title: Likelihood methods for binary responses of present components in a cluster.
abstract: In some biomedical studies involving clustered binary responses (say, disease status), the cluster sizes can vary because some components of the cluster can be absent. When both the presence of a cluster component as well as the binary disease status of a present component are treated as responses of interest, we propose a novel two-stage random effects logistic regression framework. For the ease of interpretation of regression effects, both the marginal probability of presence/absence of a component as well as the conditional probability of disease status of a present component, preserve the approximate logistic regression forms. We present a maximum likelihood method of estimation implementable using standard statistical software. We compare our models and the physical interpretation of regression effects with competing methods from literature. We also present a simulation study to assess the robustness of our procedure to wrong specification of the random effects distribution and to compare finite-sample performances of estimates with existing methods. The methodology is illustrated via analyzing a study of the periodontal health status in a diabetic Gullah population.
authors.affiliation: Department of Statistics, Florida State University, Tallahassee, Florida 32306, USA. xli@stat.fsu.edu
authors.forename: Xiaoyun
authors.initials: X
authors.lastname: Li
authors.forename: Dipankar
authors.initials: D
authors.lastname: Bandyopadhyay
authors.forename: Stuart
authors.initials: S
authors.lastname: Lipsitz
authors.forename: Debajyoti
authors.initials: D
authors.lastname: Sinha
mesh_terms: D001699:Biometry / Q000379:methods*; D016000:Cluster Analysis; D003198:Computer Simulation; D048909:Diabetes Complications; D004194:Disease; D006801:Humans; D016013:Likelihood Functions; D016015:Logistic Models; D015233:Models, Statistical; D010510:Periodontal Diseases / Q000453:epidemiology; D011336:Probability
references.citation: Ann Periodontol. 1999 Dec;4(1):1-6
references.pmid: 10863370
references.citation: Stat Med. 2008 Feb 20;27(4):543-55
references.pmid: 17640035
references.citation: Biometrics. 2003 Sep;59(3):521-30
references.pmid: 14601753
references.citation: Biometrics. 2003 Mar;59(1):36-42
references.pmid: 12762439
references.citation: J Periodontol. 2009 Jul;80(7):1062-8
references.pmid: 19563285
references.citation: IARC Sci Publ. 1980;(32):5-338
references.pmid: 7216345
references.citation: Stat Med. 2007 Apr 30;26(9):2017-35
references.pmid: 17016864
references.citation: Biometrics. 2010 Mar;66(1):287-93
references.pmid: 19432772