The DDIs and single drug effects were compared by combining hydroxychloroquine and diltiazem, as shown by the box plot in Fig. 3 for APD90, qNet, and CaD90. The box plot of the features shows several essential pieces of information. In a single data plot, the cross line refers to the average value of the feature; the lower, middle, and upper lines of the box refer to the first quartile, median, and third quartile, respectively; the upper and lower lines outside the box refer to maximum and minimum values excluding the outliers; circles represent the outliers. For the results of APD90 in panel (A) of Fig. 3, hydroxychloroquine shows higher values of APD90 compared to diltiazem and their combinations. Furthermore, the diltiazem yields the lowest APD90 values among them and displays the only negative trend of ADP90 values (APD shortening) as drug concentration increases. In 1×cmax, the lowest APD90 value is 284.5 ms by diltiazem and the highest is 344 ms by hydroxychloroquine; and in 4×cmax, it becomes 277.5 ms for diltiazem and 383.5 ms for hydroxychloroquine. The combined drugs show APD90 values in between with a positive trend (APD90 prolongation) as hydroxychloroquine, indicating DDIs effects on APD90 are strongly influenced by hydroxychloroquine.

Furthermore, the qNet results are presented in panel (B) of Fig. 3. The diltiazem produces the highest qNet values, the hydroxychloroquine generates the lowest qNet data, and their combination yields anything in between. Interestingly, the only positive trend of qNet as a function of drug concentration is produced by diltiazem. In \(1\times \text{c}\text{m}\text{a}\text{x}\), the highest qNet value is \(0.082 \mu C/\mu F\) by diltiazem and the lowest one is \(0.063 \mu C/\mu F\) by hydroxychloroquine. In high concentration of \(4\times \text{c}\text{m}\text{a}\text{x}\), the pattern is similar that the highest qNet is about \(0.088 \mu C/\mu F\) by diltiazem and the lowest is \(0.055 \mu C/\mu F\). In addition, the combined hydroxychloroquine-diltiazem results in the qNet trend that follow the hydroxychloroquine’s qNet tendency towards higher concentration of drugs (negative direction), indicating that hydroxychloroquine affects more in lowering the qNet values of the combined drug.

Moreover, we can observe from panel (C) of Fig. 3 that the combined drugs can yield a higher value of CaD90 compared to results from single drug effects, while the least CaD90 values were produced by hydroxychloroquine. In 1×cmax, the CaD90 values ranged from 762 ms (yielded by hydroxychloroquine) to 880 ms (generated by combined hydroxychloroquine and diltiazem). The CaD90 values by hydroxychloroquine for higher drug concentrations show a small increment with a maximum of 786 at 4×cmax. On the other hand, diltiazem and combined hydroxychloroquine-diltiazem show quite a considerable rise in CaD90 values as the drug concentration increases. In addition, the data of CaD90 from hydroxychloroquine show a considerable gap to both diltiazem and combined one, indicating DDIs effects are affected more by diltiazem than hydroxychloroquine in producing high CaD90 values.

The results of averaged qNet distribution for 12 CiPA drugs are shown in Fig. 4. There are two qNet threshold values in the figure, the \(\mathbf{t}\mathbf{h}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{h}\mathbf{o}\mathbf{l}{\mathbf{d}}_{1}=0.0652 {\mu }\text{C}/{\mu }\text{F}\) and \(\mathbf{t}\mathbf{h}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{h}\mathbf{o}\mathbf{l}{\mathbf{d}}_{2}=0.0516 {\mu }\text{C}/{\mu }\text{F}\). qNet values higher than \(\mathbf{t}\mathbf{h}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{h}\mathbf{o}\mathbf{l}{\mathbf{d}}_{1}\) are classified as low risk, between \(\mathbf{t}\mathbf{h}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{h}\mathbf{o}\mathbf{l}{\mathbf{d}}_{1}\) and \(\mathbf{t}\mathbf{h}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{h}\mathbf{o}\mathbf{l}{\mathbf{d}}_{2}\) are classified as intermediate risk, and below \(\mathbf{t}\mathbf{h}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{h}\mathbf{o}\mathbf{l}{\mathbf{d}}_{2}\) for high-risk drugs. The high-risk drugs (quinidine, bepridil, dofetilide, and sotalol) generally generated low qNet values, except the sotalol that produced qNet between \(\mathbf{t}\mathbf{h}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{h}\mathbf{o}\mathbf{l}{\mathbf{d}}_{1}\) and \(\mathbf{t}\mathbf{h}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{h}\mathbf{o}\mathbf{l}{\mathbf{d}}_{2}\). Furthermore, the intermediate-risk drugs (cisapride, terfenadine, ondansetron, and chlorpromazine) were typically within two thresholds with some exceptions for cisapride, terfenadine, and ranolazine that generated some qNet data outside this region. Finally, the low-risk drugs (ranolazine, mexiletine, diltiazem) produced qNet values mostly above \(\mathbf{t}\mathbf{h}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{h}\mathbf{o}\mathbf{l}{\mathbf{d}}_{1}\) except verapamil that yielded qNet within the two thresholds. The two threshold values will be utilized for further analysis in drug combination maps of DDIs effects.

