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Biometrika 1999 86(3):691-702; doi:10.1093/biomet/86.3.691
© 1999 by Biometrika Trust
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A semiparametric additive regression model for longitudinal data

T MartinussenA1 and TH ScheikeA2

A1 Department of Mathematics and Physics, The Royal Veterinary and Agricultural University, Thorvaldsenvej 40, DK-1871 Frederiksberg C, Denmark E-mail: torbenm@dina.kvl.dk A2 Department of Biostatistics, University of Copenhagen, Blegdamsvej 3, DK-2200 Copenhagen N, Denmark E-mail: ts@biostat.ku.dk

In previous work we have studied a nonparametric additive time-varying regression model for longitudinal data recorded at irregular intervals. The model allows the influence of each covariate to vary separately with time. For small datasets, however, only a limited number of covariates may be handled in this way. In this paper, we introduced a semiparametric regression model for longitudinal data. The influence of some of the covariates varies nonparametrically with time while the effect of the remaining covariates are constant. No smoothing is necessary in the estimation of the parametric terms of the model. Asymptotics are derived using martingale techniques for the cumulative regression functions, which are much easier to estimate and study than the regression functions themselves. The approach is applied to longitudinal data from the Copenhagen Study Group for Liver Diseases (Schlichting et al., 1983).

Key Words: Dynamic linear model; Local estimating equation; Longitudinal data; Martingale; Marked point process; Time-varying coefficients


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