Abstract
In this article we consider a semiparametric generalized mixed-effects model, and propose combining local linear regression, and penalized quasilikelihood and local quasilikelihood techniques to estimate both population and individual parameters and nonparametric curves. The proposed estimators take into account the local correlation structure of the longitudinal data. We establish normality for the estimators of the parameter and asymptotic expansion for the estimators of the nonparametric part. For practical implementation, we propose an appropriate algorithm. We also consider the measurement error problem in covariates in our model, and suggest a strategy for adjusting the effects of measurement errors. We apply the proposed models and methods to study the relation between virologic and immunologic responses in AIDS clinical trials, in which virologic response is classified into binary variables. A dataset from an AIDS clinical study is analyzed.
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References
Breslow N.E., Clayton D.G. (1993). Approximate inference in generalized linear mixed models. Journal of the American Statistical Association 88, 9–25
Buonaccorsi J.P., Demidenko E., Tosteson T.D. (2000). Estimation in longitudinal random effects models with measurement error. Statistica Sinica 10, 885–904
Carroll R.J., Fan J., Gijbels I., Wand M.P. (1997). Generalized partially single-index models. Journal of the American Statistical Association 92, 477–489
Carroll R.J., Ruppert D., Stefanski L.A. (1995). Nonlinear measurement error models. New York, Chapman and Hall
Davidian M., Giltinan D. (1995). Nonlinear models for repeated measurement data. New York, Chapman and Hall
Eubank R.L. (1999). Nonparametric regression and spline smoothing. New York, Marcel Dekker
Fan J., Gijbels I. (1996). Local polynomial modeling and its applications. London, Chapman and Hall
Fuller W.A. (1987). Measurement error models. New York, Wiley
Higgins K.M., Davidian M., Giltinan D.M. (1997). A two-step approach to measurement error in time-dependent covariates in nonlinear mixed-effects models, with application to IGF-I pharmacokinetics. Journal of the American Statistical Association 92, 436–448
Ke C.L., Wang Y.D. (2001). Semiparametric nonlinear mixed-effects models and their applications (with discussions). Journal of the American Statistical Association 96, 1272–1298
Laird N.M., Ware J.H. (1982). Random effects models for longitudinal data. Biometrics 38, 963–974
Liang H., Ren H.B. (2005). Generalized partially linear measurement error models. Journal of Computational and Graphical Statistics 14, 237–250
Liang H., Wu H.L., Carroll R.J. (2003). The relationship between virologic and immunologic responses in AIDS clinical research using mixed-effect varying-coefficient semiparametric models with measurement error. Biostatistics 4, 297–312
Lin X.H., Carroll R.J. (2001). Semiparametric regression for clustered data using generalized estimating equations. Journal of the American Statistical Association 96, 1045–1056
Lin X.H., Zhang D.W. (1999). Inference in generalized additive mixed models by using smoothing splines. Journal of the Royal Statistical Society, Series B 61, 381–400
Pinheiro J.C., Bates D.M. (2000). Mixed-effects models in S and S-PLUS. New York, Springer
Pollard D. (1991). Asymptotics for least absolute deviation regression estimators. Econometric Theory 7, 186–199
Ruppert D. (1997). Empirical-bias bandwidths for local polynomial nonparametric regression and density estimation. Journal of the American Statistical Association 92, 1049–1062
Rice J.A., Wu C.O. (2001). Nonparametric mixed effects models for unequally sampled noisy curve. Biometrics 57, 253–259
Schall R. (1991). Estimation in generalized linear models with random effects. Biometrika 78, 717–727
Scott Z.A., Chadwick E.G., Gibson L.L. et al. (2001). Infrequent detection of HIV-1-specific, but not cytomegalovirus-specific, CD8+T cell responses in young HIV-1-infected infants. Journal of Immunology 167, 7134–7140
Severini T.A., Staniswalis J.G. (1994). Quasilikelihood estimation in semiparametric models. Journal of the American Statistical Association 89, 501–511
Shi M., Weiss R.E., Taylor J.M.G. (1996). An analysis of pediatric CD4+ counts for acquired immune deficiency syndrome using flexible random curves. Applied Statistics 45, 151–163
Stefanski L.A., Cook J.R. (1995). Simulation-extrapolation: the measurement error jackknife. Journal of the American Statistical Association 90, 1247–1256
Wang N.S., Lin X.H., Gutierrez R.G., Carroll R.J. (1998). Bias analysis and SIMEX approach in generalized linear mixed measurement error models. Journal of the American Statistical Association 93, 249–261
Wu H.L., Kuritzkes D.R., Clair M.S., Spear G., Connick E., Landay A., Lederman M.M. (1999). Characterizing individual and population viral dynamics in HIV-1-infected patients with potent antiretroviral therapy: correlations with host-specific factors and virological endpoints. Journal of Infectious Disease 179, 799–897
Wu H.L., Zhang J.T. (2002). Semiparametric nonlinear mixed-effects models for longitudinal data application to an AIDS clinical study. Statistics in Medicine 21, 3655–3675
Wu L. (2002). A joint model for nonlinear mixed-effects models with censoring and covariates measured with error, with application to AIDS studies. Journal of the American Statistical Association 97, 955–964
Zeger S.L., Karim M.R. (1991). Generalized linear models with random effects: a gibbs sampling approach. Journal of the American Statistical Association 6, 79–86
Zhang D. (2004). Generalized linear mixed models with varying coefficients for longitudinal data. Biometrics 60, 8–15
Zhang D., Lin X., Raz J., Sowers M. (1998). Semiparametric stochastic mixed models for longitudinal data. Journal of the American Statistical Association 93, 710–719
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Liang, H. Generalized partially linear mixed-effects models incorporating mismeasured covariates. Ann Inst Stat Math 61, 27–46 (2009). https://doi.org/10.1007/s10463-007-0146-0
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DOI: https://doi.org/10.1007/s10463-007-0146-0