**1. Introduction**

Drug-induced adverse events (AEs) caused by individual drugs and drug combinations not only hinder treatment but also cause new health hazards. To alleviate this problem, AEs caused by individual drug candidates are closely monitored and investigated during the drug development and approval process [1]. Pre-marketing randomized clinical trials are performed under certain conditions associated with age, gender, and co-morbidities, and some AEs may not be detected. In particular, in pre-marketing randomized clinical trials, patients on combination therapy are usually excluded because the focus is to establish the safety and efficacy of single drugs and not to investigate drug–drug interactions [2]. However, in the real world, many patients suffer from a variety of co-morbidities and use a number of drugs to treat them. The concomitant use of two or more drugs increases the risk of AEs due to drug–drug interactions; the proportion of such AEs is estimated to be up to 30% of unexpected AEs [3].

Therefore, in order to use drugs appropriately in the real world, it is important to understand, in advance, the AEs caused by drug–drug interactions. Post-marketing analysis of AE reports could significantly contribute to the discovery of AEs caused by single drugs or drug–drug interactions that could not be detected before marketing.

For the safety surveillance of drugs, AE reports collected post-marketing are maintained by regulatory agencies as a spontaneous reporting system. There are several algorithms for detecting adverse event signals using the spontaneous reporting system [4]. Of these, the algorithms commonly used for quantitative signal detection include the proportional reporting ratio (PRR) [5], the reporting odds ratio (ROR) [6], the Bayesian confidence propagation neural network (BCPNN) [7], and the empirical Bayesian geometric mean (EBGM) [8].

Additionally, multiple statistical algorithms have been proposed for detecting drug–drug interaction signals [9,10]. However, calculation of the PRR, similar to the risk ratio, and the ROR, similar to the odds ratio, is simple, but that of other algorithms (particularly the algorithm for detecting drug–drug interaction signals) is very complicated.

Therefore, in order to detect the drug–drug interaction signals between *drug D*1 and *drug D*2, the subset analysis that detects the signal of *drug D*1 using the ROR, which is easy to calculate in a subset of patient groups, is often reported [11–13].

Of previous studies, several [11,12] have used animal experiments and/or pharmacological data to ensure signal reliability, but the signals obtained with this analysis model are not strictly drug–drug interaction signals; they only showed the e ffect of drug combinations for the following two reasons [14]:


On the other hand, because the ROR, often used in subset analysis, is easy to calculate, if these shortcomings are improved and the appropriate detection criterion can be set, it might lead to early detection of AEs caused by drug–drug interactions.

In this study, we proposed a new detection criterion for the subset analysis (the newly proposed subset analysis) and verified the detection power using the spontaneous reporting system.

#### **2. Materials and Methods**

The design of this study is based on a previous paper that discussed trends in methods to detect the signals of AEs caused by individual drugs [15] or drug–drug interactions [14].

### *2.1. Data Sources*

The validation dataset was created from the Japanese Adverse Drug Event Report database (JADER), using data from the first quarter of 2004 to the fourth quarter of 2015. The JADER consists of four comma-separated values (csv) files as data tables: DEMO.csv (patient information), DRUG.csv (medicine information), HIST.csv (patient past history), and REAC.csv (AE event information). This study used 374,327 cases registered in the verification dataset.

However, the Japanese authority, the Pharmaceuticals and Medical Devices Agency (PMDA), which owns these data, does not permit sharing the data directly. Therefore, we do not own the JADER. It can be accessed directly here: [http://www.info.pmda.go.jp/fukusayoudb/CsvDownload.jsp] (in Japanese only).

#### *2.2. Definitions of Adverse Drug Events*

The drugs targeted for the survey are all registered and classified as "suspect drugs" in the validation dataset. The AEs in JADER are based on the preferred terms (PTs) in the Medical Dictionary for Regulatory Activities Japanese version (MedDRA/J). The AE targeted for this study was Stevens–Johnson syndrome (SJS), which was extracted from the dataset using the PT in MedDRA/J. However, the choice of target adverse events is the same as in previous similar studies [14,15], and there was no medical or pharmacological reason for this choice.

#### *2.3. "Hypothetical" True Data of Adverse Events for Comparative Verification*

The signals obtained from the spontaneous reporting system including the JADER used in this study included unknown AEs that were also detected, which needs to be verified in order to confirm they were true AEs. Moreover, the information provided by the regulatory authorities, of course, does not include unknown AEs. That is, there are no "real" true data for every AE. Therefore, we set "hypothetical" true data because we cannot use "real" true data for validation in this study.

To verify the power of the subset analysis, we prepared "hypothetical" true data of AEs. To generate "hypothetical" true data, we excluded the Ω shrinkage measure model [16] that detected the most conservative signal and the combination risk ratio model [17], which would not detect a signal with a small number of reports, from the five detection algorithms. That is, this study used the combination of signals detected by three algorithms (the additive model [18], the multiplicative model [18], and the chi-square statistical model [19]) as "hypothetical" true data.

#### *2.4. Statistical Models and Criteria*
