Interest m the use of random effects in the survrval analysis settmg has been mcreasmg How-ever, the computational complexity of such fradty models has hmrted then general use. Whrle fittmg frarlty models has traditronally been standard algorithms for fittmg Cox semr-parametrrc and parametrrc regression models can be readily extended to m&de penahzed regres-sron We demonstrate that solutrons for gamma shared frarlty models can be obtained exactly VEI penahzed estlmatlon Smularly, Gauasmn barlty models are closely linked to penabzed mod-els Thus makes rt possible to apply penalized estrmation to other frarlty models usmg Laplace approxrmatrons. Fitting frarlty models wrth penalized bkebhoods can be made quite rapid by tak-mg advantage of computatronal methods avadable for penahzed models. We have nnplemented penalized regression for the coxph function of S-plus and rllustrate the algorrthms wrth examples usmg the Cox model KEY WORDS Cox model, penabzed bkehhood, proportional hazards, random effects
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