approval for continuation of the project. As a courtesy, a renewal notice will be sent to you prior to your expiration date; however, it is your responsibility as the Principal Investigator to timely request renewal of your approval from the Committee.
You are advised that any change in protocol for this project must be reviewed and approved by the Committee prior to implementation of the proposed change in the protocol. A protocol change/amendment form is required to be submitted for approval by the Committee. In addition, federal regulations require that the Principal Investigator promptly report, in writing any unanticipated problems or adverse events involving risks to research subjects or others.
By copy of this memorandum, the chairman of your department and/or your major professor is reminded that he/she is responsible for being informed concerning research projects involving human subjects in the department, and should review protocols as often as needed to insure that the project is being conducted in compliance with our institution and with DHHS regulations.
This institution has an Assurance on file with the Office for Human Research Protection. The Assurance Number is IRB00000446.
Cc: Elizabeth Slate, Advisor HSC No. 2019.26786
APPENDIX B
IRB APPROVALS
Office of the Vice President for Research Human Subjects Committee
Tallahassee, Florida 32306-2742 (850) 644-8673 · FAX (850) 644-4392 APPROVAL MEMORANDUM Date: 04/29/2019
To: Pengpeng Wang
Address: 214 Rogers Building (OSB), 117 N. Woodward Ave., Tallahassee, Florida 32306 Dept.: STATISTICS DEPARTMENT
From: Thomas L. Jacobson, Chair Re: Use of Human Subjects in Research
A Bayesian Semiparametric Joint Model for Longitudinal and Survival Data
The application that you submitted to this office in regard to the use of human subjects in the proposal referenced above have been reviewed by the Secretary, the Chair, and two members of the Human Subjects Committee. Your project is determined to be Exempt per 45 CFR § 46.110(b)7 and has been approved by an expedited review process.
The Human Subjects Committee has not evaluated your proposal for scientific merit, except to weigh the risk to the human participants and the aspects of the proposal related to potential risk and benefit. This approval does not replace any departmental or other approvals, which may be required.
If you submitted a proposed consent form with your application, the approved stamped consent form is attached to this approval notice. Only the stamped version of the consent form may be used in recruiting research subjects.
If the project has not been completed by 04/27/2020 you must request a renewal of approval for continuation of the project. As a courtesy, a renewal notice will be sent to you prior to your expiration date; however, it is your responsibility as the Principal Investigator to timely request renewal of your approval from the Committee.
You are advised that any change in protocol for this project must be reviewed and approved by the Committee prior to implementation of the proposed change in the protocol. A protocol change/amendment form is required to be submitted for approval by the Committee. In addition, federal regulations require that the Principal Investigator promptly report, in writing any unanticipated problems or adverse events involving risks to research subjects or others.
By copy of this memorandum, the chairman of your department and/or your major professor is reminded that he/she is responsible for being informed concerning research projects involving human subjects in the department, and should review protocols as often as needed to insure that the project is being conducted in compliance with our institution and with DHHS regulations.
This institution has an Assurance on file with the Office for Human Research Protection. The Assurance Number is IRB00000446.
Cc: Elizabeth Slate, Advisor HSC No. 2019.27195
BIBLIOGRAPHY
[1] Donald I. Abrams, Anne I. Goldman, Cynthia Launer, Joyce A. Korvick, James D. Neaton, Lawrence R. Crane, Michael Grodesky, Steven Wakefield, Katherine Muth, Sandra Kornegay, David L. Cohn, Allen Harris, Roberta Luskin-Hawk, Norman Markowitz, James H. Sampson, Melanie Thompson, and Lawrence Deyton. A comparative trial of didanosine or zalcitabine after treatment with zidovudine in patients with human immunodeficiency virus infection. New England Journal of Medicine, 330(10):657–662, 1994.
[2] Theodore W. Anderson. The statistical analysis of time series, volume 19. John Wiley & Sons, 2011.
[3] Charles E. Antoniak. Mixtures of dirichlet processes with applications to Bayesian nonpara-metric problems. The annals of statistics, pages 1152–1174, 1974.
