Skip to main content

Advertisement

SpringerLink
Log in

Semiparametric marginal and association regression methods for clustered binary data

  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Abstract

Clustered data arise commonly in practice and it is often of interest to estimate the mean response parameters as well as the association parameters. However, most research has been directed to inference about the mean response parameters with the association parameters relegated to a nuisance role. There is little work concerning both the marginal and association structures, especially in the semiparametric framework. In this paper, our interest centers on inference on the association parameters in addition to the mean parameters. We develop semiparametric methods for both complete and incomplete clustered binary data and establish the theoretical results. The proposed methodology is illustrated through numerical studies.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Aerts M., Claeskens G. (1997) Local polynomial estimation in multiparameter likelihood models. Journal of the American Statistical Association 92: 1536–1545

    Article  MATH  MathSciNet  Google Scholar 

  • Carey V., Zeger S.L., Diggle P.J. (1993) Modelling multivariate binary data with alternating logistic regressions. Biometrika 80: 517–526

    Article  MATH  Google Scholar 

  • Carroll R.J., Fan J., Gijbels I., Wand M.P. (1997) Generalized partially linear single-index models. Journal of the American Statistical Association 92: 477–489

    Article  MATH  MathSciNet  Google Scholar 

  • Chaudhuri P., Doksum K., Samarov A. (1997) On average derivative quantile regression. The Annals of Statistics 25: 715–744

    Article  MATH  MathSciNet  Google Scholar 

  • Chen K., Jin Z. (2005) Local polynomial regression analysis of clustered data. Biometrika 92: 59–74

    Article  MATH  MathSciNet  Google Scholar 

  • Claeskens G., Aerts M. (2000) Bootstrapping local polynomial estimators in likelihood-based models. Journal of Statistical Planning and Inference 86: 63–80

    Article  MATH  MathSciNet  Google Scholar 

  • Fan J., Li R. (2004) New estimation and model selection procedures for semiparametric modeling in longitudinal data analysis. Journal of the American Statistical Association 99: 710–723

    Article  MATH  MathSciNet  Google Scholar 

  • Fan J., Heckman N.E., Wand M.P. (1995) Local polynomial kernel regression for generalized linear models and quasi-likelihood functions. Journal of the American Statistical Association 90: 141–150

    Article  MATH  MathSciNet  Google Scholar 

  • Fitzmaurice G.M., Laird N.M. (1993) A likelihood-based method for analysing longitudinal binary responses. Biometrika 80: 141–151

    Article  MATH  Google Scholar 

  • Hall D.B., Severini T.A. (1998) Extended generalized estimating equations for clustered data. Journal of the American Statistical Association 93: 1365–1375

    Article  MATH  MathSciNet  Google Scholar 

  • Huang J.Z., Liu L. (2006) Polynomial spline estimation and inference of proportional hazards regression models with flexible relative risk form. Biometrics 62: 793–802

    Article  MATH  MathSciNet  Google Scholar 

  • Ichimura H. (1993) Semiparametric least squares (SLS) and weighted SLS estimation of single-index models. Journal of Econometrics 58: 71–120

    Article  MATH  MathSciNet  Google Scholar 

  • Kim S., Chen M.H., Dey D.K. (2008) Flexible generalized t-link models for binary response data. Biometrika 95: 93–106

    Article  MATH  MathSciNet  Google Scholar 

  • Kraft P., Bauman L., Yuan J.Y., Horvath S. (2003) Multivariate variance-components analysis of longitudinal blood pressure measurements from the Framingham heart study. BMC Genetics 4(Suppl 1): S55

    Article  Google Scholar 

  • Liang K.Y., Zeger S.L. (1986) Longitudinal data analysis using generalized linear models. Biometrika 73: 13–22

    Article  MATH  MathSciNet  Google Scholar 

  • Liang H., Wang S., Robins J.M., Carroll R.J. (2004) Estimation in partially linear models with missing covariates. Journal of the American Statistical Association 99: 357–367

    Article  MATH  MathSciNet  Google Scholar 

  • Lin X.H., Carroll R.J. (2001a) Semiparametric regression for clustered data using generalized estimating equations. Journal of the American Statistical Association 96: 1045–1056

    Article  MATH  MathSciNet  Google Scholar 

  • Lin X.H., Carroll R.J. (2001b) Semiparametric regression for clustered data. Biometrika 88: 1179–1185

