×

zbMATH — the first resource for mathematics

Generalized partially linear mixed-effects models incorporating mismeasured covariates. (English) Zbl 1294.62147
Summary: 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.

MSC:
62J02 General nonlinear regression
62F10 Point estimation
62F12 Asymptotic properties of parametric estimators
62G05 Nonparametric estimation
62P10 Applications of statistics to biology and medical sciences; meta analysis
92C50 Medical applications (general)
Software:
MEMSS; S-PLUS
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Breslow N.E., Clayton D.G. (1993). Approximate inference in generalized linear mixed models. Journal of the American Statistical Association 88, 9–25 · Zbl 0775.62195 · doi:10.2307/2290687
[2] Buonaccorsi J.P., Demidenko E., Tosteson T.D. (2000). Estimation in longitudinal random effects models with measurement error. Statistica Sinica 10, 885–904 · Zbl 0970.62035
[3] 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 · Zbl 0890.62053 · doi:10.2307/2965697
[4] Carroll R.J., Ruppert D., Stefanski L.A. (1995). Nonlinear measurement error models. New York, Chapman and Hall · Zbl 0853.62048
[5] Davidian M., Giltinan D. (1995). Nonlinear models for repeated measurement data. New York, Chapman and Hall
[6] Eubank R.L. (1999). Nonparametric regression and spline smoothing. New York, Marcel Dekker · Zbl 0936.62044
[7] Fan J., Gijbels I. (1996). Local polynomial modeling and its applications. London, Chapman and Hall · Zbl 0873.62037
[8] Fuller W.A. (1987). Measurement error models. New York, Wiley · Zbl 0800.62413
[9] 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 · Zbl 0890.62079 · doi:10.2307/2965691
[10] 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 · Zbl 1073.62528 · doi:10.1198/016214501753381913
[11] Laird N.M., Ware J.H. (1982). Random effects models for longitudinal data. Biometrics 38, 963–974 · Zbl 0512.62107 · doi:10.2307/2529876
[12] Liang H., Ren H.B. (2005). Generalized partially linear measurement error models. Journal of Computational and Graphical Statistics 14, 237–250 · doi:10.1198/106186005X37481
[13] 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 · Zbl 1141.62350 · doi:10.1093/biostatistics/4.2.297
[14] 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 · Zbl 1072.62566 · doi:10.1198/016214501753208708
[15] 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 · Zbl 0915.62062 · doi:10.1111/1467-9868.00183
[16] Pinheiro J.C., Bates D.M. (2000). Mixed-effects models in S and S-PLUS. New York, Springer · Zbl 0953.62065
[17] Pollard D. (1991). Asymptotics for least absolute deviation regression estimators. Econometric Theory 7, 186–199 · Zbl 04504753 · doi:10.1017/S0266466600004394
[18] Ruppert D. (1997). Empirical-bias bandwidths for local polynomial nonparametric regression and density estimation. Journal of the American Statistical Association 92, 1049–1062 · Zbl 1067.62531 · doi:10.2307/2965570
[19] Rice J.A., Wu C.O. (2001). Nonparametric mixed effects models for unequally sampled noisy curve. Biometrics 57, 253–259 · Zbl 1209.62061 · doi:10.1111/j.0006-341X.2001.00253.x
[20] Schall R. (1991). Estimation in generalized linear models with random effects. Biometrika 78, 717–727 · Zbl 0850.62561 · doi:10.1093/biomet/78.4.719
[21] 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
[22] Severini T.A., Staniswalis J.G. (1994). Quasilikelihood estimation in semiparametric models. Journal of the American Statistical Association 89, 501–511 · Zbl 0798.62046 · doi:10.2307/2290852
[23] 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 · Zbl 0875.62574 · doi:10.2307/2986151
[24] Stefanski L.A., Cook J.R. (1995). Simulation-extrapolation: the measurement error jackknife. Journal of the American Statistical Association 90, 1247–1256 · Zbl 0868.62062 · doi:10.2307/2291515
[25] 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 · Zbl 0906.62069 · doi:10.2307/2669621
[26] 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 · doi:10.1086/314670
[27] 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 · doi:10.1002/sim.1317
[28] 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 · Zbl 1048.62111 · doi:10.1198/016214502388618744
[29] 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 · doi:10.2307/2289717
[30] Zhang D. (2004). Generalized linear mixed models with varying coefficients for longitudinal data. Biometrics 60, 8–15 · Zbl 1130.62350 · doi:10.1111/j.0006-341X.2004.00165.x
[31] 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 · Zbl 0918.62039 · doi:10.2307/2670121
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.