Drug combination maps of DDIs effects on TdP risks of drugs can be seen in Fig. 5. Three panels (A, B, and C) show different classes of TdP risk based on the value of qNet on each drug sample. In one drug combination map, there are 25 combinations of drug concentrations from \(0-4\times \text{c}\text{m}\text{a}\text{x}\). Each combination of drug concentrations contains 100 samples of data of qNets from which one can classify whether it is low, intermediate, or high-risk compounds using threshold values of \(\mathbf{t}\mathbf{h}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{h}\mathbf{o}\mathbf{l}{\mathbf{d}}_{1}\) and \(\mathbf{t}\mathbf{h}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{h}\mathbf{o}\mathbf{l}{\mathbf{d}}_{2}\). The total number of samples (in percentage) that belong to each class of risk is presented as color from black (0%) to white (100%). For example, in panel (A), black color represents no sample belonging to the low-risk drug, and white color show all samples classified as low-risk drugs. The consistency of the results can be assessed from the single drug effects (drug concentration is \(0\times \text{c}\text{m}\text{a}\text{x}\)) in the first axis of each combination map.

From Fig. 5, the combinations of both high-risk drugs mostly yield high-risk compounds, as shown in the upper part of all panels. However, a mixture of sotalol \(\left(1\times \text{c}\text{m}\text{a}\text{x}\right)\) with dofetilide \(\left(1\times \text{c}\text{m}\text{a}\text{x}\right)\) can produce some intermediate-risk compounds. Furthermore, the blends of high and intermediate-risk drugs also primarily generate high-risk and some intermediate-risk combinations. When combining chlorpromazine and ondansetron with dofetilide and sotalol, they can produce intermediate-risk compounds when the high-risk components (dofetilide or sotalol) are at low concentrations. Moreover, combinations of high and low-risk drugs can yield all categories of compounds (low, intermediate, and high) with various combinations of drug concentrations. 100% low-risk regions can be yielded when combining diltiazem \(\left(1-4\times \text{c}\text{m}\text{a}\text{x}\right)\) with dofetilide \(\left(1\times \text{c}\text{m}\text{a}\text{x}\right)\) and sotalol \(\left(1-2\times \text{c}\text{m}\text{a}\text{x}\right)\), mexiletine \(\left(3-4\times \text{c}\text{m}\text{a}\text{x}\right)\) with bepridil \(\left(1\times \text{c}\text{m}\text{a}\text{x}\right)\), mexiletine \(\left(2-4\times \text{c}\text{m}\text{a}\text{x}\right)\) with dofetilide \(\left(1-2\times \text{c}\text{m}\text{a}\text{x}\right)\), and mexiletine \(\left(1-4\times \text{c}\text{m}\text{a}\text{x}\right)\) with sotalol \(\left(1-4\times \text{c}\text{m}\text{a}\text{x}\right)\). However, the 100% intermediate regions are produced partially by all combinations of high and low-risk drugs. Finally, the 100% high-risk regions are yielded by the combination of quinidine \(\left(1-4\times \text{c}\text{m}\text{a}\text{x}\right)\) with all low-risk drugs, bepridil \(\left(1-4\times \text{c}\text{m}\text{a}\text{x}\right)\) with verapamil \(\left(1-4\times \text{c}\text{m}\text{a}\text{x}\right)\), bepridil \(\left(2-4\times \text{c}\text{m}\text{a}\text{x}\right)\) with ranolazine \(\left(1-4\times \text{c}\text{m}\text{a}\text{x}\right)\), bepridil \(\left(3-4\times \text{c}\text{m}\text{a}\text{x}\right)\) with mexiletine \(\left(1\times \text{c}\text{m}\text{a}\text{x}\right)\) and diltiazem \(\left(1-4\times \text{c}\text{m}\text{a}\text{x}\right)\), dofetilide \(\left(1-4\times \text{c}\text{m}\text{a}\text{x}\right)\) with verapamil \(\left(1-4\times \text{c}\text{m}\text{a}\text{x}\right)\), dofetilide \(\left(3-4\times \text{c}\text{m}\text{a}\text{x}\right)\) with ranolazine \(\left(1-4\times \text{c}\text{m}\text{a}\text{x}\right)\), and dofetilide \(\left(4\times \text{c}\text{m}\text{a}\text{x}\right)\)with mexiletine \(\left(1\times \text{c}\text{m}\text{a}\text{x}\right)\).

