To study the homogeneity of the agent effect across demographic levels and time, interaction terms were also evaluated. Where an interaction with demographic factor was observed, separate models were developed to explore the possibility of effect modification by those factors. For homogeneity of the agent effect across the time, we studied the interaction with time to diagnosis. Time to diagnosis was categorized as follows: greater than 2 years, 1-2 years, 0.5-1 year, less than 0.5 year before diagnosis, and after diagnosis. The interaction with time to diagnosis shows the temporal effect of antibody level and describes the consistency of risk across time periods. The interactions of the agents with demographic factors show the heterogeneity of the agent effect by those factors.