Ripatti S, Palmgren J
Rolf Nevanlinna Institute, University of Helsinki, P.O. Box 4, FIN-00014 Helsinki, Finland.
Biometrics. 2000 Dec;56(4):1016-22. doi: 10.1111/j.0006-341x.2000.01016.x.
There exists a growing literature on the estimation of gamma distributed multiplicative shared frailty models. There is, however, often a need to model more complicated frailty structures, but attempts to extend gamma frailties run into complications. Motivated by hip replacement data with a more complicated dependence structure, we propose a model based on multiplicative frailties with a multivariate log-normal joint distribution. We give a justification and an estimation procedure for this generally structured frailty model, which is a generalization of the one presented by McGilchrist (1993, Biometrics 49, 221-225). The estimation is based on Laplace approximation of the likelihood function. This leads to estimating equations based on a penalized fixed effects partial likelihood, where the marginal distribution of the frailty terms determines the penalty term. The tuning parameters of the penalty function, i.e., the frailty variances, are estimated by maximizing an approximate profile likelihood. The performance of the approximation is evaluated by simulation, and the frailty model is fitted to the hip replacement data.
关于伽马分布的乘法共享脆弱模型的估计，现有文献越来越多。然而，通常需要对更复杂的脆弱结构进行建模，但扩展伽马脆弱性的尝试会遇到复杂情况。受具有更复杂依赖结构的髋关节置换数据的启发，我们提出了一种基于具有多元对数正态联合分布的乘法脆弱性的模型。我们给出了这种一般结构的脆弱模型的合理性证明和估计程序，它是麦吉尔克里斯特（1993年，《生物统计学》49卷，221 - 225页）提出的模型的推广。估计基于似然函数的拉普拉斯近似。这导致基于惩罚固定效应偏似然的估计方程，其中脆弱项的边际分布决定惩罚项。惩罚函数的调整参数，即脆弱性方差，通过最大化近似轮廓似然来估计。通过模拟评估近似的性能，并将脆弱模型应用于髋关节置换数据。
