2×2表参数置信域的几何方法

Geometry method of confidence interval on 2×2 table

对于生物医学统计中的一类二次感染问题,提出了一种研究其简单差和危险率的区间估计几何方法.比较系统地研究了非线性多项分布模型参数置信域的几何理论,通过基于曲率的置信域和基于Score检验的置信域这2种方法得到了3个关于参数置信域的定理.抽象出二次感染问题为一个特殊的非线性多项分布(三项分布)模型,其概率密度为p(Y;π(θ))=n!∏3i=1(πyii(θ)/yi!),其中Y={y1,y2,y3}T,∑3i=1πi(θ)=1,∑3i=1yi=n,并进一步指出这些定理对于2×2表以及二次感染问题的应用.

A geometry method is brought forward in this article to analyze the interval estimate of the simple difference （SD） and risk ratio （RR） between the proportions of the primary infection and the secondary infection in biomedical statistics. A geometry theory of multinomial nonlinear models is also analyzed systematically study and three theorems about confidence interval of parameter are proved. The secondary infection given the primary infection is regarded as a special multinomial nonlinear model as follows：ρ（Y；π（θ））=n!3↑∏↓i=1（π^yi i，（θ）／yi!），Y={Y1，Y2，Y3}^T，3↑∑↓iπi（θ）=1，3↑∑↓iyi=n，And the three theorems proved above are applied to the 2 x 2 table and the secondary infection given the primary infection and the primary infection。