A New Algorithm Optimized for Initial Dose Settings of Vancomycin Using Machine Learning

Abstract

This study aimed to construct an optimal algorithm for initial dose settings of vancomycin (VCM) using machine learning (ML) with decision tree (DT) analysis. Patients who were administered intravenous VCM and underwent therapeutic drug monitoring (TDM) at the Hokkaido University Hospital were enrolled. The study period was November 2011 to March 2019. In total, 654 patients were included in the study. Patients were divided into two groups, training (patients who received VCM from November 2011 to December 2017; n = 496) and testing (patients who received VCM from January 2018 to March 2019; n = 158) groups. For the training group, DT analysis of the classification and regression tree algorithm was performed to construct an algorithm (called DT algorithm) for the initial dose settings of VCM. For the testing group, the rates of attaining the VCM therapeutic range (trough value = 10–15 and 10–20 mg/L) with the DT algorithm and three conventional dose-setting methods were compared for model evaluation. The DT algorithm was constructed to be used for patients with estimated glomerular filtration rate ≥50 mL/min and body weight ≥40 kg. As a result, the recommended daily doses ranged from 20.0 to 58.1 mg/kg. In model evaluation, the DT algorithm obtained the highest rates of attaining the VCM therapeutic range compared to conventional dose-setting methods. Therefore, our DT algorithm can be applied to clinical practice. In addition, ML is useful for setting drug doses.

INTRODUCTION

Machine learning (ML) refers to the scientific algorithms and statistical models that machines learn from experience.¹⁾ ML involves different approaches such as decision tree (DT), neural network, and support vector machine, which are usually used for predictive models.¹⁾ ML is used in various fields. For example, Mark et al. determined the usefulness of a neural network to forecast rainfall; this approach can replace the existing methods.²⁾ Previous studies have constructed risk prediction models of adverse drug reactions (ADRs) using DT analysis.^3,4) These findings strongly indicate that ML can replace or compensate for older techniques.

Generally, dose settings of drugs such as antibiotics are made on the basis of population pharmacokinetics (PPK) parameters.^5,6) For example, in Japan, the initial dose settings of vancomycin (VCM), an anti-methicillin-resistant Staphylococcus aureus (anti-MRSA) agent, are determined using therapeutic drug monitoring (TDM) analysis software that incorporates Japanese PPK parameters.^5–7) However, there are no reports of applying ML to drug dose setting, although it is possible that ML can help achieve accurate drug dose settings.

DT models have a flowchart-like framework, so users can easily evaluate the risk of ADRs compared to conventional statistics models.^3,4) In addition, DT models are suitable for clinical application because users do not require any special software, unlike other ML methods.^3,4) Therefore, in this study, we selected a DT model to validate the usefulness of ML for drug dose setting. Our aim was to construct an optimal algorithm for initial dose settings of VCM using ML with DT analysis.

MATERIALS AND METHODS

Study Subjects

Patients who were administered intravenous VCM and underwent TDM at the Hokkaido University Hospital were enrolled into this retrospective study (n = 1534). The study period was November 2011 to March 2019. Of these, 689 patients met the following inclusion criteria for the study: (i) age ≥ 18 years, (ii) VCM trough value measured at the steady state (defined over 5 half-lives), and (iii) target trough value at initial TDM = 10–15 mg/L. The half-lives of VCM were calculated individually on the basis of Japanese PPK parameters.⁵⁾ The exclusion criteria were as follows: (i) patients who underwent hemodialysis, including continuous hemodiafiltration; (ii) patients who experienced nephrotoxicity during VCM therapy; and (iii) patients with missing data. Nephrotoxicity was defined as an increase from the baseline in serum creatinine (Scr) of ≥ 0.5 mg/dL or ≥ 50% on the basis of the consensus statement of the Infectious Diseases Society of America.⁸⁾ The number of patients with estimated glomerular filtration rate (eGFR) < 50 mL/min and body weight (BW) < 40 kg was low (25 and 10 patients, respectively), and these patients were excluded. Finally, 654 patients were included in the study. Patients were divided into two groups, training (patients who received VCM from November 2011 to December 2017; n = 496) and testing (patients who received VCM from January 2018 to March 2019; n = 158) groups. The training group was used to build the DT model, while the testing group was used for model evaluation (Fig. 1).

Fig. 1. Flowchart of the Process of Including Patients in This Study

VCM, vancomycin; HD, hemodialysis; CHDF, continuous hemodiafiltration; TDM, therapeutic drug monitoring; eGFR, estimated glomerular filtration rate; BW, body weight.

