# Estimation of Ganciclovir Exposure in Adults Transplant Patients by Machine Learning

Hamza Sayadi, Yeleen Fromage, Marc Labriffe, Pierre-André Billat, Cyrielle Codde, Selim Arraki Zava, Pierre Marquet, Jean-Baptiste Woillard

<figure><img src="image_1.png" /></figure>

## ► To cite this version:

Hamza Sayadi, Yeleen Fromage, Marc Labriffe, Pierre-André Billat, Cyrielle Codde, et al., Estimation of Ganciclovir Exposure in Adults Transplant Patients by Machine Learning. AAPS Journal, 2025, 27 (2), pp.53. 10.1208/s12248-025-01034-9. hal-04996501

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# Estimation of Ganciclovir Exposure in Adults Transplant Patients by Machine Learning

Hamza Sayadi<fnref n="1" /> · Yeleen Fromage<fnref n="1" /> · Marc Labriffe<fnref n="1" />,<fnref n="2" /> · Pierre-André Billat<fnref n="4" /> · Cyrielle Codde<fnref n="2" />,<fnref n="3" /> · Selim Arraki Zava<fnref n="1" /> · Pierre Marquet<fnref n="1" />,<fnref n="2" /> · Jean-Baptiste Woillard<fnref n="1" />,<fnref n="2" /> ID

Received: 13 August 2024 / Accepted: 31 January 2025

© The Author(s) 2025

## Abstract

**Introduction** Valganciclovir, a prodrug of ganciclovir (GCV), is used to prevent cytomegalovirus infection after transplantation, with doses adjusted based on creatinine clearance (CrCL) to target GCV AUC0-24 h of 40–60 mg*h/L. This sometimes leads to overexposure or underexposure. This study aimed to train, test and validate machine learning (ML) algorithms for accurate GCV AUC0-24 h estimation in solid organ transplantation.

**Methods** We simulated patients for different dosing regimen (900 mg/24 h, 450 mg/24 h, 450 mg/48 h, 450 mg/72 h) using two literature population pharmacokinetic models, allocating 75% for training and 25% for testing. Simulations from two other literature models and real patients provided validation datasets. Three independent sets of ML algorithms were created for each regimen, incorporating CrCL and 2 or 3 concentrations. We evaluated their performance on testing and validation datasets and compared them with MAP-BE.

**Results** XGBoost using 3 concentrations generated the most accurate predictions. In testing dataset, they exhibited a relative bias of -0.02 to 1.5% and a relative RMSE of 2.6 to 8.5%. In the validation dataset, a relative bias of 1.5 to 5.8% and 8.9 to 16.5%, and a relative RMSE of 8.5 to 9.6% and 10.7% to 19.7% were observed depending on the model used. XGBoost algorithms outperformed or matched MAP-BE, showing enhanced generalization and robustness in their estimates. When applied to real patients’ data, algorithms using 2 concentrations showed relative bias of 1.26% and relative RMSE of 12.68%.

**Conclusions** XGBoost ML models accurately estimated GCV AUC0-24 h from limited samples and CrCL, providing a strategy for optimized therapeutic drug monitoring.

**Keywords** ganciclovir · machine learning · MIPD · population pharmacokinetics · simulations

## Introduction

Cytomegalovirus (CMV) is a double-stranded DNA virus with an estimated seroprevalence of 83% worldwide (1). CMV infection often goes unnoticed in individuals with an

intact immune response, as the virus enters a latent phase without symptoms. Reactivation is possible, rendering the virus transmissible without overt clinical signs. However, in patients undergoing immunosuppressive therapy following solid organ transplantation (SOT), whether the infection is initial or a reactivation, it can precipitate severe complications. These complications encompass an increased risk of graft rejection, as well as elevated morbidity and mortality. These underscores the essential need for effective prevention strategies (2–5).

The main approaches to CMV prevention in SOT recipients are preemptive therapy and universal prophylaxis. Preemptive therapy is based on weekly monitoring of viral load to detect any early replicative activity and allow for the prompt initiation of antiviral treatment aimed at preventing progression to CMV disease. This approach requires complex logistical coordination. Consequently, many hospital

<figure><img src="image_3.png" /></figure>

<footnote>Jean-Baptiste Woillard
jean-baptiste.woillard@unilim.fr</footnote>

<footnote n="1">¹ Department of Pharmacology, Toxicology and Pharmacovigilance, CHU de Limoges, Limoges, France</footnote>

<footnote n="2">² Pharmacology & Transplantation, INSERM U1248, Université de Limoges, 2 Rue du Pr Descottes, F-87000 Limoges, France</footnote>

<footnote n="3">³ Service de Maladies Infectieuses et Tropicales, CHU Dupuytren, Limoges, France</footnote>

<footnote n="4">⁴ INERIS, Experimental Toxicology and Modeling Unit (TEAM), Parc ALATA BP2, Verneuil en Halatte, France</footnote>
centers are opting for universal prophylaxis. This approach administers antivirals to either all transplant recipients or a subset of those considered at-risk, for a duration of three to six months post-transplant (5, 6).

