A Dose‐Aware Model for Revealing Dose‐Risk Relationship of Drug–Drug Interaction

ABSTRACT

Drug–drug interaction (DDI) is a common cause of adverse drug events (ADEs). Despite real‐world data‐based studies have developed knowledge on DDI, the precise relationships between doses of two‐drug combinations exposure and the risks of ADEs remain largely unknown. The estimation of the dose‐risk relationship (DRR) under commonly used regression models could be subject to model misspecification or overspecification. We developed a dose‐aware model (DAM) for revealing DRR. DAM could improve the DRR estimation by identifying the optimal model from a large number of meaningful models of doses of two‐drug combinations exposure and risks of ADE. We compared DAM with commonly used models (e.g., exposed‐versus‐unexposed model, dose‐response model, and saturated model), in which DAM had higher performance metrics on model fitting in real‐world data analyses and DRR estimation in a simulation study. In conclusion, DAM is a powerful tool for estimating DRR for potential adverse two‐drug combinations, which could be used to mitigate DDI‐induced harm.

Study Highlights.

• What is the current knowledge on the topic?

  • ○
    Drug–drug interaction‐induced (DDI‐induced) adverse drug event (ADE) is a significant health concern. Despite commonly used regression models are powerful for detecting DDI, the estimated dose‐risk relationships (DRRs) could be subject to model mis‐specification or overspecification.
• What question did this study address?

  • ○
    To identify the optimal DRR from an astronomical number of potential DRRs is a significant challenge.
• What does this study add to our knowledge?

  • ○
    We developed a dose‐aware model (DAM) to identify the optimal DRR from a large amount of meaningful DRRs. DAM, compared with commonly used regression models, had higher performance metrics on model fitting in real‐world data analyses and DRR estimation in simulation study.
• How might this change drug discovery, development, and/or therapeutics?

  • ○
    DAM is a powerful tool for deriving DDR, which could be used to mitigate DDI‐induced harm.

Abbreviations

ADE

adverse drug event

AIC

Akaike information criterion

AKI

acute kidney injury

BIC

Bayesian information criterion

CLRM

conditional logistic regression model

DAM

dose‐aware model

DDI

drug–drug interaction

DRR

dose‐risk relationship

EARB

empirical absolute relative bias

ED

emergency department

ERB

empirical relative bias

FDR

false discovery rate

GI

gastrointestinal

MG

milligram

RWD

real‐world data

1. Introduction

Drug–drug interaction‐induced (DDI‐induced) adverse drug event (ADE) is a common cause of drug‐induced harm [1], and often involves dose‐dependent risk [2, 3]. Specifically, an analysis of labeled adverse DDIs identifies that 36% of the drug labels recommend dose adjustment to mitigate the risk of ADE [3], which suggests dose as an important risk factor of adverse DDI. Dose could relate to ADE risk in both pharmacokinetic (i.e., metabolic) DDI and pharmacodynamic DDI. In pharmacokinetic DDI, ADE could be caused by an elevated body concentration of the victim drug due to the perpetrator's inhibitory effect on the clearance of the victim drug. Doses of the victim drug and perpetrator with a moderate/low inhibitory effect could both relate to the ADE risk, while the dose of a perpetrator with a strong inhibitory effect might be less likely to relate to the ADE risk. For instance, the combination of warfarin (i.e., the victim) and amiodarone (i.e., the perpetrator) could increase the risk of bleeding, while the risk could be mitigated by warfarin dose reduction [2]. In pharmacodynamic DDI, ADE could be caused by a synergistic effect of both drugs on a specific organ or system. For instance, diuretics and angiotensin‐converting‐enzyme (ACE) inhibitors could be nephrotoxic [4]; and the combination of a diuretic and an ACE inhibitor could further increase the risk of acute kidney injury (AKI), while the risk could be mitigated by dose adjustments of both drugs [5]. As use of drug combination is a common clinical practice in real‐world settings [6], real‐world data (RWD) become a major data source for developing knowledge of adverse DDI.

