新陈代谢GM(1，1)模型在中国HIV／AIDS流行趋势预测中的应用

Application of Metabolic GM( 1,1) Model on Forecasting the Epidemic Tendency of HIV /AIDS in China

目的对我国HIV/ADIS流行趋势进行分析和预测,为今后制定艾滋病防治策略提供科学依据。方法以全国2006-2011年艾滋病疫情报告数据为基础建立GM(1,1)模型,在此基础上根据新陈代谢原理对2012-2015年发病趋势进行预测。结果最终建立了三个GM(1,1)模型用于HIV/AIDS、AIDS、HIV流行趋势预测,三个模型拟合优度检验均为1级。预测分析结果显示,2012-2015年我国HIV/AIDS发病数分别为81832例、91576例、103618例、117494例,AIDS发病数分别为24442例、30467例、37174例、45500例,HIV发病数分别为57926例、62349例、68795例、76050例。结论2006年以来我国HIV/AIDS疫情逐年上升,预测分析结果表明未来4年仍将延续持续上升的长期趋势,艾滋病防治形势严峻,需要进一步加大防治力度。

Objective To analyze and forecast the epidemic tendency of HIV/AIDS in China, which may provide a scientific basis for developing prevention and control staregies for HIV/AIDS in the future. Methods We fit GM（ 1,1 ） models based on the epidemic data of HIV/ ADS from 2006 to 2011 in China, and then predicted the incidence levels in 2012 -2015 in accordance with the metabolic principles. Results Three metabolic GM（ 1,1 ） models was fitted for HIV/ADIS, AIDS and HIV, re- spectively. The fitting effects of these models were all ideal. The predicted case numbers in 2012 - 2015 would be 81832,91576,103618,117494 for HIV/AIDS, 24442,30467,37174,45500 for AIDS, and 57926,62349, 68795,76050 for HIV, respectively. Conclusion Since 2006, the inci- dence of HIV/AIDS in China has gone up rapidly year by year. What＇s more, the forecast analysis showed that the long-term trend of rising would be continued in next four years. The study indicats that the situation of pre-gression coefficient or its standard error from PS regression, were close to parameters estimated from standard regression model, compared to the com- mon logistic regression. These differences of parameter estimates were grad- ually disappeared along with increase of sample size. （2） Given sample size of 1000 and 500 and 4% positive proportion of outcome variable, we estimated regression coefficient and its standard error from three models a- long with degree of collinearity. The trend of parameters estimated from PS regression was parallel with the trend of standard model. It means the differ- ence between these two models is consistent. However, the change of re- gression coefficient and standard error estimated from the common logistic regression were parallel with changes of two models mentioned above when r is in a low level. But it changes its direction at r = 0.5 （ n = 1000） or r = 0. 3 （ n = 500 ）. Conclusion The parameters estimated from PS regres- sion were more reliable than the common logistic regression, especially un- der the conditions of small sample size and data with severe collinearity. Therefore, PS regression could be one of excellent methods in dealing with collinearity data.