Valganciclovir (VGCV) is the most used prophylactic treatment. It is a prodrug of ganciclovir (GCV) with significantly increased oral bioavailability (~60% for VGCV compared to ~6% for GCV). Following gastrointestinal absorption, VGCV is rapidly metabolized into active GCV by intestinal and hepatic esterase's. GCV mimics guanosine and inhibits viral DNA polymerase, preventing viral replication. It is mainly excreted renally in unchanged form through glomerular filtration and tubular secretion (7–9).

The dosage should be adjusted according to the manufacturer's recommendations based on renal function, with doses of 900 mg/24 h, 450 mg/24 h, 450 mg/48 h, and 450 mg/72 h for creatinine clearance (CrCL) ≥ 60 mL/min, 40–59 mL/min, 25–39 mL/min, and 15–24 mL/min respectively (10). Despite this adjustment, GCV exhibits high interindividual pharmacokinetic (PK) variability, which can lead to underexposure or overexposure. Wiltshire *et al.* followed the manufacturer's recommendations by administering reduced doses of VGCV, resulting in lower drug exposure in patients with a CrCl between 25 and 40 mL/min (AUC0–24 h = 22.6 ± 4.2 mg*h/L) compared to those with a CrCl of 40 to 60 mL/min (AUC0–24 h = 38.6 ± 11.1 mg*h/L) or greater than 60 mL/min (AUC0–24 h = 49.9 ± 15.0 mg*h/L) (9). In contrast, Manuel *et al.* administered a standard dose of 450 mg/24 h of VGCV to all patients, regardless of renal function, and found that patients with a CrCl of 25 to 40 mL/min achieved an exposure (AUC0–24 = 59.3 (39.0–85.3) mg*h/L) similar to that of patients with normal renal function receiving 900 mg/24 h of VGCV (11).

Wiltshire *et al.* demonstrated that increased exposure to GCV after oral administration of VGCV compared to GCV is associated with a reduced risk of viremia during prophylactic treatment in SOT recipients, proposing a target AUC0–24 h range of 40 to 60 mg*h/L (12). However, these findings have not yet been widely confirmed. Padulles *et al.* supported these results, observing that patients within the 40 to 50 mg*h/L target AUC0–24 h range experienced faster CMV clearance, lower viremia, and reduced recurrence of CMV disease (13). Increasingly, studies are emphasizing the significant interindividual variability in GCV exposure and the need for close monitoring of GCV blood levels (14–17). In clinical practice, complete PK profiles required for accurate AUC calculations are often unavailable. Consequently, maximum a posteriori Bayesian estimation (MAP-BE) is commonly employed to estimate AUC based on limited sampling strategies (LSS). This approach combines prior knowledge of parameter distributions from population pharmacokinetic (popPK) model with observed individual concentrations data and covariates to estimate individual PK

parameters (18, 19). However, the accuracy of MAP-BE can be influenced by model assumptions and parameter variability, offering opportunities for improvement through machine learning (ML) approaches.

In recent years, ML has emerged as a powerful tool in pharmacometrics and precision dosing, offering an alternative to traditional popPK modeling. For instance, Woillard *et al.* demonstrated that ML models achieved predictive performance comparable (or numerically better) to traditional MAP-BE for tacrolimus AUC in transplant patients, while reducing the number of required samples and improving generalizability across different types of transplantation (20). Similarly, Destere *et al.* showed the added benefit of using an ML model to enhance MAP-BE predictions, thereby improving the accuracy of exposure predictions for iohexol and isavuconazole (21, 22). These examples highlight ML's ability to improve predictive accuracy and enhance therapeutic drug monitoring in clinical practice. Building on this work, this study aimed to train, test and validate ML algorithms in simulated and real patients to accurately estimating the inter-dose AUC of GCV at steady state (AUCss) in adult post-SOT prophylaxis, using only two or three blood concentrations and CrCL. A secondary objective is to compare the performances of these ML algorithms with MAP-BE based on LSS in the validation datasets.

# Methods

## Patients and Data

### Training and Testing Set

To address variations in dosing based on CrCL, we simulated 5,000 PK profiles for each dose of VGCV; 900 mg/24 h, 450 mg/24 h, and 450 mg/48 h; using the mrgsolve R package (23). These Monte Carlo simulations were based on the popPK models of Vezina *et al.* and Lalagkas *et al.* (2,500 PK profiles per model and per dose) (24, 25). Monte Carlo simulations involve generating repeated random samples from the probability distributions of PK parameters estimated in the popPK models. For each iteration, PK parameter values were drawn based on their estimated means and variabilities, resulting in unique PK profiles. The Vezina *et al.* model does not include patients with CrCL below 30 mL/min. Therefore, for the 450 mg/72 h dose, we only simulated 2,500 profiles using the Lalagkas model, which accommodates such CrCL levels. Both the two popPK models used were developed based on European populations of renal, liver, heart, and lung transplant patients. Briefly, they consisted in a two-compartment structure with delayed oral absorption and first-order elimination. The model by Vezina incorporates the influence of CrCL via the Cockcroft & Gault formula and body weight
<figure><img src="image_4.png" /><figcaption>**Fig. 1** Pharmacokinetics profiles of plasma ganciclovir</figcaption></figure>

