一种新的数学模型在肺炎克雷伯菌氨基糖甙类耐药指数拟合与推测中的应用

A novel algorithm to define trends in fitting and predicting the resistance indexes of Klebsiella pneumoniae to aminoglycosides

目的构建派生于灰色模型与神经网络模型的灰色神经网络模型,探讨其在肺炎克雷伯菌氨基糖甙类耐药指数拟合及推测的应用。方法收集中国期刊全文数据库(CNKI)及国内相关数据库文献报道的1995—2009年期间肺炎克雷伯菌氨基糖甙类药物的耐药性数据,分别应用灰色模型GM(1,1)、BP神经网络模型进行拟合推测,最后构建派生于这两种模型的GBP神经网络模型。以χ2拟合优度检验及平均绝对误差(MAE)、误差标准差(RSE)、平均绝对百分误差(MAPE)衡量拟合及推测结果的合理性及准确性。结果 1995—2009年期间肺炎克雷伯菌氨基糖甙类药物的耐药指数经三种模型拟合,显示拟合优度检验结果均为χ2<χ20.995,P>0.995,且对比2007—2009年推测值各精度衡量标准MAE、SDE、MAPE值以GBP模型最小,提示其推测效果最佳。结论灰色神经网络模型能以较高精度(MAPE<5%)拟合细菌耐药性发展趋势,提高了拟合与推测结果的稳定性及可靠性,有利于为抗菌药物的选择应用及细菌耐药性控制提供参考依据。

Objective To construct the Grey neural network model derived from the Grey Model and the Neural Network model, and to probe application of the model in fitting and predicting resistance indexes of Klebsiella pneumoniae to aminoglycosides. Methods The data about drug-resistance of Klebsiella pneumoniae to aminoglycosides which reported in the Chinese documents were collected from 1995 to 2009 in China National Knowledge Infrastructure （CNKI） and other related Chinese databases. The Grey Model GM （1,1） and BP neural network model were applied respectively to fit and predict the data,and at last the Grey Back Propagation neural network model（GBP） derived from the two models was constructed. The rationality and accuracy of fitting and predicting were measured respectively by the chi-square goodness-of-fit testing, Mean Absolute Error （MAE）, Relative Standard Error（RSE）, Mean Absolute Percentage Error（MAPE）. Results Fitted by the three models respectively, the result of the chi-square goodness-of-fit testing about the resistance indexes of klebsiella pneumoniae to Aminoglycosides from 1995 to 2009 were χ^2〈χ^2 0.995, P〉0.995. And predicted by the GBP model,the measure precision values of MAE, RSE, MAPE from 2007 to 2009 were the least, which indicated that the predicting effect of the GBP model was the best.Conclusion The development of bacterial drug-resistance can be fitted exactly by the GBP （MAPE〈5%）, so that the stability and reliability of fitting and predicting results have a good improvement. It can provide the valuable reference to selection of antibacterial drugs and control of bacterial drug-resistance.