Data-driven Approach to Determine Optimal Coefficient Value for MDDC Boxplot Method for Controlling FDR

This algorithm describes a method to determine the value of c in the cutoff formula \(Q_3 + c \times IQR\) for controlling the False Discovery Rate (FDR) using the MDDC Boxplot method.

Steps:

1. For a given contingency table of dimension \(I \times J\) calculate the \(n_{\cdot \cdot}\), and the \(\underset{\sim}{p} = p_{11}, p_{12}, \ldots p_{IJ}\).

2. Generate a large number of \(I\times J$\) tables \(r=1,\ldots,R\) under the assumption of independence from multinomial distribution using the \(n_{\cdot \cdot}\) and \(\underset{\sim}{p}\) determined in Step 1.

3. Compute the standardized Pearson residuals.

4. Compute the upper limits of the boxplot statistic with \(c = 1.5\), and calculate the FDR.

5. If \(FDR < 0.05\), stop. Otherwise, if \(FDR > 0.05\), use a grid search to find the optimal c such that \(FDR \leq 0.05\).