RWD‐based study for DDI is a top‐down approach, which could identify potential DDI that could not be predicted by standard in vitro assays (i.e., pharmacodynamic DDI). RWD‐based study for DDI can be hypothesis‐driven [7, 8]. For instance, an altered drug response of a diabetic drug due to concomitant exposure to another drug may increase the risk of hypoglycemia. Such a hypothesis can be examined by comparing hypoglycemia risks of diabetic drug exposure between with and without concurrent exposure to other drugs [9, 10]. Additionally, high‐throughput hypothesis‐free data mining can investigate all two‐drug combinations under a case–control setting, in which commonly used statistical methods (e.g., logistic regression model and conditional logistic regression model [CLRM]) can be applied to examine all two‐drug combinations [11]. Newer high‐throughput DDI detection algorithms have been developed to penalize and/or control false positives in high‐throughput mining [12, 13, 14, 15, 16]. The application of these methods has successfully derived knowledge on potential DDI‐induced ADE. However, these studies are based on an exposed‐versus‐unexposed setting without leveraging doses of drug exposure [17, 18, 19]. As the risk of DDI‐induced ADE could depend on the doses of both drugs [2, 3], data mining for DDI shall be expanded to a dose‐aware setting.

Regression models can naturally utilize doses of two drugs and their interaction as covariates. In RWD, an ordinal variable (i.e., dose level) can be used for doses of a drug. For instance, $X$ = 0, 1, 2, 3, 4 can be used for unexposed, and 10, 20, 40 and 80 mg/day for atorvastatin (i.e., a common lipid lowering drug). Let $X_1$ and $X_2$ denote dose levels of two drugs (e.g., $X_1$ and $X_2$ = 0, 1, 2, 3, 4), and $\alpha$ denote the random effect for a matched pair in a matched case–control study. Under CLRMs, a drug–drug interaction effect (e.g., ${\beta }_3$ in Equations (1) and (2)) can be tested under a dose–response model Equation (1) or an exposed‐versus‐unexposed model Equation (2). While both models Equations (1) and (2) facilitate unbiased test of the DDI effect under the null hypothesis, the dose‐risk relationships (DRRs) might be mis‐specified for true DDIs (i.e., under the alternative hypothesis). Saturated CLRM Equation (3) could be used to mitigate risk of model mis‐specification but is subject to potential model overspecification.

$$\text{logitProb}\left(\mathrm{ADE}=1\right)=\alpha +{\beta }_1{X}_1+{\beta }_2{X}_2+{\beta }_3{X}_1{X}_2$$ (1)

$$\begin{array}{c}\text{logitProb}\left(\mathrm{ADE}=1\right)=\alpha +{\beta }_{1}1\left(X_1>0\right)+{\beta }_{2}1\left(X_2>0\right)\hfill \\ +{\beta }_{3}1\left(X_1{X}_2>0\right)\hfill \end{array}$$ (2)

$$\begin{array}{c}\text{logitProb}\left(\mathrm{ADE}=1\right)=\alpha +\sum _i{\beta }_{i}1\left(X_1=i\right)+\sum _j{\theta }_{j}1\left(X_2=j\right)\hfill \\ +\sum _{\mathit{ij}}{\delta }_{\mathit{ij}}1\left(X_1=i \& X_2=j\right),\text{for}i\text{and}j=1,2,3,4\hfill \end{array}$$ (3)

To identify the optimal DRR for DDI is a significant challenge, as the number of potential DRRs is astronomical. For instance, two 5‐level covariates for two drugs (e.g., $X_1$ and $X_2$ = 0, 1, 2, 3, 4) generate 25 dose levels for a two‐drug combination (e.g., (0, 1, 2, 3, 4) $\otimes$ (0, 1, 2, 3, 4) = (0, 0), …, (4, 4)), which yield > 33 million (e.g., 2²⁵) potential DRRs by assuming the 25 dose levels to be risky or not, let alone for more complex assumptions. Despite state‐of‐the‐art deep learning models could comprise over millions of parameters [20], their high requirements on computational resource are considered as a significant challenge [21], and they could generate less clinical meaningful DRRs without restricting the model space (Figure 1). In this work, we propose a dose‐aware model (DAM) for improving the estimation of DRR. As certain DRRs could be more realistic (i.e., meaningful) compared with others (Figure 1), the rational of DAM is to search for a large amount of meaningful DRRs instead of testing all DRRs.

FIGURE 1.

Examples of meaningful and less‐meaningful dose‐risk relationships.

