数学
审查(临床试验)
统计
似然比检验
单调多边形
边际似然
置信区间
似然函数
最大似然
推论
经验似然
限制最大似然
标称水平
协变量
计量经济学
记分测验
应用数学
计算机科学
几何学
人工智能
作者
Georg Heinze,M. Schemper
出处
期刊:Biometrics
[Wiley]
日期:2001-03-01
卷期号:57 (1): 114-119
被引量:295
标识
DOI:10.1111/j.0006-341x.2001.00114.x
摘要
The phenomenon of monotone likelihood is observed in the fitting process of a Cox model if the likelihood converges to a finite value while at least one parameter estimate diverges to +/- infinity. Monotone likelihood primarily occurs in small samples with substantial censoring of survival times and several highly predictive covariates. Previous options to deal with monotone likelihood have been unsatisfactory. The solution we suggest is an adaptation of a procedure by Firth (1993, Biometrika 80, 27-38) originally developed to reduce the bias of maximum likelihood estimates. This procedure produces finite parameter estimates by means of penalized maximum likelihood estimation. Corresponding Wald-type tests and confidence intervals are available, but it is shown that penalized likelihood ratio tests and profile penalized likelihood confidence intervals are often preferable. An empirical study of the suggested procedures confirms satisfactory performance of both estimation and inference. The advantage of the procedure over previous options of analysis is finally exemplified in the analysis of a breast cancer study.
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