    Article  MATH  MathSciNet  Google Scholar 

  • Lipsitz S.R., Laird N.M., Harrington D.P. (1991) Generalized estimating equations for correlated binary data: using the odds ratio as a measure of association. Biometrika 78: 153–160

    Article  MathSciNet  Google Scholar 

  • Little R.J.A., Rubin D.B. (2002) Statistical analysis with missing data, 2nd edn. Wiley, New York

    MATH  Google Scholar 

  • Molenberghs G., Lesaffre E. (1994) Marginal modelling of correlated ordinal data using an n-Way plackett distribution. Journal of the American Statistical Association 89: 633–644

    Article  MATH  Google Scholar 

  • Pepe M.S., Anderson G.L. (1994) A cautionary note on inference for marginal regression models with longitudinal data and general correlated response data. Communications in Statistics, Simulation and Computation 23: 939–951

    Article  Google Scholar 

  • Prentice R.L. (1988) Correlated binary regression with covariates specific to each binary observation. Biometrics 44: 1033–1048

    Article  MATH  MathSciNet  Google Scholar 

  • Ruppert D., Sheather S.J., Wand M.P. (1995) An effective bandwidth selector for local least squares regression. Journal of the American Statistical Association 90: 1257–1270

    Article  MATH  MathSciNet  Google Scholar 

  • Severini T.A., Staniswalis J.G. (1994) Quasilikelihood estimation in semiparametric models. Journal of the American Statistical Association 89: 501–511

    Article  MATH  MathSciNet  Google Scholar 

  • Wang N. (2003) Marginal nonparametric kernel regression accounting for within-subject correlation. Biometrika 90: 43–52

    Article  MATH  MathSciNet  Google Scholar 

  • Wang N., Carroll R.J., Lin X. (2005) Efficient semiparametric marginal estimation for longitudinal/clustered data. Journal of the American Statistical Association 100: 147–157

    Article  MATH  MathSciNet  Google Scholar 

  • Xia Y. (2007) A constructive approach to the estimation of dimension reduction directions. The Annals of Statistics 35: 2654–2690

    Article  MATH  MathSciNet  Google Scholar 

  • Xia Y., Härdle W. (2006) Semi-parametric estimation of partially linear single-index models. Journal of Multivariate Analysis 97: 1162–1184

    Article  MATH  MathSciNet  Google Scholar 

  • Xia Y., Tong H., Li W.K. (1999) On extended partially linear single-index models. Biometrika 86: 831–842

    Article  MATH  MathSciNet  Google Scholar 

  • Yi G.Y., Cook R.J. (2002) Marginal methods for incomplete longitudinal data arising in clusters. Journal of the American Statistical Association 97: 1071–1080

    Article  MATH  MathSciNet  Google Scholar 

  • Yi G.Y., He W., Liang H. (2009) Analysis of correlated binary data under partially linear single-index logistic models. Journal of Multivariate Analysis 100: 278–290

    Article  MATH  MathSciNet  Google Scholar 

  • Yi G.Y., Thompson M.E. (2005) Marginal and association regression models for longitudinal binary data with drop-outs: a likelihood-based approach. The Canadian Journal of Statistics 33: 3–20

    Article  MATH  MathSciNet  Google Scholar 

  • Zeger S.L., Diggle P.J. (1994) Semi-parametric models for longitudinal data with applications to CD4 cell numbers in HIV seroconverters. Biometrics 50: 689–699

    Article  MATH  Google Scholar 

  • Zeger S.L., Liang K.Y. (1986) Longitudinal data analysis for discrete and continuous outcomes. Biometrics 42: 121–130

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Grace Y. Yi

  2. Department of Statistical and Actuarial Sciences, University of Western Ontario, London, ON, N6A 5B7, Canada

    Wenqing He

  3. Department of Biostatistics and Computational Biology, University of Rochester Medical Center, 601 Elmwood Avenue, Box 630, Rochester, NY, 14642, USA

    Hua Liang

Authors
  1. Grace Y. Yi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wenqing He
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hua Liang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hua Liang.

About this article

Cite this article

Yi, G.Y., He, W. & Liang, H. Semiparametric marginal and association regression methods for clustered binary data. Ann Inst Stat Math 63, 511–533 (2011). https://doi.org/10.1007/s10463-009-0239-z

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10463-009-0239-z

Keywords

Search

Navigation