[4] Maurice S. Bartlett and D. G. Kendall. The statistical analysis of variance-heterogeneity and the logarithmic transformation. Supplement to the Journal of the Royal Statistical Society, 8(1):128–138, 1946.
[5] Jonathan R. Bradley, Scott H. Holan, and Christopher K. Wikle. Computationally efficient multivariate spatio-temporal models for high-dimensional count-valued data (with discussion).
Bayesian Analysis, 13(1):253–310, 2018.
[6] Elizabeth R. Brown and Joseph G. Ibrahim. A Bayesian semiparametric joint hierarchical model for longitudinal and survival data. Biometrics, 59(2):221–228, 2003.
[7] Larry C. Clark, Gerald F. Combs, Bruce W. Turnbull, Elizabeth H. Slate, Dan K. Chalker, James Chow, Loretta S. Davis, Renee A. Glover, Gloria F. Graham, Earl G. Gross, Arnon Krongrad, Jack L. Lesher Jr, H. Kim Park, Beverly B. Sanders Jr, Cameron L. Smith, and J. Richard Taylor. Effects of selenium supplementation for cancer prevention in patients with carcinoma of the skin: a randomized controlled trial. Jama, 276(24):1957–1963, 1996.
[8] Gavin E. Crooks. The amoroso distribution. arXiv preprint arXiv:1005.3274, 2015.
[9] David B. Dahl. Model-based clustering for expression data via a Dirichlet process mixture model. Bayesian Inference for Gene Expression and Proteomics, 4:201–218, 2006.
[10] Persi Diaconis and David Freedman. An elementary proof of Stirling’s formula. The American Mathematical Monthly, 93(2):123–125, 1986.
[11] Bradley Efron. The two sample problem with censored data. Proceedings of the fifth Berke-ley symposium on mathematical statistics and probability, 4(University of California Press, Berkeley, CA):831–853, 1967.
[12] Michael D. Escobar and Mike West. Bayesian density estimation and inference using mixtures.
Journal of the American Statistical Association, 90(430):577–588, 1995.
[13] Andrew Gelman et al. Two simple examples for understanding posterior p-values whose dis-tributions are far from uniform. Electronic Journal of Statistics, 7:2595–2602, 2013.
[14] Richard D. Gill. Censoring and stochastic integrals. Statistica Neerlandica, 34(2):124–124, 1980.
[15] Anne I. Goldman, Bradley P. Carlin, Lawrence R. Crane, Cynthia Launer, Joyce A. Korvick, Lawrence Deyton, and Donald I. Abrams. Response of CD4 lymphocytes and clinical con-sequences of treatment using ddI or ddC in patients with advanced HIV infection. JAIDS Journal of Acquired Immune Deficiency Syndromes, 11(2):161–169, 1996.
[16] Major Greenwood. A report on the natural duration of cancer. A Report on the Natural Duration of Cancer, (33), 1926.
[17] Xu Guo and Bradley P. Carlin. Separate and joint modeling of longitudinal and event time data using standard computer packages. The American Statistician, 58(1):16–24, 2004.
[18] W. Keith Hastings. Monte carlo sampling methods using Markov chains and their applications.
1970.
[19] Lawrence Hubert and Phipps Arabie. Comparing partitions. Journal of Classification, 2(1):193–218, 1985.
[20] Edward L. Kaplan and Paul Meier. Nonparametric estimation from incomplete observations.
Journal of the American Statistical Association, 53(282):457–481, 1958.
[21] John P. Klein and Melvin L. Moeschberger. Survival analysis: techniques for censored and truncated data, pages 91–104. Springer Science & Business Media, 2006.
[22] John A Laurmann and W Lawrence Gates. Statistical considerations in the evaluation of climatic experiments with atmospheric general circulation models. Journal of the Atmospheric Sciences, 34(8):1187–1199, 1977.
[23] Erich Leo Lehmann. Elements of large-sample theory. Springer Science & Business Media, 2004.
[24] Haiqun Lin, Bruce W Turnbull, Charles E McCulloch, and Elizabeth H Slate. Latent class models for joint analysis of longitudinal biomarker and event process data: application to longitudinal prostate-specific antigen readings and prostate cancer. Journal of the American Statistical Association, 97(457):53–65, 2002.