on the drug elimination clearance, as well as the influence of body weight on inter-compartmental clearance. The Lalagkas model estimates CrCL using the CKD-EPI formula and integrates the influence of CrCL and body weight on the drug elimination clearance. The body weight distribution was modeled for all simulations as follows: mean ± standard deviation [minimum–maximum] = 70 ± 17 [43–131] kg. CrCL levels for VGCV dosing were specified as follows: 90 ± 15 [60–120] mL/min for the 900 mg/24 h dose, 50 ± 10 [40–59] mL/min for the 450 mg/24 h dose, 32 ± 10 [25–39] mL/min for the 450 mg/48 h dose, and 17 ± 10 [10–24] mL/min for the 450 mg/72 h dose; with these values representing the mean ± standard deviation [minimum–maximum] for each respective dose. Residual variability was removed to focus on the impact of covariates and inter-individual variability, thereby optimizing performance in real external patients as previously shown (20, 26). We simulated concentrations hourly at steady state from trough concentration (C0) up to concentration at 24 h (C24), concentration at 48 h (C48), or concentration at 72 h (C72), depending on the duration of the interval between VGCV doses. The corresponding inter-dose AUCss was calculated using the trapezoidal method. We removed extreme profiles, that is, those whose GCV AUCss outside the 1st and 99th percentiles as well as those not achieving steady state. A total of 105 profiles for the 900 mg/24 h dose, 107 for 450 mg/24 h, 103 for 450 mg/48 h, and 53 for 450 mg/72 h were excluded. The data were split into a training set (75%) and a testing set (25%).

## Simulated Validation Set

To externally validate our ML algorithms and assess their generalization to different populations, a simulated

validation dataset was created using two different popPK models (Caldés et al., Chen et al.) (27, 28). We simulated 200 patients for 900 mg/24 h, 450 mg/24 h and 450 mg/48 h doses of VGCV (100 patients per model and per dose). For the 450 mg/72 h dose, only 100 patients were generated using the Caldés model, as the Chen model did not include patients with CrCL below 30 mL/min. Based on a two-compartment structure with first-order elimination, these models incorporate the effect of CrCL, estimated by the Cockcroft & Gault formula, on the drug elimination clearance. All simulations followed the methodologies previously applied (CrCL levels were set as indicated above) and residual variability was removed. Measurements were taken every hour, ranging from the C0 up to C24, C48, or C72 h. The inter-dose AUCss was calculated using the trapezoidal method, and aberrant profiles were excluded as described above.

## Validation in Real Patients

To further evaluate our ML algorithms, we included the patients from the ProGGRess trial, which examined the PK of GCV in adult renal transplant patients (29). This trial included 22 patients monitored at the nephrology department of Limoges University Hospital in France as part of the EPHEGREN study (reference no. 130–2013-30). All participants provided written informed consent, and the trial adhered to the ethical standards of the Declaration of Helsinki, as amended in Tokyo, with approval from the regional ethics committee of Limoges (approval no. 164–2015-01). In this trial, patients received VGCV (Rovalcyte®, Roche, Switzerland) to prevent CMV infections, with dosages adjusted based on their CrCL as defined in the Summary of Product Characteristics. Seventeen patients received a dose of 450 mg once daily,
three received 900 mg once daily, and two received 450 mg every two days. All patients were sampled during the third month post-transplantation. Blood samples were collected in EDTA tubes at pre-dose and at 1, 2, 3, and 5 h after the morning dose of VGCV. The cells and plasma were immediately separated, and the plasma was stored at -20°C. GCV concentrations in plasma were measured using a validated LC-MS/MS method. Concentrations below 5 µg/L, the method's limit of quantification, were considered null. The inter-dose AUCss was also calculated using the trapezoidal method. Concentrations used by the algorithms to predict AUCss, which were not directly measured, were extrapolated after linking the measured concentrations.

## Feature Engineering

To predict the inter-dose AUCss, we used CrCL along with thirteen concentration levels from C0 to concentration at 12 h (C12) as predictive variables. We deliberately omitted body weight, as it is not related to PK parameters in the popPK models (Caldés *et al.* and Chen *et al.*.) used to generate the simulated validation data. Since these models do not account for body weight as a covariate, it would not influence AUCss estimation. All predictive variables were normalized to ensure uniform scaling and improve prediction accuracy. Additionally, the Yeo-Johnson transformation was applied to the concentration data to address any potential non-normality and enhance model performance. Subsequently, variable importance plots generated using random permutation were used to assess and select the most impactful predictors.

We then developed three distinct ML algorithms with LSS for each VGCV dose, using combinations of CrCL and either two or three GCV concentrations between C0 and C12. For simplified routine applications, we also developed an LSS using CrCL with three concentrations sampled between C0 and concentration at 6 h (C6). A total of twelve separate ML algorithms were created depending on the eGFR group and number and timing of samples included in the LSS.

As a baseline comparator, we compare the performance of ML algorithms to a multiple linear regression based on C0 and peak concentration (C2) used to predict the inter-dose AUCss.

## Preprocessing of Data and ML Model Development

For all the steps of the ML analyses, the tidymodels framework was used (https://www.tidymodels.org/).