2. Methods

2.1. Dose‐Aware Model (DAM)

DAM was based on meaningful partitions of dose levels (i.e., potential dose‐risk relationships [DRRs]) of a two‐drug combination (Figure 1). Assuming 5 dose levels (e.g., 0, 1, 2, 3, 4) for each drug, a two‐drug combination could have 25 dose levels (e.g., (0, 1, 2, 3, 4) $\otimes$ (0, 1, 2, 3, 4) = (0, 0), …, (4, 4)). Let $\left(i,j\right)$ s denote the dose levels for a two‐drug combination (e.g., $\left(i,j\right)$ = $\left(0,0\right)$, …, $\left(4,4\right)$), and $\mathcal{G}$ denote a group including a collection of $\left(i,j\right)$ s (e.g., ${\mathcal{G}}_1$ = { $\left(0,0\right)$, $\left(0,1\right)$, $\left(0,2\right)$, $\left(1,0\right)$, $\left(1,1\right)$, $\left(1,2\right)$, $\left(2,0\right)$, $\left(2,1\right)$, $\left(3,2\right)$ } in Figure 2). We defined the following three types of groups:

• $\mathcal{G}$ was a continuous group, if for any $\left(i,j\right)$ and $\left(i^{*},j^{*}\right)$ $\in$ $\mathcal{G}$, $\left(i,j\right)$ and $\left(i^{*},j^{*}\right)$ could be connected by the dose levels within $\mathcal{G}$ (Figure 1). In other words, all dose levels within a continuous group were not separated (Figure 1).

• $\mathcal{G}$ was a monotonic group, if for any $\left(i,j\right)$ $\in$ $\mathcal{G}$, $\min \left[\left(i-i^{*}\right),\left(j-j^{*}\right)\right]$ ≥ 0 implied $\left(i^{*},j^{*}\right)$ $\in$ $\mathcal{G}$. In other words, if a dose level was included in a monotonic group, then all “lower” dose levels were also included in the same group (Figure 1).

• $\mathcal{G}$ was a null group, if $\mathcal{G}$ was continuous and monotonic, and (0, 0) $\in$ $\mathcal{G}$ (Figure 2).

FIGURE 2.

(A) An illustration of a set difference‐based algorithm to identify meaningful partitions of doses. (B) An illustration of the dose‐aware model (DAM) for estimating the optimal dose‐risk relationship.

We briefly illustrated our algorithm to identify meaningful partitions in this paragraph. Please see github.com/PengyueLab/DAM for model codes. First, we determined null groups and set the number of groups in a partition (i.e., K), the maximum number of dose levels in the group containing (0, 0) (i.e., N ₀), and the minimum number of dose levels in other groups not containing (0, 0) (i.e., N ₁). Second, we enumerated permutations including K‐1 null groups with the number of dose levels < 25 and used set differences of the null groups to define groups in partitions (e.g., Figure 2). Please note that the number of permutations could be limited by N ₀ and N ₁ in this step to improve computational efficiency. Third, we excluded partitions with non‐continuous groups and/or partitions with noncompliant group size (i.e., fail to satisfy constraints on N ₀ and N ₁). To determine continuity for a group, we tested whether all dose levels could be included by continuously expanding dose level(s) with adjacent dose level(s) from a starting dose level.

We searched for three‐, four‐, and five‐group partitions (i.e., K = 3, 4, 5). We included meaningful partitions with the number of dose levels in the group containing (0, 0) ≤ 10 (i.e., N ₀ = 10), and the minimum number of dose levels in other groups ≥ 4 (i.e., N ₁ = 4). We identified 5775 three‐group partitions, 39,235 four‐group partitions, and 55,125 five‐group partitions.

Let ${\mathbb{G}}_m$ = (${\mathcal{G}}_{m1}$, …, ${\mathcal{G}}_{\mathit{mk}}$) denote a $m$‐th meaningful partition of dose levels (i.e., a potential DRR). DAM could investigate all potential DRRs (i.e., all ${\mathbb{G}}_m$ $\in$ $\mathit{G}$) under CLRM Equation (4) and identify the optimal DRR according to Akaike information criterion (AIC) or Bayesian information criterion (BIC; Figure 2B). In application, BIC was recommended for datasets with a larger sample size [22].

