A medical test and accuracy of diagnosis are often discussed with contingency tables. However, it is difficult to apply a  contingency table to multivariate cases because the number of possible categories increases exponentially. We hypothesize that randomly assigning Boolean operators and focusing on frequencies of Boolean operators could explain the outcome correctly, obtain the tendencies of operators, and overcome difficulties in analyzing large numbers of variables and categories. The aims of this paper are introducing a method to obtain tendencies of Boolean operators and expanding 2 by 2 contingency tables to multivariate cases. To test this method, we construct two types of data: 1) when variables and outcome were randomly determined and 2 ) when the outcome depends on one variable. Analysis of the first type of data by this method showed that there was no significant result. Analysis of the second type of data reflected the bias of the data. As far as we know, this is the first attempt to use a frequentist approach to randomly assigned Boolean operators .
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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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
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) when the outcome depends on one variable. Analysis of the first type of data by this method showed that there was no significant result. Analysis of the second type of data reflected the bias of the data. As far as we know, this is the first attempt to use a frequentist approach to randomly assigned Boolean operators
by 2 contingency table in multivariate situation by this method