There is a wide variety of supervised learning ML models. We initially developed and compared five ML models,

including XGBoost, random forests, a linear regression model combining RIDGE and LASSO penalization (glmnet), linear support vector machines (SVM) and multivariate adaptive regression spline (MARS), to predict the inter-dose AUCss. XGBoost is a gradient boosting algorithm that builds an ensemble of weak decision trees applied in series to improve prediction accuracy (30). Random forests aggregate independent predictions from multiple decision trees, reducing overfitting and enhancing model generalizability (31). The glmnet algorithm applies both Ridge and LASSO penalizations to linear regression, balancing feature selection and regularization (32). SVM for regression works by finding the optimal hyperplane that best fits the data while minimizing prediction errors (33). Finally, MARS create piecewise linear models, adapting to nonlinear relationships by automatically detecting changes in data patterns (34).

To tune the hyperparameters and evaluate the performance of the different models, tenfold cross-validation was applied on the four training sets. This evaluation was based on several metrics: root mean square error (RMSE, expressed in mg*h/L) between the predicted and reference AUCss, R-squared (R²), relative mean prediction error (MPE; %), and relative RMSE (%). The best-performing model in each training set, prioritizing relative MPE first and relative RMSE second, was then further developed to predict the AUCss.

Subsequently, the ML algorithms obtained were evaluated on a testing dataset by measuring the RMSE, R², relative MPE, relative RMSE, and the proportion of estimations with a relative MPE value outside the ±20% range. Scatter plots of predicted vs. reference AUCss and plots of bias (AUCss predicted – AUCss reference) as a function of reference AUCss values were also created.

## External Evaluation and Comparison to MAP-BE

We assessed the performance separately of the 12 selected ML algorithms on both the simulated and real patient validation dataset, employing the same performances metrics as those used on the testing dataset.