$$\begin{array}{c}\text{logitProb}\left(\mathrm{ADE}=1\right)=\alpha +{\sum }_k{\beta }_{\mathit{mk}}\times 1\left[\left(i,j\right)\in {\mathcal{G}}_{\mathit{mk}}\right]\hfill \\ \left(k>1\text{for using}{\mathcal{G}}_{m1}\mathrm{as}\text{baseline}\right),\hfill \\ \text{and}{\mathrm{DRR}}_{\mathrm{DAM}}=\arg \underset{{\mathbb{G}}_m\in \mathit{G}}{\min }\mathrm{AIC}\left({\mathbb{G}}_m\right)\hfill \\ \text{or}\mathrm{BIC}\left({\mathbb{G}}_m\right)\hfill \end{array}$$ (4)

2.2. Simulation Study and Real‐World Data (RWD) Analyses

First, we conducted a simulation study. We simulated 10,000 datasets under different DRRs (Figure 3). Please see Data S1 for details on data simulation. We used DAM Equation (4), and dose–response, exposed‐versus‐unexposed, and saturated CLRMs Equations ((1), (2), (3)) to estimate the DRRs and BIC values. In each simulation, we evaluated the relative bias of the estimated odds ratios (OR) for all dose levels Equation (5) and BIC values. We computed the empirical relative bias (ERB) values Equation (6) and the empirical absolute relative bias (EARB) values Equation (7) based on all simulations. Please note that an overfitted model might have low ERB values but high EARB values. Additionally, we evaluated the empirical type‐1 error rate and power (Please see Data S1 for details).

$$\text{relative bias}\left(i,j\right)=\frac{\text{Estimated OR}\left(\mathrm{i},\mathrm{j}\right)-\text{True OR}\left(\mathrm{i},\mathrm{j}\right)}{\text{True OR}\left(\mathrm{i},\mathrm{j}\right)}$$ (5)

$$\mathrm{ERB}\left(i,j\right)=\text{average of relative bias}\left(i,j\right)\text{in}\mathrm{all}\text{simulations}$$ (6)

$$\text{EARB}\left(i,j\right)=\text{average of}\left|\text{relative bias}\left(i,j\right)\right|\text{in}\mathrm{all}\text{simulations}$$ (7)

FIGURE 3.

Simulation settings and results.

Second, we derived datasets for twenty drug–drug‐ADE combinations from a large‐scale US nationwide insurance claim data. Please see Data S2 for details on data preparation. In short words, the datasets included covariate‐matched ADE‐case‐and‐control pairs for acute kidney injury (AKI, N = 315,728 pairs) and gastrointestinal (GI) bleeding (N = 265,426 pairs), and all drug–drug combinations had false discovery rate < 0.05 for testing the drug–drug interaction (DDI) effect under dose–response and/or exposed‐versus‐unexposed CLRMs Equations (1) and (2). Each analytical dataset included case status (0/1) and dose levels (e.g., $X_1$ and $X_2$ = 0, 1, 2, 3, 4) of drug exposure. We used DAM Equation (4), and dose–response, exposed‐versus‐unexposed, and saturated CLRMs Equations ((1), (2), (3)) to estimate the DRRs (i.e., model parameters) and BIC values. All analyses were conducted in R.

3. Results

3.1. Simulation Study

Figure 3A–D show simulation results under four true dose‐risk relationships (DRRs). In Figure 3A–D, the “true odds ratio” section on the top left presents the true DRR; the “% of best BIC” section on the bottom left presents the percentage of models that reached the best BIC; the “ERB” section on the middle presents the empirical relative bias (ERB) values under all 4 models; and the “boxplot of EARB for all dose levels” section on the right presents the boxplots of the empirical absolute relative bias (EARB) values for all 25 dose levels under different models.

In Figure 3A, the true DRR was the dose–response CLRM. Dose–response CLRM and DAM achieved the best BIC in 70% and 30% of all simulations, respectively. For ERB, DAM underestimated ORs for higher dose levels; exposed‐vs.‐unexposed CLRM overestimated ORs for lower dose levels and underestimated ORs for higher dose levels; dose–response and saturated CLRMs had low ERB values. For EARB, DAM had median = 17%; exposed‐vs.‐unexposed CLRM had median = 23%; dose–response CLRM had median = 7%; and saturated CLRM had median = 16%.