Data Collection

The following data items were collected: age, sex, BW, body mass index (BMI), Scr, eGFR,⁹⁾ creatinine clearance (CCr),¹⁰⁾ duration of therapy, concomitant medications (nonsteroidal anti-inflammatory drugs (NSAIDs), furosemide, amphotericin B, aminoglycosides, piperacillin-tazobactam (PIPC-TAZ), and vasopressor drugs (etilefrine, noradrenaline, olprinone, milrinone, dopamine, and dobutamine)⁷⁾), residence in the intensive care unit (ICU), initial VCM daily dose, initial VCM trough value, and days to initial TDM. All data items, except for duration of therapy, initial VCM trough value, and days to initial TDM, were evaluated at the beginning of VCM therapy.

Construction of the DT Model

For the training group, DT analysis was performed to construct an algorithm for initial dose settings of VCM. We used the classification and regression tree (CART) algorithm, a typical DT method.^11,12) The CART algorithm searches for independent variables and cut-off points that maximize homogeneity and with the most minimum impurity using the Gini index in each branched subgroup.^11,12) The advantage of CART is that it analyses not only categorical variables but also continuous variables as dependent variables. To construct a DT model, the corrected daily dose (mg/kg) was selected as the dependent variable, and the independent variables were age, sex, eGFR, BMI, concomitant medications (NSAIDs, furosemide, amphotericin B, aminoglycosides, PIPC-TAZ, and vasopressor drugs), and residence in the ICU; the eGFR was used instead of CCr on the basis of the TDM Guideline for Antibiotics 2016 in Japan.¹³⁾ The corrected daily dose was defined as the daily dose per BW predicted to reach a trough value of 12.5 mg/L, calculated individually as follows:

  

The target trough value of 12.5 mg/L was defined as the middle point of the initial target trough value range of 10–15 mg/L.¹³⁾ If the corrected daily dose before dividing by BW was >3000 mg, we capped them at 3000 mg daily in the interest of safety.¹³⁾

The DT was branched until any one of the following stop criteria was met: (i) each subgroup reached the lowest impurity level, (ii) each subgroup had <20 patients, or (iii) a DT branched the depth of five levels. All analyses were performed using SPSS Decision Trees ver. 25 (IBM, Tokyo, Japan).

Finally, on the basis of the constructed DT model, a VCM initial-dose-setting algorithm (hereinafter referred to as “DT algorithm”) was built.

Model Evaluation

Using the testing group, we evaluated the rates of attaining the therapeutic range (VCM trough value = 10–15 and 10–20 mg/L), recommended daily dose, and predicted trough value of the DT algorithm and three conventional dose-setting methods, which included two TDM analysis software programs incorporating Japanese PPK parameters^5–7) and one nomogram: (i) SHIONOGI-VCM-TDM ver. 2009 (VCM-TDM), (ii) vancomycin MEEK TDM analysis software ver. 2.0 (MEEK), and (iii) maintenance dose of nomogram presented in the TDM guideline (Nomogram).^7,13)

The steps in model evaluation in the testing group were as follows:

1. Dose settings were performed for individual patients, and the recommended daily dose was calculated using each method on the basis of the defined daily dose (Table 1).

Table 1. Calculation of Defined VCM Daily Doses

Calculated VCM daily dose (mg)	Defined VCM daily dose (mg)	Example of dose regimen
>2750	3000	1500 mg twice daily
2250≤ and <2750	2500	1250 mg twice daily
1750≤ and <2250	2000	1000 mg twice daily
1375≤ and <1750	1500	750 mg twice daily
1125≤ and <1375	1250	1250 mg once daily
875≤ and <1125	1000	1000 mg once daily
675≤ and <875	750	750 mg once daily

VCM, vancomycin.

2. The predicted trough value was calculated using the following formula:

  

3. The rates of attaining the therapeutic range were evaluated.

In MEEK and VCM-TDM, the recommended daily doses were set closest to the predictive VCM trough value of 12.5 mg/L.

Other Statistical Analysis

Differences in patient characteristics were assessed by the nonpaired, two-sided Mann–Whitney U-test conducted for continuous variables. Pearson’s chi-square or Fisher’s exact test was performed for categorical variables. p ≤ 0.05 was considered statistically significant. All analyses were performed using SPSS statistics ver. 25 (IBM).

Ethics

This study was conducted in accordance with the guidelines for the care for human studies. The ethics committee of the Hokkaido University Hospital approved the study protocol (no. 019-0100).

RESULTS

Patient Characteristics

Table 2 shows a comparison of patient characteristics between the training and testing groups. The patient characteristics were equivalent except for duration of therapy and rate of amphotericin B use (Table 2).