Additionally, the inter-dose AUCss for both dataset was estimated using MAP-BE with the mapbayR package, based on the popPK models from Vezina *et al.* and Lalagkas *et al.* (24, 25). The final parameters from these models served as prior distribution of PK parameters. The weight covariate was set to the median value specified in the models. The GCV concentrations and C1Cr covariate were the same as those employed in the ML algorithms. The optimization algorithm 'L-BFGS-B' was utilized for the mapbayest function. These MAP-BE estimations were also compared with the reference AUCss and the performances metrics were calculated.
<table><caption>**Table 1** Characteristics of Training, Testing and Simulated Validation Populationsª</caption><thead><tr><th></th><th></th><th>Training (n=3,671)</th><th>Testing (n=1,224)</th><th>Validation: Caldés et al. model (n=98)</th><th>Validation: Chen et al. Model (n=98)</th></tr></thead><tbody><tr><td rowspan="6">900 mg/24 h of VGCV</td><td>Weight (kg)</td><td>71.1 [60.6–81.7]</td><td>71.1 [60.4–81.7]</td><td>-</td><td>-</td></tr><tr><td>Creatinine clearance</td><td>90.5 [81.2–99.9]</td><td>89.5 [80.3–99.4]</td><td>94.3 [81.4–102.3]</td><td>94.9 [81.4–102.3]</td></tr><tr><td>C3, mg/L</td><td>6.34 [5.31–7.59]</td><td>6.38 [5.36–7.54]</td><td>7.83 [6.06–9.31]</td><td>5.63 [4.67–7.18]</td></tr><tr><td>C4, mg/L</td><td>5.08 [4.16–6.18]</td><td>5.13 [4.22–6.20]</td><td>6.09 [4.77–7.48]</td><td>5.02 [4.13–6.09]</td></tr><tr><td>C6, mg/L</td><td>3.32 [2.53–4.25]</td><td>3.34 [2.51–4.26]</td><td>3.93 [2.89–5.23]</td><td>3.65 [2.90–4.50]</td></tr><tr><td>C12, mg/L</td><td>1.37 [0.90–1.99]</td><td>1.37 [0.90–2.02]</td><td>1.49 [1.01–2.37]</td><td>1.29 [1.01–1.94]</td></tr><tr><td rowspan="6">450 mg/24 h of VGCV</td><td>AUC0-24ss, mg*h/L</td><td>55.9 [44.0–71.1]<br>(n=3,670)</td><td>55.9 [44.0–72.0]<br>(n=1,223)</td><td>64.6 [51.3–82.7]<br>(n=98)</td><td>48.4 [40.2–60.6]<br>(n=98)</td></tr><tr><td>Weight (kg)</td><td>70.8 [60.2–81.0]</td><td>71.2 [60.7–81.9]</td><td>-</td><td>-</td></tr><tr><td>Creatinine clearance</td><td>49.6 [45.0–54.1]</td><td>49.7 [45.2–54.1]</td><td>52.4 [45.4–55.4]</td><td>52.4 [45.2–55.4]</td></tr><tr><td>C0, mg/L</td><td>0.66 [0.32–1.11]</td><td>0.66 [0.32–1.11]</td><td>0.64 [0.35–1.05]</td><td>0.35 [0.22–0.55]</td></tr><tr><td>C3, mg/L</td><td>3.85 [3.25–4.72]</td><td>3.89 [3.26–4.76]</td><td>5.26 [4.10–6.42]</td><td>3.57 [2.88–4.59]</td></tr><tr><td>C4, mg/L</td><td>3.30 [2.72–4.07]</td><td>3.31 [2.72–4.04]</td><td>4.45 [3.53–5.21]</td><td>3.20 [2.60–3.96]</td></tr><tr><td rowspan="6">450 mg/48 h of VGCV</td><td>C5, mg/L</td><td>2.81 [2.27–3.54]</td><td>2.79 [2.26–3.50]</td><td>4.00 [2.9–4.43]</td><td>2.82 [2.39–3.45]</td></tr><tr><td>C12, mg/L</td><td>1.22 [0.84–1.78]</td><td>1.22 [0.84–1.78]</td><td>1.76 [1.33–2.44]</td><td>0.93 [0.79–1.49]</td></tr><tr><td>AUC0-24ss, mg*h/L</td><td>40.7 [31.2–53.8]<br>(n=3,672)</td><td>40.6 [31.2–53.8]<br>(n=1,225)</td><td>56.8 [44.0–71.2]<br>(n=98)</td><td>33.5 [27.8–41.2]<br>(n=98)</td></tr><tr><td>Weight (kg)</td><td>71.0 [60.4–81.6]</td><td>71.8 [61.3–82.3]</td><td>-</td><td>-</td></tr><tr><td>Creatinine clearance</td><td>31.9 [28.7–35.6]</td><td>32.3 [28.9–35.3]</td><td>33.8 [28.9–36.1]</td><td>33.6 [29.0–36.1]</td></tr><tr><td>C0, mg/L</td><td>0.31 [0.10–0.76]</td><td>0.33 [0.10–0.76]</td><td>0.33 [0.18–0.64]</td><td>0.16 [0.09–0.24]</td></tr><tr><td rowspan="6">450 mg/72 h of VGCV</td><td>C5, mg/L</td><td>2.91 [2.42–3.50]</td><td>2.86 [2.40–3.53]</td><td>4.45 [3.73–5.54]</td><td>2.94 [2.39–3.65]</td></tr><tr><td>C6, mg/L</td><td>2.52 [2.07–3.07]</td><td>2.49 [2.06–3.08]</td><td>4.06 [3.39–5.07]</td><td>3.20 [2.60–3.96]</td></tr><tr><td>C12, mg/L</td><td>1.34 [0.97–1.77]</td><td>1.30 [0.97–1.76]</td><td>2.66 [2.13–3.45]</td><td>0.99 [0.75–1.34]</td></tr><tr><td>AUC0-48ss, mg*h/L</td><td>54.6 [40.5–74.3]<br>Training (n=1,835)</td><td>54.6 [40.5–74.3]<br>Testing (n=612)</td><td>88.8 [69.5–115.2]</td><td>40.3 [32.5–47.4]<br>Validation: Caldés et al. model (n=98)</td></tr><tr><td>Weight (kg)</td><td>70.7 [60.3–81.3]</td><td>71.6 [62.2–82.9]</td><td>-</td><td>-</td></tr><tr><td>Creatinine clearance</td><td>17.1 [13.7–20.2]</td><td>17.0 [14.2–20.5]</td><td>18.8 [13.9–21.1]</td><td>18.8 [13.9–21.1]</td></tr><tr><td>C0, mg/L</td><td>0.97 [0.62–1.43]</td><td>0.96 [0.64–1.41]</td><td>0.53 [0.29–1.10]</td><td>0.53 [0.29–1.10]</td></tr><tr><td>C5, mg/L</td><td>3.86 [3.20–4.75]</td><td>3.89 [3.17–4.86]</td><td>5.74 [4.59–7.27]</td><td>5.74 [4.59–7.27]</td></tr><tr><td>C6, mg/L</td><td>3.43 [2.80–4.21]</td><td>3.45 [2.76–4.33]</td><td>5.33 [4.27–6.70]</td><td>5.33 [4.27–6.70]</td></tr><tr><td>C7, mg/L</td><td>3.08 [2.47–3.80]</td><td>3.07 [2.44–3.93]</td><td>5.06 [3.98–6.42]</td><td>5.06 [3.98–6.42]</td></tr><tr><td>C12, mg/L</td><td>2.13 [1.61–2.78]</td><td>2.08 [1.57–2.82]</td><td>4.07 [3.18–5.43]</td><td>4.07 [3.18–5.43]</td></tr><tr><td>AUC0-72ss, mg*h/L</td><td>121 [92.3–158]</td><td>122 [92.3–158]</td><td>147 [113–207]</td><td>147 [113–207]</td></tr></tbody></table>

## Influence of Deviation from Theoretical Sampling Times

We evaluated the impact of deviations from theoretical sampling times on the sensitivity of machine learning models by analyzing adjusted sampling times within the validation set. Specifically, we tested the effect of replacing C12 with C10 for the 900 mg/24 h, 450 mg/24 h, and 450 mg/48 h doses, and replacing C7 with C6 for the 450 mg/72 h dose, as these later sampling times are often challenging to implement in routine clinical settings.

## Results

### Patients and Data

A total of 4,895 simulated PK profiles for the 900 mg/24 h dose, 4,893 for 450 mg/24 h, 4,897 for 450 mg/48 h, and 2,447 for 450 mg/72 h were used to train and test the ML algorithms after exclusion of extreme or non-SS profiles.