In Figure 3B, the true DRR was the exposed‐vs.‐unexposed CLRM. Exposed‐vs.‐unexposed CLRM and DAM achieved the best BIC in 32% and 68% of all simulations, respectively. For ERB, all of DAM, exposed‐vs.‐unexposed CLRM, and saturated CLRM had low ERB values, while dose–response CLRM underestimated ORs, especially for lower dose levels. For EARB, DAM had median = 12%; exposed‐vs.‐unexposed CLRM had median = 9%; dose–response CLRM had median = 28%; and saturated CLRM had median = 17%.

In Figure 3C, the true DRR was covered by a meaningful 4‐group partition in DAM, in which higher risk and adverse drug–drug interactions (DDI) occurred at higher dose levels. DAM achieved the best BIC in all simulations. For ERB, DAM and saturated CLRM had low ERB values, while exposed‐vs.‐unexposed and dose–response CLRMs had high ERB values. For EARB, DAM had median = 7%; exposed‐vs.‐unexposed CLRM had median = 23%; dose–response CLRM had median = 20%; and saturated CLRM had median = 16%.

In Figure 3D, the true DRR was not covered by any model, which represented a potentially complex adverse DDI. DAM achieved the best BIC in all simulations. For ERB, DAM and saturated CLRM had low ERB values, while exposed‐vs.‐unexposed and dose–response CLRMs had high ERB values. For EARB, DAM had median = 12%; exposed‐vs.‐unexposed CLRM had median = 48%; dose–response CLRM had median = 26%; and saturated CLRM had median = 16%.

For testing the effect of DDI, we observed all methods had empirical type‐1 error rates between 0.049 and 0.052 without DDI (i.e., under the null hypothesis), which were close to the desired level of 0.05. Figure 4 shows the empirical powers under the alternative hypothesis (i.e., with DDI). Dose–response CLRM had the best empirical power when it was correctly specified (i.e., Figures 3A and 4A), followed by saturated CLRM, DAM, and exposed‐vs.‐unexposed CLRM. Exposed‐vs.‐unexposed CLRM and DAM had similar empirical powers when exposed‐vs.‐unexposed CLRM was the true model (i.e., Figures 3B and 4B), and they had better performance than the other models. DAM had the best empirical power when it was correctly specified (i.e., Figures 3C and 4C). All models had powers ≥ 0.99 for the last pattern (i.e., Figures 3D and 4D).

FIGURE 4.

Empirical statistical powers in simulation study.

3.2. Real‐World Data (RWD) Analysis

We analyzed 20 datasets. DAM had the best BIC values in 17 datasets. Dose–response CLRM had the best BIC values in 3 datasets, in all of which DAM had the second‐best BIC values. We presented two datasets with the best BIC values achieved by DAM (Figure 5A,B), and one dataset with the best BIC value achieved by dose–response CLRM in this section (Figure 5C), while all analysis results were presented in Table S1.

FIGURE 5.

Real‐world data analyses results (A, B for dose: A < dose ≤ B). (A) Lisinopril, gabapentin, and acute kidney injury (AKI); (B) meloxicam, clopidogrel, and gastrointestinal bleeding; (C) lisinopril, spironolactone, and AKI.

Figure 5A,B presented two examples that DAM had best BIC values. Figure 5A presented the estimated DRRs of lisinopril, gabapentin, and acute kidney injury (AKI). For the 24 dose levels with at least one drug exposure (i.e., excluding unexposed for both drugs), DAM had 4 estimated risk groups (ORs: 1.3–2.5); exposed‐vs.‐non‐exposed CLRM had 3 estimated risk groups (ORs: 1.2–2.0); dose–response CLRM had ORs between 1.1 and 3.8; and saturated CLRM had ORs between 1.1 and 2.9. For both drug exposure, DAM (four different ORs between 1.3 and 2.5) compared with exposed‐vs.‐non‐exposed CLRM (one OR = 2.0) had a more complex DRR.

Figure 5B presented the estimated DRRs of meloxicam, clopidogrel, and gastrointestinal (GI) bleeding. For the 24 dose levels with at least one drug exposure, both DAM and exposed‐vs.‐non‐exposed CLRM had 3 estimated risk groups with similar ORs (DAM ORs: 1.2–2.1, and exposed‐vs.‐non‐exposed ORs: 1.2–2.2); dose–response CLRM had ORs between 1.1 and 9.1; and saturated CLRM had ORs between 1.1 and 6.0. DAM compared to exposed‐vs.‐non‐exposed model assigned a higher OR for high dose meloxicam single drug exposure (OR = 2.1 vs. 1.2).

