Bradley R Lewis, Dipankar Bandyopadhyay, Stacia M DeSantis, Mike T John
{"title":"Augmenting beta regression for periodontal proportion data via the SAS NLMIXED procedure.","authors":"Bradley R Lewis, Dipankar Bandyopadhyay, Stacia M DeSantis, Mike T John","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>Often in clinical dental research, clinical attachment level (CAL) is recorded at several sites throughout the mouth to assess the extent of periodontal disease (PD). One might be interested to quantify PD at the tooth-level via the proportion of diseased sites per tooth type (say, incisors, canines, pre-molars and molars) per subject. However, these studies might consist of relatively disease-free and highly diseased subjects leading to the proportion responses distributed in the interval [0, 1]. While beta regression (BR) is often the model of choice to assess covariate effects for proportion data, the presence (and/or abundance) of zeros and/or ones makes it inapplicable here because the beta support is defined in the interval (0, 1). Avoiding ad hoc data transformation, we explore the potential of the augmented BR framework which augments the beta density with non-zero masses at zero and one while accounting for the clustering induced. Our classical estimation framework using maximum likelihood utilizes the potential of the SAS® Proc NLMIXED procedure. We explore our methodology via simulation studies and application to a real cross-sectional dataset on PD, and we assess the gain in model fit and parameter estimation over other ad hoc alternatives. This reveals newer insights into risk quantification on clustered proportion responses. Our methods can be implemented using standard SAS software routines. The augmented BR model results in a better fit to clustered periodontal proportion data over the standard beta model. We recommend using it as a parametric alternative for fitting proportion data, and avoid ad hoc data transformation.</p>","PeriodicalId":38394,"journal":{"name":"Journal of Applied Probability and Statistics","volume":"12 1","pages":"49-66"},"PeriodicalIF":0.0,"publicationDate":"2017-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6191203/pdf/nihms882113.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36597716","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Shimin Zheng, Uma Rao, Alfred A Bartolucci, Karan P Singh
{"title":"Random Regression Models Based On The Skew Elliptically Contoured Distribution Assumptions With Applications To Longitudinal Data.","authors":"Shimin Zheng, Uma Rao, Alfred A Bartolucci, Karan P Singh","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>Bartolucci et al.(2003) extended the distribution assumption from the normal (Lyles et al., 2000) to the elliptical contoured distribution (ECD) for random regression models used in analysis of longitudinal data accounting for both undetectable values and informative drop-outs. In this paper, the random regression models are constructed on the multivariate skew ECD. A real data set is used to illustrate that the skew ECDs can fit some unimodal continuous data better than the Gaussian distributions or more general continuous symmetric distributions when the symmetric distribution assumption is violated. Also, a simulation study is done for illustrating the model fitness from a variety of skew ECDs. The software we used is SAS/STAT, V. 9.13.</p>","PeriodicalId":38394,"journal":{"name":"Journal of Applied Probability and Statistics","volume":"4 1","pages":"21-32"},"PeriodicalIF":0.0,"publicationDate":"2009-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3104683/pdf/nihms137734.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"29910869","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Random Regression Models Based On The Skew Elliptically Contoured Distribution Assumptions With Applications To Longitudinal Data.","authors":"S. Zheng, Uma Rao, A. Bartolucci, Karan P. Singh","doi":"10.22237/JMASM/1067645340","DOIUrl":"https://doi.org/10.22237/JMASM/1067645340","url":null,"abstract":"Bartolucci et al.(2003) extended the distribution assumption from the normal (Lyles et al., 2000) to the elliptical contoured distribution (ECD) for random regression models used in analysis of longitudinal data accounting for both undetectable values and informative drop-outs. In this paper, the random regression models are constructed on the multivariate skew ECD. A real data set is used to illustrate that the skew ECDs can fit some unimodal continuous data better than the Gaussian distributions or more general continuous symmetric distributions when the symmetric distribution assumption is violated. Also, a simulation study is done for illustrating the model fitness from a variety of skew ECDs. The software we used is SAS/STAT, V. 9.13.","PeriodicalId":38394,"journal":{"name":"Journal of Applied Probability and Statistics","volume":"4 1 1","pages":"21-32"},"PeriodicalIF":0.0,"publicationDate":"2003-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68263186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}