The simulated validation set consisted in a total of 196 PK profiles (98 PK profiles per popPK model) for the

<footnote>ªMedian [IQR] is presented for continuous data; AUCss area under the curve at steady state obtained by trapezoidal method; IQR interquartile range; CX concentration at x hour after valganciclovir dose</footnote>
<table><caption>**Table 2** Observed Exposure Indices to Ganciclovir</caption><thead><tr><th rowspan="2"></th><th colspan="3">Valganciclovir dose</th></tr><tr><th>900 mg/24 h (n=2)</th><th>450 mg/24 h (n=14)</th><th>450 mg/48 h (n=2)</th></tr></thead><tbody><tr><td>Inter-dose AUC<sub>ss</sub> (mg.h/L)</td><td>94.6±46.9</td><td>61.2±26.5</td><td>109±38.2</td></tr><tr><td>Trough Concentration (mg/L)</td><td>2.19±1.75</td><td>1.10±1.13</td><td>0.19±0.11</td></tr><tr><td>Peak Concentration (mg/L)</td><td>8.72±4.10</td><td>5.94±2.73</td><td>8.69±5.96</td></tr><tr><td>Time of Peak Concentration (h)</td><td>2.45±0.97</td><td>1.94±0.91</td><td>2.10±1.39</td></tr><tr><td>Creatinine clearance (ml/min)</td><td>74.7±18.3</td><td>51.5±16.4</td><td>32.3±10.3</td></tr></tbody></table>

Results are given as mean±SD; AUC<sub>ss</sub> area under the curve at steady state obtained by trapezoidal method

doses of 900 mg/24 h, 450 mg/24 h, and 450 mg/48 h, and 98 profiles for the 450 mg/72 h dose. The characteristics and the references inter-dose AUC<sub>ss</sub> of the training, testing, and simulated validation sets are presented in the Table 1. Details of the simulated data and scripts used for these analyses are available on Hamza SAYADI's GitHub repository at the following link: https://github.com/SAYADI-hamza/Estimation-of-Ganciclovir-Exposure-in-adults-transplant-patients-by-Machine-Learning. A comprehensive summary of demographic and clinical data for the 22 renal transplant patients is provided in the supplemental data (Table S1). Of these, a total of 18 patients were included in the validation set. In detail, three patients were excluded due to consistently low plasma concentrations of GCV, even after the expected morning dose, and the data for one patient could not be retrieved. The observed concentration-time profiles of GCV for these 18 patients are shown in Fig. 1 and the exposure indices for GCV are presented in Table 2.

## ML Model

Among the ML models investigated, XGBoost demonstrated the best performance on the four training sets based on the relative MPE. Interestingly, the SVM exhibited a performance very close to that of XGBoost. Detailed results are available in the supplemental data (Table S2).

Analyzing the impact of the different predictive concentrations with XGBoost, we observed variations according to the VGCV dosage: for 900 mg/24 h, C4 > C12 > C3 > C6; for 450 mg/24 h, C12 > C4 > C3 > C5 ≈ C0; for 450 mg/48 h, C12 > C0 > C5 > C6; and for 450 mg/72 h, C0 > C7 > C12 > C6 ≈ C5. The importances plots obtained in the training sets are presented in Fig. 2. CrCL was always shown to be one of the least influential predictors. The predictive concentrations ultimately selected for each XGBoost algorithm and each VGCV dosage are detailed in Table 3.

The 12 XGBoost algorithms demonstrated excellent performance in terms of RMSE and R² across both training and testing datasets. In the testing sets, the models

showed relative MPEs close to zero, relative RMSEs below 8.5%. All results are presented in Table 4. Notably, the XGBoost algorithms consistently outperformed the multiple linear regression models. Detailed results are available on supplemental data (Table S3).

## Evaluation of XGBoost Algorithms Using Simulated Validation Set

Simulations based on the Caldés model showed higher concentrations and AUC<sub>ss</sub> values, while those based on the Chen model led to lower values compared to the data used to train the XGBoost algorithms.

When evaluating XGBoost algorithms using two concentrations between C0 and C12 (XGBoost_2C0-C12) for all VGCV doses combined, patients simulated by the Caldés model exhibited relative biases ranging from -3.48% to 7.65% and relative RMSEs from 8.16% to 13.6%. In contrast, for patients simulated with the Chen model, relative biases ranged from 3.86% to 15.0% and relative RMSEs were between 15.6% and 20.8%.

For the XGBoost algorithms using three concentrations between C0 and C12 (XGBoost_3C0-C12), the Caldés model patients showed relative biases from -4.30% to 11.4% and relative RMSEs from 8.50% to 14.50%. For the Chen model patients, relative biases ranged from 8.9% to 16.5% and relative RMSEs from 10.7% to 19.7%.

With XGBoost algorithms using three concentrations between C0 and C6 (XGBoost_3C0-C6), patients simulated with the Caldés model had relative biases from -8.67% to 5.84% and relative RMSEs from 9.62% to 15.5%. In comparison, Chen model patients exhibited relative biases ranging from 14.2% to 27.5% and relative RMSEs from 18.5% to 33.0%.

All detailed results are available in Table 5. Scatterplots of the predicted AUC<sub>ss</sub> compared to the reference AUC<sub>ss</sub> are presented in Fig. 3. Additionally, scatterplots of biases as a function of the reference AUC<sub>ss</sub> values are available in the supplemental Figure S1.

The XGBoost algorithms consistently outperformed the multiple linear regression models (Supplemental Table S4).