Figure 5C presented the estimated DRRs of spironolactone, lisinopril, and AKI, in which the dose–response model and DAM had the best and second‐best BIC values. For the 24 dose levels with at least one drug exposure, DAM had 4 estimated risk groups (ORs: 1.4–3.8); exposed‐vs.‐non‐exposed CLRM had 3 estimated risk groups (ORs: 1.4–3.2); dose–response CLRM had ORs between 1.2 and 9.9; and saturated CLRM had ORs between 1.3 and 7.6. For both drug exposures, DAM (four different ORs between 1.4 and 3.8) compared with the exposed‐vs.‐non‐exposed model (one OR = 3.2) had a more complex DRR.

In all three examples (Figure 5A–C), the dose–response model had much higher ORs under high dose levels for both drugs (dose–response model ORs: 3.8–9.9, and other models ORs ≤ 3.8); and the saturated model had non‐monotonic DRRs (i.e., non‐monotonic relationships between dose levels and ORs).

4. Discussion

We propose a dose‐aware model (DAM) for estimating the dose‐risk relationship (DRR) for two‐drug combination and adverse drug event (ADE), as dose of exposure is a significant risk factor for adverse DDI [2, 3]. Identifying the optimal DRR from an astronomical number of potential DRRs is a significant challenge. For instance, there are ≈33 million (e.g., 2²⁵) potential 2‐group partitions (i.e., high risk and low risk) for splitting 25 dose levels of a two‐drug combination (i.e., 2²⁵ potential DRRs), let alone 3‐, 4‐, and 5‐group partitions. DAM addresses this challenge by using null groups and set differences to find potential clinically meaningful DRRs, which could maintain the common monotonicity relationship between dose and toxicology. In simulation studies, DAM compared to frequently used models (e.g., exposed‐versus‐unexposed, dose–response and saturated models) has a lower bias on DRR estimation when dose–response and exposed‐vs.‐unexposed models are mis‐specified (Figure 3). In 17 out of 20 real‐world data (RWD) analyses, DAM had the best model fitting, which reassures the importance of incorporating dose and DAM in DDI data mining.

DAM compared with the exposed‐vs.‐unexposed model could identify more complex DRRs. As shown in Figure 3C,D DAM has a better performance in revealing the true DDRs when the dose–response and exposed‐vs.‐unexposed models are mis‐specified. As shown in Figure 5A (lisinopril, gabapentin and acute kidney injury [AKI]) and 5C (lisinopril, spironolactone and AKI), DAM compared with the exposed‐vs.‐unexposed model generates more complex DRRs, while all of the involved drugs (lisinopril, gabapentin, spironolactone) could cause AKI [23]. For meloxicam single drug exposure > 19.5 mg/day and gastrointestinal (GI) bleeding (Figure 5B), DAM compared with the exposed‐vs.‐unexposed model has a higher estimated OR, which is supported by observations from clinical trials [24]. Additionally, DAM‐estimated DRRs compared with the dose–response and saturated models could be more meaningful. The dose–response model could yield a high bias if mis‐specified (Figure 3B–D). As shown in Figure 5B (meloxicam, clopidogrel, and GI bleeding), the estimated OR under the dose–response model for the dose level [4] is much higher than that of other models (i.e., OR = 9.1 vs. 2.1–2.8), while both meloxicam and clopidogrel are linked to GI bleeding [23]. Thus, DAM‐derived DDRs could be more clinically meaningful and be used for mitigating the risk of ADE in a dose‐aware manner.

Despite our exemplified analyses being based on CLRM and the case–control setting, DAM can be applied to other models (e.g., logistic regression model, Cox model, etc.) and other settings (e.g., exposed‐vs.‐unexposed design). DAM is a top‐down approach to infer potential DDI from RWD. DAM could infer DDI without conducting wet lab experiments (i.e., standard in vitro assays) and could infer pharmacodynamics DDI that might not be predicted by standard in vitro assays. Additionally, compared to bottom‐up approaches, the application of DAM does not require in‐depth knowledge of mechanisms and model parameters [25]. However, DAM cannot reveal the mechanism of the potential DDI and is subject to the common limitations of mining RWD. For instance, as the study data source is based on US individuals with commercial health insurance or Medicare Advantage plans, the results might not be generalized to other populations. Additionally, we largely assume records on diagnosis and pharmacy claims could represent true clinical outcomes and drug exposure. However, outcome and exposure could be misclassified. Moreover, our results are subject to residual and unmeasured confounding effects besides covariate matching.

