Shen Yu, Ning Jing, Qin Jing
Department of Biostatistics, MD Anderson Cancer Center, The University of Texas, Houston, Texas 77030, U.S.A. ,
Biometrika. 2012 Jun;99(2):363-378. doi: 10.1093/biomet/ass008. Epub 2012 Mar 30.
The full likelihood approach in statistical analysis is regarded as the most efficient means for estimation and inference. For complex length-biased failure time data, computational algorithms and theoretical properties are not readily available, especially when a likelihood function involves infinite-dimensional parameters. Relying on the invariance property of length-biased failure time data under the semiparametric density ratio model, we present two likelihood approaches for the estimation and assessment of the difference between two survival distributions. The most efficient maximum likelihood estimators are obtained by the em algorithm and profile likelihood. We also provide a simple numerical method for estimation and inference based on conditional likelihood, which can be generalized to -arm settings. Unlike conventional survival data, the mean of the population failure times can be consistently estimated given right-censored length-biased data under mild regularity conditions. To check the semiparametric density ratio model assumption, we use a test statistic based on the area between two survival distributions. Simulation studies confirm that the full likelihood estimators are more efficient than the conditional likelihood estimators. We analyse an epidemiological study to illustrate the proposed methods.
统计分析中的全似然方法被视为估计和推断的最有效手段。对于复杂的长度偏倚失效时间数据，计算算法和理论性质并不容易获得，尤其是当似然函数涉及无限维参数时。基于半参数密度比模型下长度偏倚失效时间数据的不变性，我们提出了两种似然方法来估计和评估两个生存分布之间的差异。通过期望最大化（EM）算法和轮廓似然获得了最有效的最大似然估计量。我们还提供了一种基于条件似然的简单估计和推断数值方法，该方法可推广到多组设置。与传统生存数据不同，在适度的正则条件下，给定右删失的长度偏倚数据，可以一致地估计总体失效时间的均值。为检验半参数密度比模型假设，我们使用基于两个生存分布之间面积的检验统计量。模拟研究证实全似然估计量比条件似然估计量更有效。我们分析了一项流行病学研究以说明所提出的方法。
