Abstract
In data analysis, it is very common to encounter variables with 2 levels. The 2 levels of such variables may represent conditions with or without a certain property. For example, a variable indicating whether taking a medicine, a variable indicating whether a gene is mutated and protein expression is abnormal, and a variable indicating whether a chemical is applied, are such variables. For two such variables $A$ and $B$, we discuss how to identify whether they have synergistic or antagonistic interactions. The former is a positive interaction while the latter is a negative one. The synthetic lethal effect, for example, in genetic research is a synergistic interaction. The conventional method to identity synergistic and/or antagonistic interactions is based on the test significance of the main effects and interaction defined under sum coding system. In the work, we discuss the inadequacy of the approach. The main purpose of this study is to propose a more appropriate analysis method for the identification of synergistic and/or antagonistic interactions. Our method adopts the Helmert coding system to define effects. For quantitative and qualitative responses, we use linear models and generalized linear models respectively to develop a new identification method. A simulation study is conducted to validate the new method and to compare its performance to previous methods. The new method is also applied to a CRC real data. It identifies more synthetic lethal protein pairs than the previous method.