Eppley Institute, University of Nebraska Medical Center, Omaha, Nebraska, United States of America.
PLoS One. 2012;7(4):e34362. doi: 10.1371/journal.pone.0034362. Epub 2012 Apr 4.
The Age-Period-Cohort (APC) analysis is aimed at estimating the following effects on disease incidence: (i) the age of the subject at the time of disease diagnosis; (ii) the time period, when the disease occurred; and (iii) the date of birth of the subject. These effects can help in evaluating the biological events leading to the disease, in estimating the influence of distinct risk factors on disease occurrence, and in the development of new strategies for disease prevention and treatment.
METHODOLOGY/PRINCIPAL FINDINGS: We developed a novel approach for estimating the APC effects on disease incidence rates in the frame of the Log-Linear Age-Period-Cohort (LLAPC) model. Since the APC effects are linearly interdependent and cannot be uniquely estimated, solving this identifiability problem requires setting four redundant parameters within a set of unknown parameters. By setting three parameters (one of the time-period and the birth-cohort effects and the corresponding age effect) to zero, we reduced this problem to the problem of determining one redundant parameter and, used as such, the effect of the time-period adjacent to the anchored time period. By varying this identification parameter, a family of estimates of the APC effects can be obtained. Using a heuristic assumption that the differences between the adjacent birth-cohort effects are small, we developed a numerical method for determining the optimal value of the identification parameter, by which a unique set of all APC effects is determined and the identifiability problem is solved.
CONCLUSIONS/SIGNIFICANCE: We tested this approach while estimating the APC effects on lung cancer occurrence in white men and women using the SEER data, collected during 1975-2004. We showed that the LLAPC models with the corresponding unique sets of the APC effects estimated by the proposed approach fit very well with the observational data.
年龄-时期-队列（APC）分析旨在估计疾病发病率的以下影响因素：（i）疾病诊断时受试者的年龄；（ii）疾病发生的时期；（iii）受试者的出生日期。这些影响因素有助于评估导致疾病的生物学事件，估计不同危险因素对疾病发生的影响，并制定新的疾病预防和治疗策略。
方法/主要发现：我们在对数线性年龄-时期-队列（LLAPC）模型框架内开发了一种估计 APC 对疾病发病率影响的新方法。由于 APC 效应是线性相互依赖的，不能唯一估计，因此解决这个可识别性问题需要在一组未知参数中设置四个冗余参数。通过将三个参数（时期和出生队列效应中的一个以及相应的年龄效应）设置为零，我们将这个问题简化为确定一个冗余参数的问题，然后将其用作与锚定时期相邻的时期效应。通过改变这个识别参数，可以得到 APC 效应的一组估计值。我们使用一个启发式假设，即相邻出生队列效应之间的差异较小，开发了一种确定识别参数最优值的数值方法，通过该方法确定了所有 APC 效应的唯一集合，并解决了可识别性问题。
结论/意义：我们使用 SEER 数据测试了这种方法，这些数据是在 1975-2004 年期间收集的，用于估计 APC 对白人和女性肺癌发病的影响。我们表明，使用所提出的方法估计的 APC 效应的 LLAPC 模型与观察数据非常吻合。
