  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.
