A partially linear additive model for clustered proportion data

Weihua Zhao, Heng Lian, Dipankar Bandyopadhyay

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


Proportion data with support lying in the interval [0,1] are a commonplace in various domains of medicine and public health. When these data are available as clusters, it is important to correctly incorporate the within-cluster correlation to improve the estimation efficiency while conducting regression-based risk evaluation. Furthermore, covariates may exhibit a nonlinear relationship with the (proportion) responses while quantifying disease status. As an alternative to various existing classical methods for modeling proportion data (such as augmented Beta regression) that uses maximum likelihood, or generalized estimating equations, we develop a partially linear additive model based on the quadratic inference function. Relying on quasi-likelihood estimation techniques and polynomial spline approximation for unknown nonparametric functions, we obtain the estimators for both parametric part and nonparametric part of our model and study their large-sample theoretical properties. We illustrate the advantages and usefulness of our proposition over other alternatives via extensive simulation studies, and application to a real dataset from a clinical periodontal study.

Original languageEnglish (US)
Pages (from-to)1009-1030
Number of pages22
JournalStatistics in Medicine
Issue number6
StatePublished - Mar 15 2018

Bibliographical note

Funding Information:
We thank the anonymous associate editor and 2 reviewers, whose constructive criticism led to a significantly improved version of the manuscript. We also thank the Center for Oral Health Research at MUSC for providing the motivating data and the context of this work. This research was partially supported by National Social Science Fund of China (15BTJ027), Natural Science Fund of Nantong University (14B28), and also by grants R03DE023372 and R01DE024984 from the United States National Institutes of Health.

Funding Information:
National Social Science Fund of China, Grant/Award Number: 15BTJ027; Natural Science Fund of Nantong University, Grant/Award Number: 14B28, R03DE023372 and R01DE024984; United States National Institutes of Health

Publisher Copyright:
Copyright © 2017 John Wiley & Sons, Ltd.


  • clustered data
  • proportion data
  • quadratic inference function
  • quasi-likelihood
  • semiparametric


Dive into the research topics of 'A partially linear additive model for clustered proportion data'. Together they form a unique fingerprint.

Cite this