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Varying Coefficient Model with Unknown WithinâSubject Covariance for Analysis of Tumor Growth Curves
- Krafty, Robert T., Gimotty, Phyllis A., Holtz, David, Coukos, George, Guo, Wensheng
- Biometrics 2008 v.64 no.4 pp. 1023-1031
- animal ovaries, biometry, chemotherapy, covariance, least squares, mice, models, neoplasms
- In this article we develop a nonparametric estimation procedure for the varying coefficient model when the withinâsubject covariance is unknown. Extending the idea of iterative reweighted least squares to the functional setting, we iterate between estimating the coefficients conditional on the covariance and estimating the functional covariance conditional on the coefficients. Smoothing splines for correlated errors are used to estimate the functional coefficients with smoothing parameters selected via the generalized maximum likelihood. The covariance is nonparametrically estimated using a penalized estimator with smoothing parameters chosen via a KullbackâLeibler criterion. Empirical properties of the proposed method are demonstrated in simulations and the method is applied to the data collected from an ovarian tumor study in mice to analyze the effects of different chemotherapy treatments on the volumes of two classes of tumors.