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Likelihood Methods for Binary Responses of Present Components in a Cluster
Author(s) -
Li Xiaoyun,
Bandyopadhyay Dipankar,
Lipsitz Stuart,
Sinha Debajyoti
Publication year - 2011
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.1541-0420.2010.01483.x
Subject(s) - logistic regression , statistics , robustness (evolution) , binary data , component (thermodynamics) , mathematics , random effects model , regression , computer science , population , regression analysis , binary number , econometrics , data mining , medicine , arithmetic , biochemistry , chemistry , physics , meta analysis , environmental health , gene , thermodynamics
Summary 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.