Robust inference for univariate proportional hazards frailty regression models
单变量比例风险脆弱性回归模型的稳健推断AI 解读 ↓
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单变量比例风险脆弱性回归模型的稳健推断
- 研究问题
- 对于右删失生存时间，加入个体随机脆弱性的比例风险模型若设定错误，参数估计与统计推断还能具有什么性质？
- 方法与思路
- 作者采用非参数似然，同时估计回归参数、单参数脆弱性分布参数和基准风险，并研究误设下的极限及bootstrap推断。
- 材料陈述的贡献
- 摘要称估计量对伪真值一致且具有高斯过程极限，正确设定时达到半参数效率界，误设时bootstrap仍可有效推断。
- 阅读关注点
- 核对伪真值的定义、删失与协变量条件，以及随机试验中治疗效应检验有效性和回归系数比值可识别性的适用范围。
- 阅读边界
- 材料为版本未注明的OpenAlex索引摘要；稳健推断的完整条件未说明，不能将伪真值一致性解释为真实参数一致性。
原文摘要
We consider a class of semiparametric regression models which are one-parameter extensions of the Cox [J. Roy. Statist. Soc. Ser. B 34 (1972) 187–220] model for right-censored univariate failure times. These models assume that the hazard given the covariates and a random frailty unique to each individual has the proportional hazards form multiplied by the frailty. The frailty is assumed to have mean 1 within a known one-parameter family of distributions. Inference is based on a nonparametric likelihood. The behavior of the likelihood maximizer is studied under general conditions where the fitted model may be misspecified. The joint estimator of the regression and frailty parameters as well as the baseline hazard is shown to be uniformly consistent for the pseudo-value maximizing the asymptotic limit of the likelihood. Appropriately standardized, the estimator converges weakly to a Gaussian process. When the model is correctly specified, the procedure is semiparametric efficient, achieving the semiparametric information bound for all parameter components. It is also proved that the bootstrap gives valid inferences for all parameters, even under misspecification. We demonstrate analytically the importance of the robust inference in several examples. In a randomized clinical trial, a valid test of the treatment effect is possible when other prognostic factors and the frailty distribution are both misspecified. Under certain conditions on the covariates, the ratios of the regression parameters are still identifiable. The practical utility of the procedure is illustrated on a non-Hodgkin’s lymphoma dataset.