灰色模型GM(1,1)模型预测传染病时样本量的应用探讨

Discussion about the application of sample size in the prediction of disease using GM (1,1) model

目的了解用GM(1,1)模型建立预测模型时适宜的样本数量。方法用湖北省1991-2011年甲肝、梅毒、乙脑的发病率,分别连续抽取4年、10年的数据建立模型并进行外推预测,对建模情况和预测准确性进行分析比较。结果不同样本数量比较,甲肝、梅毒拟合成功率差异无统计学意义(P>0.05),乙脑差异有统计学意义(P<0.05),预测绝对百分比误差和预测成功率3种疾病差异均无统计学意义(P>0.05)。结论原始数据呈规则的指数变化时,用尽可能小的样本数量为宜,原始数据的指数变化特征出现波动时,应收集足够的样本数量,至能充分表达出指数变化特征为止。

Objective To explore the suitable number of samples by using GM （ 1,1 ） model to build predictive mode. Methods According to the incidence of hepatitis A, syphilis and Japanese Encephalitis in Hubei province from 1991 to 2011 ,the consecutive data of 4 years and 10 years respectively were extracted to build the model and make the prediction. There after, the modeling and forecast accuracy were analyzed and compared. Results The comparison of the number of different samples showed that the success rate of fitting between hepatitis A and syphilis was of no significant difference, while there was significant difference with JE, the absolute percentage error and success rate of forecast among the three diseases showed no significant difference. Conclusions It is advisable to use the smallest possible sample size,when the original data change showed a regular exponential change. However, when the index variation characteristics of the original data fluctuated, a sufficient number of samples should be collected until it could fully express the index variation.