Martín Nirian, Li Yi
Dept. Statistics, Carlos III University of Madrid.
J Multivar Anal. 2011 Sep 1;102(8):1175-1193. doi: 10.1016/j.jmva.2011.03.011.
The Annual Percent Change (APC) has been adopted as a useful measure for analyzing the changing trends of cancer mortality and incidence rates by the NCI SEER program. Difficulties, however, arise when comparing the sample APCs between two overlapping regions because of the induced dependence (e.g., comparing the cancer mortality change rate of California with the national level). This paper deals with a new perspective of understanding the sample distribution of the test statistics for comparing the APCs between overlapping regions. Our proposal allows for computational readiness and easy interpretability. We further propose a more general family of estimators, namely, the so-called minimum power divergence estimators, including the maximum likelihood estimators as a special case. Our simulation experiments support the superiority of the proposed estimator to the conventional maximum likelihood estimator. The proposed method is illustrated by the analysis of the SEER cancer mortality rates observed from 1991 to 2006.
年度百分比变化（APC）已被美国国家癌症研究所监测、流行病学和最终结果（NCI SEER）计划用作分析癌症死亡率和发病率变化趋势的有用指标。然而，由于存在诱导依赖性（例如，比较加利福尼亚州的癌症死亡率变化率与全国水平），在比较两个重叠区域的样本APC时会出现困难。本文从一个新的视角来理解用于比较重叠区域APC的检验统计量的样本分布。我们的提议具备计算便利性和易于解释性。我们进一步提出了一个更通用的估计量族，即所谓的最小功率散度估计量，其中最大似然估计量是一个特殊情况。我们的模拟实验支持了所提出的估计量优于传统最大似然估计量。通过对1991年至2006年观察到的SEER癌症死亡率的分析来说明所提出的方法。
