The FAERS raw quarterly data contained 6,680,109 ICSRs, and after the cleaning procedure removing duplicates of the ICSRs, the final dataset consisted of 1,349,142 reports (20.2%). The FAERS raw quarterly data contained 17,441,164 drugs information, and after the cleaning procedure removing cases without active substance names and defined treatment duration, the final dataset consisted of 2,943,894 complete records (16.9%).

3.1 Signal Detection of DDIs Considering Time of Co-exposure

After the choice of the comparator, 122 (5.1%) out of 2372 triplets were eligible for the analysis and resulted in 61 disproportionality signals (50%) (ROR lower limit of the 95% CI greater than 1) involving 13 AEs (see ESM2, Supplementary Fig. S2); of these, eight AEs (61.5%) were included in the EMA’s IME list.

A general overview of the detected disproportionality signals is described in Table 1. Most of the interactions detected were synergic effects of the two drugs and 100% had pharmacological plausibility. Within the AEs detected with our methodology the most reported were the Medical Dictionary for Regulatory Activities (MedDRA®) Preferred Terms (PTs) “haemorrhage” and “hypotension”. Haemorrhage was reported mainly in ICSRs with a combination of platelet inhibitors, anticoagulant or fibrinolytic agents, non-steroidal anti-inflammatory drugs (NSAIDs), and antidepressants. DDIs related to hypotension were mostly described in ICSRs where there was an association with two antihypertensive drugs, or one antihypertensive drug associated with tricyclic antidepressants.

Table 1 Disproportionality signals considering time of co-exposure

Less frequently reported AEs were related to PTs “acute kidney injury”, “hyperkalaemia”, and “syncope” with angiotensin-converting enzyme (ACE) inhibitors and angiotensin II receptor blockers (ARBs). The PT “QT prolonged” was mainly reported with the concomitant use of antipsychotics and antidepressants.

3.2 Severity of Signal Detection of DDIs Considering Time of Co-exposure

Out of 2372 triplets provided by Kontsioti et al. [10], our method was able to detect 31 theoretical signals (1.3%), 17 probable signals (0.7%), and 13 established signals (0.5%) (see Fig. 4). Considering the severity of the AEs, out of 2372 triplets screened, our method was able to detect 43 major AEs (1.8%) and 18 minor AEs (0.8%) (see Fig. 4).

Fig. 4

Venn diagrams of type of triplets reported as frequencies (percentages) and retrieved considering those that were identified as a disproportionality signal for the temporal plausibility assessment using our method. Definitions of evidence and severity levels are those reported by Kontsioti et al. [10] in their work: evidence—evidence level associated with the drug–drug interaction as shown in Micromedex; severity—severity level associated with the drug–drug interaction as shown in Micromedex

3.3 Temporal Assessment Using the Time of Co-exposure

Twenty-seven (44.3%) out of 61 signals had at least ten cases reporting the triplet of interest and were assessed for temporal plausibility. After the assessment, 19 signals (70.4%) were temporally plausible after only 1 day of co-exposure (see ESM2, Supplementary Fig. S2). Below we have described in detail the approach to assess temporal plausibility for three PTs: “haemorrhage”, “hypotension”, and “hyperkalaemia”. This provides a clear example of how the flex point of the time of co-exposure can be used to identify true-positive and false-positive signals for DDIs in view of pharmacological plausibility. The complete analysis of all other MedDRA® PTs is reported in ESM2 (Supplementary Table S1 and S2).

3.3.1 Haemorrhage

Haemorrhage was mainly reported with the concomitant use of more than one platelet inhibitor or anticoagulant/antithrombotic agent. According to the two steps described in Sect. 2.5, the flex point from the cumulative reporting was found to be 1 day of co-exposure time for each triplet, including for the DDIs enoxaparin/clopidogrel and warfarin/clopidogrel (see Fig. 5).

Fig. 5

Cumulative reporting. Each graph represents the cumulative reporting of one triplet where drug A is analysed when reported (or not) in co-exposure with drug B. The x-axis represents the co-exposure time of drug A and drug B expressed in days, while the y-axis represents the cumulative incidence of reporting a certain co-exposure time for a specific adverse event in each individual case safety report

Step A: From the scientific literature, we assessed if haemorrhage was a temporal plausible event with at least 1 day of co-exposure of anticoagulant/antithrombotic agents. The short-term co-administration (even 1 day) is a common strategy in cardiology to ensure adequate anticoagulation in the transition period from one drug class to another, and it can be associated with the occurrence of bleeding [18]. Clinical guidelines and the Summary of Product Characteristics (SmPC) of drugs recommends clinical monitoring of bleedings even after 1 day of treatment [19, 20].

Step B: Among disproportionality signals involving platelet inhibitor or anticoagulant/antithrombotic agents, we used the signal of enoxaparin/clopidogrel as an example to emphasize how the machine learning method (i.e. Lasso regression) was able to identify potential confounders in our analysis. Lasso regression retrieved age and lorazepam to be related to the co-exposure time in the case of enoxaparin/clopidogrel and the occurrence of haemorrhage (see Table 2). Age is a known risk factor since major bleeding was found to increase steeply with age (≥ 75 years hazard ratio 3.10, 95% CI 2.27–4.24; p < 0.0001), in particular for fatal outcomes [21]. On the contrary, while other drug classes like antidepressants are known to increase the risk of bleeding [22], benzodiazepines seem not to interfere in this specific event. When age was examined in the univariate analysis between cases and non-cases, we found that individuals with the co-exposure were older (73.8 years vs. 71.9 years) than those without co-exposure in the ICSRs of those experiencing the AE of interest. This suggests that this signal could be potentially correlated to age. At the same time, the concomitant use of lorazepam was significantly less reported the ICSRs of those experiencing the AE of interest compared with those experiencing every other AEs (see Table 2).

Table 2 Potential confounders in cases of haemorrhage (a) and hypotension (b)3.3.2 Hypotension

Step A: DDIs related to hypotension were due to the association of two antihypertensive drugs or one antihypertensive drug associated with tricyclic antidepressants or α1 antagonists. The synergic effect of two drugs with cardiovascular effects might cause alterations in blood pressure even after 1 day of co-administration, which is why the flex time of 1 week (e.g. sildenafil ± furosemide) was temporally plausible (see Fig. 5 and ESM2, Supplementary Table S1).

Step B: Lasso regression was able to identify possible confounders concerning the DDIs of bisoprolol ± alfuzosin and bisoprolol ± doxazosin (see Table 2). From this analysis, it appeared that the disproportionality signal was confounded by age and co-reported drugs [23, 24].

3.3.3 Hyperkalaemia

Step A: Hyperkalaemia was also reported with the concomitant use of trimethoprim and ACE inhibitors. According to the scientific literature, a few days of co-exposure are not sufficient to induce hyperkalaemia [25]. Therefore, the flex point at 1 day was considered not temporally plausible (see Fig. 5).

As we did not find temporal plausibility in step A, no further analyses were performed for the signal and the signal was considered dismissed.