Interactions

The relative importance of interactive effects is rather unusual in standard regression analysis [8,5]. Traditionally, main effects are deemed to be most important; often second order interactions are disregarded. However, in these experiments it was already known that the selenium supplementation has a positive effect on selenite-dependent GPx activity when compared with baseline GPx activity in selenium-deficient cells. Of particular interest was the measure of selenite-dependent GPx synthesis in cells treated with, say, BSO as compared with selenite-dependent GPx synthesis in untreated cells. In other words, the regression coefficients for interactions such as BSO*Se becomes the focus of the inference. For instance, a negative coefficient corresponding to the interaction between Se and BSO would indicate that BSO treatment on the cells inhibits the effect of selenite supplementation on the rate of GPx activity. Similarly, second order interactions such Se*BSO*MB were included to estimate the joint effect of treating a cell line with BSO and MB simultaneously. A regression coefficient corresponding to the interaction among BSO, MB, and Se quantifies the "synergistic" effect of combined treatment of BSO and MB and of selenium supplementation on the response. This synergistic effect is beyond what would be attributed to treatment with BSO alone or MB alone. A value of zero for this coefficient, for example, would imply that any observed difference in GPx synthesis between the control cells and those treated with both MB and BSO would be due to the separate effects of MB and BSO. A negative value, on the other hand, would imply that there is an additional inhibiting effect on GPx synthesis due to the synergistic combination of the joint MB and BSO treatment. Figure 1 dispays an example of interaction plots for the data in Day 7. A value of 0 for the variable Se on the x-axis refers to the control cells; a value of 1 refers to the selenium-supplemented cells. Note the strong inhibiting effect of BSO and the even stronger inhibiting effect of MB. Additionally, the presence of MB and BSO together are more strongly inhibiting than either MB or BSO separately. Additional similar plots can be found in the Appendix.

Figure 1: Example of interaction plots