Gray R J
Department of Biostatistics, Dana-Farber Cancer Institute, Boston, Massachusetts 02115.
Biometrics. 1994 Sep;50(3):640-52.
This paper examines a method for testing hypotheses on covariate effects in a proportional hazards model, and also on how effects change over time in regression analysis of survival data. The technique used is very general and can be applied to testing many other aspects of parametric and semiparametric models. The basic idea is to formulate a flexible parametric alternative using fixed knot splines, together with a penalty function that penalizes noisy alternatives more than smooth ones, to focus the power of the tests toward smooth alternatives. The test statistics are the analogs of ordinary likelihood-based statistics, only computed from a penalized likelihood formed by subtracting the penalty function from the ordinary log-likelihood. Large-sample approximations to the distributions are found when the number of knots is held fixed as the sample size increases. Numerical results suggest these approximations may be adequate with moderate sized samples.
本文研究了一种用于检验比例风险模型中协变量效应假设的方法，以及在生存数据回归分析中效应如何随时间变化的方法。所使用的技术非常通用，可应用于检验参数模型和半参数模型的许多其他方面。基本思想是使用固定节点样条来制定一个灵活的参数替代方案，并结合一个惩罚函数，该惩罚函数对噪声较大的替代方案的惩罚比对平滑替代方案的惩罚更多，以使检验的功效集中在平滑替代方案上。检验统计量是普通基于似然的统计量的类似物，只是从通过从普通对数似然中减去惩罚函数而形成的惩罚似然中计算得出。当节点数量随着样本量的增加而保持固定时，可得到分布的大样本近似值。数值结果表明，对于中等规模的样本，这些近似值可能是足够的。
