Letters Epidemiology• Volume 24, Number 5, September 2013

774| www. epidem. com© 2013 Lippincott Williams & Wilkins interaction”(there are persons for whom the outcome would occur if and only if both factors are present). relying on standard asymptotic (large sample) theory, VanderWeele3 recently presented a spreadsheet program to calculate sample sizes for additive interactions. still, the sampling distribution of rerI is difficult to approximate with a small-to-moderate sample size. 4–8 For better accuracy, I propose brute-force Monte-Carlo simulations for sample size calculations. sAs codes are presented in the eAppendix. For cohort studies, one can specify a total of ten parameters (three parameters related to the study population, four parameters related to risks, and three parameters related to the hypothesis testing to be conducted). the three population parameters are the prevalence of the 1st factor, the prevalence of the 2nd factor, and the odds ratio between the two factors (1.0, if the two factors are independent to each other). the 4 risk parameters are:(1) the background disease risk (the disease risk for those exposed to neither factor),(2) the risk ratio comparing those exposed to the 1st but not the 2nd factor with those exposed to neither,(3) the risk ratio comparing those exposed to the 2nd but not the 1st factor with those exposed to neither, and (4) the risk ratio comparing those exposed to both factors with those exposed to neither. the three test parameters are the level of significance (α level), the target power, and the threshold of the test (zero for additive interaction, one for sufficient cause interaction, and two for singular interaction). For case-control studies, the rare disease assumption is invoked. One can also specify a total of ten parameters. the three population parameters and the three test parameters are the same as those in cohort studies. there is no background disease risk now; one can specify the control-to-case matching ratio instead. As for the other 3 risk parameters, they are now in terms of odds ratios. As an initial value, the program first calculates a sample size (N0) using the asymptotic method. 3 the program