S1. Illustration of Interaction Between Two Drugs

SupplementaryMaterial for “Utilization of chi-square statistics for screening adverse drug-drug interactions in spontaneous reporting systems”

S1. Illustration of interaction between two drugs

Figure S1. Schematic illustration of an interaction between drugs D1 and D2 on a linear probability model (additive model). The bars correspond to the frequency of the event of interest (i) in the absence of both D1 and D2, (ii) with D1 but not D2, (iii) with D2 but not D1, and (iv) with D1 and D2. The shades correspond to the marginal relative frequency of the event (lightest), the increased frequency attributable to D1, the increased frequency attributable to D2, and the increased frequency attributable to an interaction between D1 and D2 (darkest).

S2. Simulation study

S2.1 Data generation

For simplicity, the eight cell frequencies shown in Table 1 in the manuscript were independently generated based on a binary distribution. For this generation, we assumed the number of prescriptions in the absence of both D1 and D2, in the presence of either D1 or D2, and in the presence of both D1 and D2 to be 10,000,000, 100,000, and 10,000, respectively. The incidence probability excluding “ADR A” was set to 0.05 (%) regardless of the prescriptions. For example, was generated via , where “+1” was introduced as a term to prevent the number of reports being zero. The incidence probabilities in Table 1 varied depending on simulation scenario.

In scenario 1, we investigated the false positive rate for the proposed method. In this case, there was no DDI. As a result, we set (1-1) , (1-2) , and (1-3) (Figure 1 in the manuscript). In (1-2) and (1-3), there was an additive effect between D1 and D2, but there was no interaction under additive assumption because . In scenario 2, we investigated the sensitivity. In this scenario, there was a positive DDI because . Under this assumption, we set (2-1) , (2-2) , and (2-3) (Figure 1). The details of this setting are shown in Figure 1 and Tables 2 and 3 in the manuscript. The values of in Tables 2 and 3 were the average of the generated . Data generation was repeated 100,000 times in each setting.

S2.2 Drawing ROC curve

We assumed that there were no signals for DDIs in any of the data sets generated from scenario 1 and that there were DDIs in each of the data sets generated from scenario 2. One hundred data sets were randomly selected using a stratified random sampling approach within strata by scenarios (2-1), (2-2), and (2-3), respectively, because we assumed that 1 out of 1,000 assessed combinations corresponded to true adverse drug interactions. Thus, 300 positive controls and 300,000 negative controls were used for presenting the ROC analysis by each .

S2.3 Additional result

Figure S2. Rescaled ROC curves for , , and by incidence probability for ADR with D1 and D2 () from simulations. (a) Corresponds to the case of . (b) Corresponds to the case of . (c) Corresponds to the case of . (d) Corresponds to the case of .