一种利用布尔算子趋向性展开2 × 2列联表的方法--布尔蒙特卡罗法
A Method Expanding 2 by 2 Contingency Table by Obtaining Tendencies of Boolean Operators: Boolean Monte Carlo Method
摘要：
医学检验和诊断的准确性经常用2 × 2列联表来讨论。然而，很难将2 × 2列联表应用于多变量情况，因为可能的类别数量呈指数级增加。本研究的目的是介绍一种方法，通过它我们可以获得布尔算子的趋势，并建立一个2 × 2列联表，以多元情况。在这种方法中，我们随机分配布尔运算符之间的二元变量，并专注于频率的布尔运算符，可以正确地解释结果。我们通过卡方检验确定布尔算子的趋势。作为应用，我们对一个数据集，其中包括患者的年龄，体重指数（BMI），平均动脉压（MAP）和糖尿病进展的定量测量（$Y$）进行了这种方法。我们为每个变量设置截止值，并将其视为二进制变量。年龄、BMI和MAP的交互作用被确定为年龄$and$ BMI $and$ MAP（$p<0.0001$）在估计$Y$中的敏感性、特异性、阳性预测值和阴性预测值分别为0.50、0.85。0.59、0.80。用这种方法可以确定布尔算子的趋势，并构造多元情况下的2 × 2列联表。
英文摘要：
Accuracy of medical test and diagnosis are often discussed by 2 by 2 contingency tables. However, it is difficult to apply a 2 by 2 contingency table to multivariate cases because the number of possible categories increases exponentially. The aims of this study is introducing a method by which we can obtain trends of boolean operators and construct a 2 by 2 contingency tables to multivariate cases. In this method, we randomly assigned boolean operators between binary variables and focused on frequencies of boolean operators which could explain outcomes correctly. We determined trends of boolean operators by chi-square test. As an application, we performed this method for a dataset which included patient's age, body mass index (BMI), mean arterial pressure (MAP) and the quantitative measure of diabetes progression ($Y$). We set cutoff to each variable and considered these as binary variables. Interactions of age, BMI and MAP were determined as age $and$ BMI $and$ MAP ($p<0.0001$ for both operators) in estimating $Y$ and sensitivity, specificity, positive and negative predicting value were 0.50, 0.85. 0.59, 0.80 respectively. We may be able to detemine trends of boolean operators and construct a 2 by 2 contingency table in multivariate situation by this method.
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