Marschner I C
Department of Biostatistics, Harvard School of Public Health, Boston, Massachusetts 02115, USA.
Biometrics. 1997 Dec;53(4):1384-98.
This paper considers nonparametric estimation of age- and time-specific trends in disease incidence using serial prevalence data collected from multiple cross-sectional samples of a population over time. The methodology accounts for differential selection of diseased and undiseased individuals resulting, for example, from differences in mortality. It is shown that when a log-linear incidence odds model is adopted, an EM algorithm provides a convenient method for carrying out maximum likelihood estimation, primarily using existing generalized linear models software. The procedure is quite general, allowing a range of age-time incidence models to be fitted under the same framework. Furthermore, by making use of existing software for fitting generalized additive models, the procedure can be generalized with virtually no extra complexity to allow maximization of a penalized likelihood for smooth nonparametric estimation. Automatic choice of smoothing level for the penalized likelihood estimates is discussed, using generalized cross-validation. The method is applied to a data set on serial toxoplasmosis prevalence, which has previously been analyzed under the assumption of nondifferential selection. A variety of age-time incidence models are fitted, and the sensitivity to plausible differential selection patterns is considered. It is found that nonmultiplicative models are unnecessary and that qualitative incidence trends are fairly robust to differential selection.
本文考虑使用从某一人群随时间的多个横断面样本收集的系列患病率数据，对疾病发病率的年龄和时间特异性趋势进行非参数估计。该方法考虑了患病个体和未患病个体的差异选择，例如由死亡率差异导致的差异选择。结果表明，当采用对数线性发病比模型时，期望最大化（EM）算法提供了一种方便的方法来进行最大似然估计，主要利用现有的广义线性模型软件。该过程非常通用，允许在相同框架下拟合一系列年龄-时间发病率模型。此外，通过利用现有的拟合广义相加模型的软件，该过程几乎可以在不增加额外复杂性的情况下进行推广，以允许对惩罚似然进行最大化，从而实现平滑非参数估计。使用广义交叉验证讨论了惩罚似然估计的平滑水平的自动选择。该方法应用于一个关于系列弓形虫病患病率的数据集，该数据集之前是在无差异选择的假设下进行分析的。拟合了各种年龄-时间发病率模型，并考虑了对合理的差异选择模式的敏感性。结果发现，非乘法模型是不必要的，并且定性的发病率趋势对差异选择相当稳健。