The combinations of both intermediate-risk drugs mainly generate high and intermediate-risk compounds. Combining chlorpromazine with ondansetron can produce a 100% intermediate-risk region, as shown in panel (B). Furthermore, the combination of cisapride and terfenadine shows 100% high-risk regions, while other combinations mostly yield both high and intermediate-risk regions in various drug concentration pairs. Moreover, the mixtures of intermediate and low-risk drugs can generate all types of compounds’ risks (low, intermediate, and high) under various drug concentrations. The combinations with the most 100% low-risk regions generated are chlorpromazine \(\left(1-4\times \text{c}\text{m}\text{a}\text{x}\right)\) with diltiazem \(\left(1-4\times \text{c}\text{m}\text{a}\text{x}\right)\) and mexiletine \(\left(1-4\times \text{c}\text{m}\text{a}\text{x}\right)\), mexiletine \(\left(2-4\times \text{c}\text{m}\text{a}\text{x}\right)\) with cisapride \(\left(1-4\times \text{c}\text{m}\text{a}\text{x}\right)\) and terfenadine \(\left(1-4\times \text{c}\text{m}\text{a}\text{x}\right)\), ondansetron \(\left(1-4\times \text{c}\text{m}\text{a}\text{x}\right)\) with mexiletine \(\left(1-4\times \text{c}\text{m}\text{a}\text{x}\right)\) and diltiazem \(\left(1-4\times \text{c}\text{m}\text{a}\text{x}\right)\). In addition, 100% intermediate-risk regions are generated following various drug concentration pairs of intermediate-low-risk drug combinations. Finally, 100% high-risk regions produced mainly by the teams of verapamil \(\left(1-4\times \text{c}\text{m}\text{a}\text{x}\right)\) with cisapride \(\left(1-4\times \text{c}\text{m}\text{a}\text{x}\right)\) and terfenadine \(\left(1-4\times \text{c}\text{m}\text{a}\text{x}\right)\), and verapamil \(\left(2-4\times \text{c}\text{m}\text{a}\text{x}\right)\) with ondansetron \(\left(2-4\times \text{c}\text{m}\text{a}\text{x}\right)\). The last combination pairs are both low-risk drugs that generate mostly low-risk with some possibility for intermediate-risk compounds. The 100% low-risk regions are produced by combining diltiazem \(\left(1-4\times \text{c}\text{m}\text{a}\text{x}\right)\) with verapamil \(\left(1-2\times \text{c}\text{m}\text{a}\text{x}\right)\), ranolazine \(\left(1-4\times \text{c}\text{m}\text{a}\text{x}\right)\), and mexiletine \(\left(1-4\times \text{c}\text{m}\text{a}\text{x}\right)\), mexiletine \(\left(1-4\times \text{c}\text{m}\text{a}\text{x}\right)\) with verapamil \(\left(1-4\times \text{c}\text{m}\text{a}\text{x}\right)\) and ranolazine \(\left(1-4\times \text{c}\text{m}\text{a}\text{x}\right)\). The combination of verapamil \(\left(2-3\times \text{c}\text{m}\text{a}\text{x}\right)\) with ranolazine \(\left(1-4\times \text{c}\text{m}\text{a}\text{x}\right)\) mostly generates intermediate-risk compounds.

Finally, the summary results of drug-risk combinations are presented in Fig. 6. It is shown that combinations of high-high and high-intermediate do not produce low-risk compounds. In addition, some intermediate-risk compounds are produced (90 samples) when combining both high-risk drugs that mainly occur at the combination of dofetilide \(\left(1\times \text{c}\text{m}\text{a}\text{x}\right)\) and sotalol \(\left(1\times \text{c}\text{m}\text{a}\text{x}\right)\). Also, the pair of both low-risk drugs may result in high-risk compounds (31 samples) that typically occur at the combination of ranolazine \(\left(1-2\times \text{c}\text{m}\text{a}\text{x}\right)\) with verapamil \(\left(4\times \text{c}\text{m}\text{a}\text{x}\right)\). Moreover, when combining both intermediate-risk drugs, one may produce low-risk compounds (27 samples), especially from a combination of chlorpromazine \(\left(1\times \text{c}\text{m}\text{a}\text{x}\right)\) with ondansetron \(\left(1\times \text{c}\text{m}\text{a}\text{x}\right)\). Finally, various risk (low, intermediate, and high) compounds can be found when combining high-low and intermediate-low risk drugs.