Table 2. Comparison of Patient Characteristics between Training and Testing Groups

Variables	Training group (n = 496)	Testing group (n = 158)	P
Age (years), median (range)	61 (18–89)	62 (19–86)	0.65c)
Sex (male), n (%)	329 (66.3)	106 (67.1)	0.86a)
Body weight (kg), median (range)	58.8 (40.0–127.0)	60.3 (40.0–107.7)	0.27c)
Body mass index, median (range)	21.9 (14.4–49.1)	22.1 (14.9–39.4)	0.17c)
Scr (mg/dL), median (range)	0.60 (0.16–1.22)	0.64 (0.16–1.21)	0.18c)
eGFR (mL/min), median (range)	97.3 (50.7–407.3)	89.5 (50.8–433.2)	0.83c)
Ccr (mL/min), median (range)	99.2 (35.4–569.6)	98.9 (52.7–333.2)	0.93c)
Duration of therapy (days), median (range)	9 (3–83)	8 (3–50)	0.03c)*
Concomitant medications, n (%)
NSAIDs	231 (46.6)	67 (42.4)	0.36a)
Furosemide	91 (18.3)	33 (20.9)	0.48a)
Piperacillin/Tazobactam	51 (10.3)	19 (12.0)	0.54a)
Amphotericin B	0 (0.0)	4 (2.53)	<0.01b)*
Aminoglycoside antibiotics	7 (1.41)	1 (0.63)	0.69b)
Vasopressor drugs	32 (6.45)	7 (4.43)	0.35a)
Residence in intensive care unit, n (%)	45 (9.07)	16 (10.1)	0.86a)
Days to initial TDM (days), median (range)	4 (3–10)	4 (3–8)	0.69c)
Initial VCM daily dose (mg/L), median (range)	2000 (750–3750)	2000 (1000–3750)	0.64c)
Initial VCM trough value (mg/L), median (range)	9.6 (2.2–36.0)	10.4 (2.1–29.5)	0.11c)

a) Chi-square test. b) Fisher’s exact test. c) Mann–Whitney U-test. * p ≤ 0.05 was considered statistically significant. Scr, serum creatinine; eGFR, estimated glomerular filtration rate; CCr, creatinine clearance; VCM, vancomycin; NSAIDs, nonsteroidal anti-inflammatory drugs; TDM, therapeutic drug monitoring.

DT Analysis

As shown in Fig. 2, three predictive variables (eGFR, age, and BMI) were automatically extracted, and their cut-off values were determined using the CART algorithm. Each box shows the number of cases and the average corrected VCM daily dose (mg/kg). In all, the DT branched into 24 subgroups.

Fig. 2. DT Model Based Prediction of Corrected Daily VCM Doses (mg/kg)

Cut-off values of predictive variables (eGFR, age, and BMI) were determined using the CART algorithm. Each box showed the number of cases, and average corrected daily VCM dose (mg/kg). DT, decision tree; VCM, vancomycin; D, average VCM daily dose; eGFR, estimated glomerular filtration rate; BW, body weight; BMI, body mass index; CART, classification and regression tree.

Figure 3 shows the DT algorithm for initial dose settings of VCM to be used on patients with eGFR ≥50 mL/min and BW ≥40 kg. The daily dose ranged from 20.0 to 58.1 mg/kg.

Fig. 3. Algorithm for Initial Dose Settings of VCM on the Basis of the DT Model

The algorithm was to be used on patients with eGFR ≥50 mL/min and BW ≥40 kg. Daily dose should not exceed 3000 mg/d. Dosing regimens are listed in Table 1. VCM, vancomycin; DT, decision tree; eGFR, estimated glomerular filtration rate; BW, body weight; BMI, body mass index.

Model Evaluation

The characteristics of recommended daily doses and predicted trough values are shown in Table 3. Between four dose-setting methods, our DT algorithm obtained the highest rate of attaining the therapeutic range (10–15 mg/L: 37.3%; 10–20 mg/L: 50.6%).

Table 3. Evaluation of the DT Algorithm Compared to Conventional Dose-Setting Methods

Variables	DT algorithm	VCM-TDM	MEEK	Nomogram
Recommend daily VCM dose, median (range)	2500 (1250–3000)	2000 (1000–3000)	1500 (750–2000)	1500 (750–3000)
Predicted VCM trough value
Median (range), mg/L	12.1 (2.52–34.2)	11.2 (2.52–34.5)	8.40 (1.26–22.4)	8.91 (1.68–25.3)
<10 mg/L, n (%)	53 (33.5)	59 (37.3)	100 (63.3)	98 (62.0)
10≤ and <15 mg/L, n (%)	59 (37.3)	52 (32.9)	41 (25.9)	44 (27.9)
15≤ and <20 mg/L, n (%)	21 (13.3)	24 (15.2)	15 (9.49)	14 (8.86)
10≤ and <20 mg/L, n (%)	80 (50.6)	76 (48.1)	56 (35.4)	58 (36.7)
≥20 mg/L, n (%)	25 (15.8)	23 (14.6)	2 (1.27)	2 (1.27)

DT, decision tree; VCM, vancomycin.