[25] Xiao-Li Meng. Posterior predictive p-values. The Annals of Statistics, 22(3):1142–1160, 1994.
[26] Bruce D. Meyer. Unemployment insurance and unemployment spells, 1988.
[27] Leslie C. Morey and Alan Agresti. The measurement of classification agreement: An adjust-ment to the Rand statistic for chance agreeadjust-ment. Educational and Psychological Measureadjust-ment, 44(1):33–37, 1984.
[28] Radford M. Neal. Markov chain sampling methods for Dirichlet process mixture models.
Journal of Computational and Graphical Statistics, 9(2):249–265, 2000.
[29] Radford M. Neal. Slice sampling. Annals of Statistics, pages 705–741, 2003.
[30] Ross L. Prentice. A log gamma model and its maximum likelihood estimation. Biometrika, 61(3):539–544, 1974.
[31] William M. Rand. Objective criteria for the evaluation of clustering methods. Journal of the American Statistical association, 66(336):846–850, 1971.
[32] Xiao Song, Marie Davidian, and Anastasios A. Tsiatis. A semiparametric likelihood approach to joint modeling of longitudinal and time-to-event data. Biometrics, 58(4):742–753, 2002.
[33] David J Spiegelhalter, Nicola G Best, Bradley P Carlin, and Angelika Van Der Linde. Bayesian measures of model complexity and fit. Journal of the royal statistical society: Series b (statis-tical methodology), 64(4):583–639, 2002.
[34] M. Stephens. Dealing with label switching in mixture models. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 62(4):795–809, 2000.
[35] J. M. Taylor, Shu-Jane Tan, Roger Detels, and Janis V. Giorgi. Applications of a computer simulation model of the natural history of CD4 T-cell number in HIV-infected individuals.
AIDS (London, England), 5(2):159–167, 1991.
[36] H. Jean Thi´ebaux and Francis W. Zwiers. The interpretation and estimation of effective sample size. Journal of Climate and Applied Meteorology, 23(5):800–811, 1984.
[37] Anastasios A. Tsiatis and Marie Davidian. Joint modeling of longitudinal and time-to-event data: an overview. Statistica Sinica, pages 809–834, 2004.
[38] David A. Van Dyk and Taeyoung Park. Partially collapsed Gibbs samplers: theory and methods. Journal of the American Statistical Association, 103(482):790–796, 2008.
[39] Yan Wang and Jeremy M. G. Taylor. Jointly modeling longitudinal and event time data with application to acquired immunodeficiency syndrome. Journal of the American Statistical Association, 96(455):895–905, 2001.
[40] Mike West. Hyperparameter estimation in Dirichlet process mixture models. Duke University ISDS Discussion Paper# 92-A03, 1992.
[41] Daowen Zhang and Marie Davidian. Linear mixed models with flexible distributions of random effects for longitudinal data. Biometrics, 57(3):795–802, 2001.
BIOGRAPHICAL SKETCH
Pengpeng Wang was born on November 25, 1991, in Tianjin, China. She grew up in Tianjin and received a Bachelor of Science in Statistics in 2014 from School of Mathematical Sciences, Nankai University, China. She joined Department of Statistics, Florida State University in 2014 and received a Master of Science in Statistics in 2016. Now she is a PhD candidate in Statistics at Florida State University. During the summer in 2018, she worked at Liberty Mutual Insurance as a Data Science Graduate Intern.
As a PhD candidate at Florida State University, Pengpeng has been advised and mentored by Dr. Elizabeth H. Slate. She had been a teaching assistant from 2014 to 2017. She was the instructor for STA1013 “Statistics Through Example”. She has been working with Dr. Elizabeth H. Slate as a research assistant since 2017. She presented this dissertation in “Yongyuan and Anna Li” students presentation competition and won the award in the department in 2019. She was one of the finalists in the Three-Minute Thesis presentation competition at Florida State University in 2018. She also gave presentations in conferences, including 2017 Southern Regional Council of Statistics and 2018 Joint Statistical Meetings. Outside of academics, Pengpeng enjoys playing table tennis. She is currently the president of FSU Table Tennis Club.