On Bayesian Estimation of Dirichlet Process Lognormal Mixture Models and Comparison of Treatments in Censoring
International Journal of Statistical Distributions and Applications
Volume 5, Issue 2, June 2019, Pages: 38-45
Received: Jun. 13, 2019; Accepted: Jul. 12, 2019; Published: Jul. 30, 2019
Views 563      Downloads 97
Henry Ondicho Nyambega, Department of Mathematics, Kisii University, Kisii, Kenya
George Otieno Orwa, Department of Statistics and Actuarial Science, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Article Tools
Follow on us
One current interest in medical research is the comparison of treatments in the analysis of survival times of patients. This is particularly problematic, especially for censored data, and when these data consists of several groups, where each group has distinct properties and characteristics but belong to the same distribution. There are various modeling schemes that have been contemplated to overcome these complexities inherent in the data. One such possibility is the Bayesian approach which integrates prior knowledge in analysis. In this paper, we focus on the use of Bayesian lognormal mixture model (MLNM) with related Dirichlet process (DP) prior distribution for estimating patient survival. The advances in the Bayesian paradigm have considerably bolstered the development and application of mixture modelling methodology in the field of survival analysis. The proposed MLN model is compared with the conventional parametric lognormal and the nonparametric Kaplan Meier (K-M) models used to estimate survival to establish model robustness. A simulation study that investigates the impact of censoring on these models is also described. Real data from past research is used to show the resulting Dirichlet process mixture model’s robustness in the comparison of censored treatment. The results indicate that the proposed lognormal mixtures provide a better fit to complex data. Further, the MLN models are able to estimate various survival distributions and therefore appropriate to compare treatments. Clinicians will find these models useful especially when confronted with the obstacle of choosing a suitable therapy for a disease.
Bayesian, Lognormal, Mixture Models, Treatment Comparison, Win BUGS
To cite this article
Henry Ondicho Nyambega, George Otieno Orwa, On Bayesian Estimation of Dirichlet Process Lognormal Mixture Models and Comparison of Treatments in Censoring, International Journal of Statistical Distributions and Applications. Vol. 5, No. 2, 2019, pp. 38-45. doi: 10.11648/j.ijsd.20190502.13
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Dunson, D. B. (2009). Nonparametric Bayes applications in biostatistics. In: Hjort N, Holmes C, Müller P, Walker S (eds) Bayesian nonparametric in practice. CUP.
Eves, W. X. and Walker, S. G. (2015). Bayesian Information for sensors. Quality of reliability engineering international, 31 (8): 1717-1724. Computational Statistics and Data Analysis, 54: 416–428.
Farcomeni, A. and Nardi, A. (2010). A two-component Weibull mixture to model early and late mortality in a Bayesian framework. Computational Statistics and Data Analysis, 54: 416–428.
Freireich, E. J., Gehan, E. A., and Frei, E. (1963). The effect of 6-mercaptopurine on the duration of steroid induced remissions in acute leukemia: A model for evaluation of other potentially useful therapy. Blood, 1: 699–716.
Ghahramani, Z. (2015). Probabilistic machine learning and artificial intelligence. Nature, 521: 452-459.
Giudici, P., Givens, G. H., and Mallick, B. K. (2009). Bayesian modeling using WinBUGS. John Wiley and sons, Inc., New Jersey.
Gupta, A., Mukherjee, B., and Upadhyay, S. K. (2008). Weibull extensionmodel: A bayes study using markov chain Monte Carlo simulation. Reliability Engineering and System Safety, 93 (10): 1434–1443.
Hanley, W. and Millea, M. (2018). Maximum entropy priors with derived parameters in a specified distribution. arXiv preprint arXiv: 1804.08143.
Kulasekera, K. B. and Zhao, M. (2008). A pointwise bayes-estimator of the survival probability with censored data. Stat Probab Lett 3, 78: 2597–2603.
Lindley, D. V. (1961). Introduction to probability and statistics from a Bayesian viewpoint: Part 2, Inference. Aberystwyth: University College of Wales.
Mclachlan, G. and Peel, D. (2000). Finite Mixture Models. John Wiely, New York.
Ntzoufras, I. (2009). Bayesian modeling using WinBUGS. John Wiley and sons, Inc., New Jersey.
Samwel Gershman,, J. and Blei David, M. (2012). A tutorial on Bayesian non-parametric model. Journal of Mathematical psychology, 56: 1-12.
WinBUGS (2001). WinBUGS User Manual:Version 1.4. UK: MRC Biostatistics Unit [computer program], Cambridge.
Yee Whye The. (2010). Dirichlet processes. In encyclopedia of machine learning, pages 280-287.
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
Tel: (001)347-983-5186