<figure><img src="image_5.png" /></figure>
<figure><img src="image_6.png" /><figcaption>Fig. 2 Importance plot of XGBoost algorithms for ganciclovir inter-dose AUCss predictions</figcaption></figure>

<table><caption>**Table 3** Predictive Concentrations by Type of XGBoost Algorithms and VGCV Dosage</caption><thead><tr><th>Dosage of VGCV</th><th>XGBoost_2C0-C12</th><th>XGBoost_3C0-C12</th><th>XGBoost_3C0-C6</th></tr></thead><tbody><tr><td>900 mg/24 h</td><td>C4 and C12</td><td>C3, C4 and C12</td><td>C3, C4 and C6</td></tr><tr><td>450 mg/24 h</td><td>C4 and C12</td><td>C3, C4 and C12</td><td>C0, C4 and C5</td></tr><tr><td>450 mg/48 h</td><td>C0 and C12</td><td>C0, C5 and C12</td><td>C0, C5 and C6</td></tr><tr><td>450 mg/72 h</td><td>C0 and C7</td><td>C0, C7 and C12</td><td>C0, C5 and C6</td></tr></tbody></table>

CX concentration at x hour after valganciclovir dose; VGCV valganciclovir, XGBoost_2C0-C12 XGBoost algorithm using two concentrations between C0 and C12; XGBoost_3C0-C12 XGBoost algorithm using three concentrations between C0 and C12; XGBoost_3C0-C6 XGBoost algorithm using three concentrations between C0 and C6

## External Evaluation of XGBoost Algorithms in Real Patients

When evaluating our XGBoost algorithms on real patients, we observed the following results: XGBoost_2C0-C12 demonstrated a relative bias of 1.26% and a relative RMSE of 12.68%. For XGBoost_3C0-C12, the relative bias increased to 2.53% and the relative RMSE rose to 14.10%. XGBoost_3C0-C6 demonstrate a relative bias of -18.02% and a relative RMSE of 19.38%.

## Comparison to popPK and MAP-BE

The performance of AUCss estimates by MAP-BE in the simulated validation datasets, based on the popPK models of Vezina and Lalagkas, were overall worse than those obtained with XGBoost algorithms. XGBoost consistently outperformed MAP-BE with the Lalagkas *et al.* model, surpassing it in 20 out of 21 relative bias comparisons, achieving lower relative RMSE values, and showing fewer MPEs outside the ±20% interval. For the Vezina *et al.*
<table><caption>**Table 4** Performances of the XGBoost algorithms in the training and testing datasets</caption><thead><tr><th></th><th>XGBoost algorithms</th><th>Data set</th><th>RMSE, mg.h/L</th><th>R<sup>2</sup></th><th>Relative MPE, %</th><th>Relative RMSE, %</th><th>Number of MPE of the ± 20% interval, n (%)</th></tr></thead><tbody><tr><td rowspan="6">900 mg/24 h of VGCV</td><td rowspan="2">C4, C12</td><td>Training set (n=3,671)</td><td>3.81<sup>a</sup></td><td>0.97<sup>a</sup></td><td>-</td><td>-</td><td>-</td></tr><tr><td>Testing set (n=1,224)</td><td>3.47</td><td>0.98</td><td>0.42</td><td>5.77</td><td>14 (1.1%)</td></tr><tr><td rowspan="2">C3, C4, C12</td><td>Training set (n=3,671)</td><td>1.84<sup>a</sup></td><td>0.96<sup>a</sup></td><td>-</td><td>-</td><td>-</td></tr><tr><td>Testing set (n=1,224)</td><td>1.76</td><td>0.99</td><td>0.13</td><td>2.69</td><td>1 (0.1%)</td></tr><tr><td rowspan="2">C3, C4, C6</td><td>Training set (n=3,671)</td><td>4.26<sup>a</sup></td><td>0.96<sup>a</sup></td><td>-</td><td>-</td><td>-</td></tr><tr><td>Testing set (n=1,224)</td><td>4.17</td><td>0.96</td><td>0.60</td><td>6.37</td><td>8 (0.7%)</td></tr><tr><td rowspan="6">450 mg/24 h of VGCV</td><td rowspan="2">C4, C12</td><td>Training set (n=3,660)</td><td>2.08<sup>a</sup></td><td>0.99<sup>a</sup></td><td>-</td><td>-</td><td>-</td></tr><tr><td>Testing set (n=1,223)</td><td>2.19</td><td>0.99</td><td>0.04</td><td>4.41</td><td>4 (0.3%)</td></tr><tr><td rowspan="2">C3, C4, C12</td><td>Training set (n=3,660)</td><td>1.29<sup>a</sup></td><td>0.99<sup>a</sup></td><td>-</td><td>-</td><td>-</td></tr><tr><td>Testing set (n=1,223)</td><td>1.29</td><td>0.99</td><td>-0.02</td><td>2.55</td><td>0 (0.0%)</td></tr><tr><td rowspan="2">C0, C4, C5</td><td>Training set (n=3,660)</td><td>2.32<sup>a</sup></td><td>0.98<sup>a</sup></td><td>-</td><td>-</td><td>-</td></tr><tr><td>Testing set (n=1,223)</td><td>2.30</td><td>0.98</td><td>-0.13</td><td>4.45</td><td>4 (0.3%)</td></tr><tr><td rowspan="6">450 mg/48 h of VGCV</td><td rowspan="2">C0, C12</td><td>Training set (n=3,672)</td><td>4.59<sup>a</sup></td><td>0.97<sup>a</sup></td><td>-</td><td>-</td><td>-</td></tr><tr><td>Testing set (n=1,225)</td><td>4.64</td><td>0.97</td><td>0.44</td><td>6.77</td><td>18 (1.5%)</td></tr><tr><td rowspan="2">C0, C5, C12</td><td>Training set (n=3,672)</td><td>3.04<sup>a</sup></td><td>0.99<sup>a</sup></td><td>-</td><td>-</td><td>-</td></tr><tr><td>Testing set (n=1,225)</td><td>3.07</td><td>0.99</td><td>0.35</td><td>4.43</td><td>5 (0.4%)</td></tr><tr><td rowspan="2">C0, C5, C6</td><td>Training set (n=3,672)</td><td>4.23<sup>a</sup></td><td>0.97<sup>a</sup></td><td>-</td><td>-</td><td>-</td></tr><tr><td>Testing set (n=1,225)</td><td>4.23</td><td>0.97</td><td>0.32</td><td>5.72</td><td>11 (0.9%)</td></tr><tr><td rowspan="6">450 mg/72 h of VGCV</td><td rowspan="2">C0, C7</td><td>Training set (n=1,835)</td><td>9.99<sup>a</sup></td><td>0.97<sup>a</sup></td><td>-</td><td>-</td><td>-</td></tr><tr><td>Testing set (n=612)</td><td>9.85</td><td>0.97</td><td>1.30</td><td>8.16</td><td>8 (1.3%)</td></tr><tr><td rowspan="2">C0, C7, C12</td><td>Training set (n=1,835)</td><td>8.20<sup>a</sup></td><td>0.97<sup>a</sup></td><td>-</td><td>-</td><td>-</td></tr><tr><td>Testing set (n=612)</td><td>8.48</td><td>0.97</td><td>1.08</td><td>7.20</td><td>3 (0.5%)</td></tr><tr><td rowspan="2">C0, C5, C6</td><td>Training set (n=1,835)</td><td>10.9<sup>a</sup></td><td>0.96<sup>a</sup></td><td>-</td><td>-</td><td>-</td></tr><tr><td>Testing set (n=612)</td><td>10.7</td><td>0.95</td><td>1.46</td><td>8.47</td><td>14 (2.3%)</td></tr></tbody></table>