DISCUSSION

In this study, we attempted to build an optimal algorithm for initial dose settings of VCM using ML with DT analysis.

In the DT algorithm, the eGFR, age, and BMI were extracted as predictive variables. These variables generally affect VCM pharmacokinetics such as clearance and/or volume of distribution.^5,6,13) Therefore, it is reasonable for these and not other variables to be extracted. As a result, our DT algorithm obtained the highest rate of attaining the therapeutic range (10–15 mg/L: 37.3%; 10–20 mg/L: 50.6%) compared to conventional dose-setting methods (Table 3). In MEEK and Nomogram, the recommended VCM daily dose and predicted trough value tended to be low (Table 3). In patients with CCr ≥85 mL/min, MEEK fixes CCr to 85 mL/min uniformly, which means that the dose is approximately fixed in these patients. There was no correlation with VCM clearance in patients with CCr ≥85 mL/min in the PPK parameters of MEEK.⁶⁾ However, in the testing group (n = 158), 107 patients had CCr ≥85 mL/min, and 71 (66.4%) of those had a VCM trough value of <10 mg/L. These results suggested that MEEK leads to a lower dose. Similar results have been reported with Nomogram,^14,15) consistent with our results. On the other hand, the rate of attaining the VCM therapeutic range in VCM-TDM (10–15 mg/L: 32.9%; 10–20 mg/L: 48.1%) was slightly different compared to the DT algorithm. In our previous study, VCM-TDM had better predictive accuracy than MEEK.¹⁶⁾ VCM-TDM rounds off Scr to 0.6 mg/dL for low Scr values in order to prevent overestimation of renal function.⁷⁾ However, rounding off Scr has a risk of underestimation of renal function, which may have led to low administration of VCM in this study.¹⁷⁾ In fact, when the construction of a DT algorithm was attempted using rounding off Scr, the rate of attainment of a therapeutic range was not improved (data not shown). Thus, rounding off Scr should only be used for patients with apparently low muscle mass. Our DT algorithm determined the highest rate for the attainment of a VCM trough value of ≥20 mg/L. Thus, careful monitoring of VCM-dose overestimation is required, and TDM must be performed.

In our DT algorithm, BMI was extracted as a predictive variable in the subgroups with “eGFR ≥90.7 mL/min” and “eGFR ≥90.7 mL/min and BMI ≥19.4.” These results indicated that patients with low BMI required a higher dose relative to their BW (Fig. 2), consistent with recent research.¹⁸⁾ In addition, the daily VCM doses were increased in younger patients and patients with better eGFR. These increases were considered to be appropriate.^13,16) Although patients with eGFR <50 mL/min could not be evaluated in this study, our DT algorithm incorporates multiple factors, including BMI. We believe this was the reason for the higher therapeutic range in the DT algorithm compared to conventional dose-setting methods.

The daily VCM doses based on the DT algorithm ranged from 20.0 to 58.1 mg/kg. The nomogram presented in the TDM guidelines also sets a dose relative to BW, but this dose range is from 15 to 40 mg/kg for patients with eGFR ≥50.¹³⁾ Thus, the recommended doses by DT algorithm are higher than those recommended by the Nomogram. Considering a previous report stating that Nomograms tends to cause under dosing,¹⁵⁾ our results are considered to be appropriate (However, caution should be taken with VCM doses >3000 mg/d, and dosage should not exceed 4000 mg/d).

Our study had a few limitations. First, it was a single-center study and might lack scientific rigor or external validity. Therefore, as mentioned above, carefully monitoring is required for clinical application. Second, we could not evaluate patients with eGFR <50 mL/min and BW <40 kg, because patients with renal impairment often undergo TDM in a nonsteady state. Third, the predicted trough value was calculated proportionally to actual and recommended daily doses of VCM. Therefore, these usages could not be considered.

Despite these limitations, our study firstly indicated the usefulness of ML for drug dose setting. By following the flowchart, clinicians and pharmacists can easily perform initial dose settings of VCM. Therefore, our DT algorithm has the potential to be applied to clinical practice. For the future, it is necessary that factors such as disease state and pathological condition and initial loading dose be incorporated in the DT algorithm. Moreover, a multicenter trial is required in order to build a more generalized model.

Conflict of Interest

The authors declare no conflict of interests.

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