Li Yi, Tiwari Ram C, Zou Zhaohui
Department of Biostatistics, Harvard University and Dana-Farber Cancer Institute, 44 Binney Street, LW211 Boston, MA 02115, USA.
Biom J. 2008 Aug;50(4):608-19. doi: 10.1002/bimj.200710430.
The annual percent change (APC) has been used as a measure to describe the trend in the age-adjusted cancer incidence or mortality rate over relatively short time intervals. The yearly data on these age-adjusted rates are available from the Surveillance, Epidemiology, and End Results (SEER) Program of the National Cancer Institute. The traditional methods to estimate the APC is to fit a linear regression of logarithm of age-adjusted rates on time using the least squares method or the weighted least squares method, and use the estimate of the slope parameter to define the APC as the percent change in the rates between two consecutive years. For comparing the APC for two regions, one uses a t-test which assumes that the two datasets on the logarithm of the age-adjusted rates are independent and normally distributed with a common variance. Two modifications of this test, when there is an overlap between the two regions or between the time intervals for the two datasets have been recently developed. The first modification relaxes the assumption of the independence of the two datasets but still assumes the common variance. The second modification relaxes the assumption of the common variance also, but assumes that the variances of the age-adjusted rates are obtained using Poisson distributions for the mortality or incidence counts. In this paper, a unified approach to the problem of estimating the APC is undertaken by modeling the counts to follow an age-stratified Poisson regression model, and by deriving a corrected Z -test for testing the equality of two APCs. A simulation study is carried out to assess the performance of the test and an application of the test to compare the trends, for a selected number of cancer sites, for two overlapping regions and with varied degree of overlapping time intervals is presented.
年度百分比变化（APC）已被用作一种衡量指标，用于描述在相对较短的时间间隔内年龄调整后的癌症发病率或死亡率的趋势。这些年龄调整率的年度数据可从美国国家癌症研究所的监测、流行病学和最终结果（SEER）计划中获取。估计APC的传统方法是使用最小二乘法或加权最小二乘法对年龄调整率的对数与时间进行线性回归，并使用斜率参数的估计值将APC定义为连续两年间率的百分比变化。为了比较两个地区的APC，人们使用t检验，该检验假定关于年龄调整率对数的两个数据集是独立的，并且服从具有共同方差的正态分布。最近已经开发出了这种检验的两种改进方法，当两个地区之间或两个数据集的时间间隔之间存在重叠时使用。第一种改进方法放宽了两个数据集独立性的假设，但仍假定有共同方差。第二种改进方法也放宽了共同方差的假设，但假定年龄调整率的方差是使用死亡率或发病率计数的泊松分布获得的。在本文中，我们通过对计数进行建模以遵循年龄分层的泊松回归模型，并通过推导用于检验两个APC相等性的校正Z检验，对估计APC的问题采用了一种统一的方法。进行了一项模拟研究以评估该检验的性能，并展示了该检验在比较两个重叠地区、具有不同重叠时间间隔程度的选定数量癌症部位的趋势方面的应用。