The application of DAM also has additional challenges and limitations. First, determination of dose levels shall be accompanied by clinical adjudication. We use summary statistics of daily dose (DD) to define five dose levels in a data‐driven manner (Table S3 and Data S2). For instance, the thresholds to define dose levels could be the first quantile (or 0.7 × median, if the first quantile = median), median, and the third quantile (or 1.3 × median, if the third quantile = median) of DDs in RWD. However, the data‐driven definitions might not be clinically meaningful, as doses of a drug might concentrate on only a few levels in real‐world settings. For instance, the user frequencies are ≥ 10% for all dose levels of gabapentin (e.g., 0–300, 300–900, 900–1200 and > 1200 mg/day); while the user frequencies are ≤ 1% for certain dose levels of meloxicam and clopidogrel. In fact, 99% of meloxicam uses have dose = 7.5, 10, or 15 mg/day; and 99% of clopidogrel users have dose = 75 mg/day. The meloxicam and clopidogrel users with other doses could be due to uncommon clinical adjustments, as these uncommon doses (e.g., meloxicam 22.5 mg/day and clopidogrel 150 mg/day) have been reported in clinical trials [26, 27]. Thus, it could be more meaningful to define two dose levels for clopidogrel (i.e., exposed [75 mg/day] versus non‐exposed). Despite the data‐driven dose levels being less clinically meaningful, DAM's results are generally consistent with the exposed‐versus‐non‐exposed model (Figure 5B), which suggests DAM might be robust to improperly defined dose levels. Additionally, DAM suggests a uniform risk of the meloxicam‐clopidogrel combination for meloxicam 7.5–15 mg/day (Figure 5B), which could not be inferred from the exposed‐versus‐non‐exposed model. Thus, DAM could generate more knowledge than existing models and is more appropriate to investigate drugs with a wide range of clinical doses, while all results are subject to clinical adjudication. Second, while we include a significant number of meaningful partitions, the DAM‐estimated DRRs in our study might not represent the true DRR. Third, despite limiting the model space to meaningful partitions, DAM might require a significant amount of computational resources in high‐throughput data mining. This challenge can be addressed by parallel computing and/or improving the efficiency of computation codes. For instance, optimization of an objective function could be faster than fitting a regression model (e.g., using the nlminb function instead using the clogit/glm functions in R). Third, as DAM is based on the optimal model, the type‐1 error rate might be inflated without any adjustment; while permutation tests could be used for type‐1 error rate control. DAM also has comparable or better statistical power to detect true DDI under permutation tests, besides better performance in estimating true DRR.

In conclusion, dose‐aware model (DAM) could reveal the relationship between dose of two‐drug combination exposure and risk of adverse drug events (ADE), and a significant portion of potential adverse drug–drug interactions (DDIs) might involve a complex dose‐risk relationship.

Author Contributions

Y.S., A.S., Y.Y., H.N., J.X., M.S., M.T.E., J.S., and P.Z. wrote the manuscript. Y.S., A.S., Y.Y., H.N., J.X., M.S., M.T.E., J.S., and P.Z. designed the research. Y.S., A.S., Y.Y., J.X., M.T.E., J.S., and P.Z. performed the research. Y.S., A.S., Y.Y., and P.Z. analyzed the data.

Ethics Statement

The authors have nothing to report.

Consent

The authors have nothing to report.

Conflicts of Interest

Mu Shan is employee of Eli Lilly and Company. All other authors declare no conflicts of interest.

Supporting information

Data S1: psp470114‐sup‐0001‐DataS1.docx.

Table S1: psp470114‐sup‐0002‐TableS1.xlsx.

Data Availability Statement

Optum's de‐identified Clinformatics Data Mart Database is not publicly available (accessibility can be obtained from Optum). Summary statistics generated during this study are included in this published article [and its Supporting Information—S1 files]. Model codes are provided in GitHub (available from: github.com/PengyueLab/DAM).