西安市出生缺陷趋势数学模型预测研究
Mathematical model for predicting birth defect trend in Xi’an

摘要：目的 采用灰色预测模型、ARIMA自回归移动平均模型和NAR非线性自回归动态神经网络模型分别预测西安市出生缺陷率，探索出生缺陷的流行趋势和可能的未来走向。方法 对2003-2015年在西安市各级开设产科的医疗保健机构出生的孕28周至生后7d所有围产儿进行出生缺陷监测并收集资料。用2003年10月至2015年9月出生缺陷监测数据对西安市出生缺陷发生率数据分别构建数据模型，将同时期实际出生缺陷发生率与模型拟合数据进行比较，评价模型的预测性能，并预测西安市2016至2017年每季度出生缺陷发生率。采用Excel软件进行数据录入，SPSS 16.0软件包进行统计学分析，Matlab软件进行灰色模型预测和神经网络模型预测，ARIMA自回归移动平均模型使用R软件进行预测。结果 灰色预测模型提示2016至2017年度西安市各季度出生缺陷率(‰)分别为9.62、9.67、9.72、9.77、9.82、9.87、9.92、9.97，呈缓慢上升趋势。ARIMA模型预测显示2016至2017年度西安市各季度出生缺陷率(‰)分别为11.98、12.83、11.28、11.78、12.23、11.73、11.80、12.00，仍在较高水平相对狭窄的区间波动。NAR神经网络模型预测西安市出生缺陷率(‰)为13.24、17.91、10.55、16.08、16.47、9.42、11.99、11.68，在2016年到达出生缺陷率峰值，2017年相比2016年开始出现下降。比较3种模型对出生缺陷发生率的发展趋势预测，灰色预测模型、ARIMA模型、NAR模型的均方根误差分别为1.353009、1.181373、0.555347。结论 NAR模型对出生缺陷数据预测更可靠，ARIMA模型次之，灰色预测模型误差相对较大；加强出生缺陷的预防和控制工作仍然是今后较长一段时间的公共卫生重点工作。
ABSTRACT: Objective To understand the trend of birth defects in Xi’an by using gray model, ARIMA and NAR. Methods The birth defects monitoring data of perinatal infants from 28-week pregnant women to 7 days after birth were collected from all the hospitals with obstetrical department in Xi’an during 2003 and 2015. The incidence of birth defects data from October 2003 to September 2015 in Xi’an City were used to construct the data model. We compared data with the actual birth defects rate from October 2003 to September 2015 to further optimize and make supplement for the model, and then predicted the incidence of birth defects in Xi’an from 2016 to 2017. Microsoft Excel 2003 was used for data input and SPSS version 16.0 was used for statistical analysis. Matlab was used for Gray Model and NAR prediction. ARIMA mathematical model was predicted by R software. Results The grey prediction model suggested that the birth defects rate in the four quarters of 2016 and 2017 was 9.62‰, 9.67‰, 9.72‰, 9.77‰, 9.82‰, 9.87‰, 9.92‰ and 9.97‰, which was in slow increase. The ARIMA model predicted that the birth defects rate in Xi’an would still fluctuate at a high level in 2016 and 2017, and the rate in the four quarters was 11.98‰, 12.83‰, 11.28‰, 11.78‰, 12.23‰, 11.73‰, 11.80‰ and 12.00‰. The NAR model predicted that the birth defects rate in Xi’an was 13.24‰, 17.91‰, 10.55‰, 16.08‰, 16.47‰, 9.42‰, 11.99‰ and 11.68‰. The birth defects rate would reach the peak in 2016 and decrease in 2017. Comparison of the above three models showed that the root mean square error of grey prediction model, ARIMA model and NAR model was 1.353009, 1.181373 and 0.555347, respectively. Conclusion Based on the prediction by the above three mathematical models, it shows that NAR model is more accurate and reliable