model, XGBoost performed better in 12 out of 18 relative bias comparisons, 12 out of 18 relative RMSE comparisons, and 13 out of 18 assessments of MPEs outside the ± 20% interval. All detailed results are available in Table 5. Figure 4 illustrates the performance of MAP-BE

using three concentrations between C0 and C12, which is the most performant among the MAP-BE models, compared to the XGBoost algorithms that use either two or three concentrations between C0 and C12, or three concentrations between C0 and C6.

<figure><img src="image_7.png" /></figure>

<footnote><sup>a</sup>Values obtained after tenfold cross-validation; CX concentration at x hour after valganciclovir dose; VGCV valganciclovir dose</footnote>
<table><caption>**Table 5** Performances of the XGBoost Algorithms and MAP-BE in the Simulated Validation Datasets</caption><thead><tr><th rowspan="2">AUCss estimation method</th><th rowspan="2">Performances</th><th colspan="6">Patients from</th></tr><tr><th>Caldés et al. model (n=98)</th><th>Chen et al. model (n=98)</th><th>Caldés et al. model (n=98)</th><th>Chen et al. model (n=98)</th><th>Caldés et al. model (n=98)</th><th>Chen et al. model (n=98)</th></tr></thead><tbody><tr><td rowspan="4">900 mg/24 h of VGCV</td><td rowspan="3">XGBoost</td><td>Relative MPE, (%)</td><td>2 samples (C4 and C12)</td><td>3 samples (C3, C4 and C12)</td><td>3 samples (C3, C4 and C6)</td><td>3 samples (C3, C4 and C6)</td><td>3 samples (C3, C4 and C6)</td></tr><tr><td>Relative RMSE, (%)</td><td>-0.10 [-2.81-2.61]</td><td>15.0 [13.2-16.8]</td><td>1.54 [-0.55-3.62]</td><td>8.89 [7.70-10.0]</td><td>5.16 [2.24-8.07]</td><td>18.1 [15.2-21.0]</td></tr><tr><td>Number of MPE of the ±20% interval</td><td>13.6</td><td>17.5</td><td>10.6</td><td>10.7</td><td>15.5</td><td>23.2</td></tr><tr><td rowspan="3">MAP-BE Vezina et al</td><td>Relative MPE, (%)</td><td>-12.4 [-15.1- -9.71]</td><td>8.96 [5.91-12.0]</td><td>-11.4 [-13.88-8.97]</td><td>8.00 [5.22-10.8]</td><td>-14.1 [-16.4-11.8]</td><td>3.04 [0.49-5.59]</td></tr><tr><td>Relative RMSE, (%)</td><td>18.4 s</td><td>17.7</td><td>16.6</td><td>16.1</td><td>18.2</td><td>13.2</td></tr><tr><td>Number of MPE of the ±20% interval</td><td>33 (33.7%)</td><td>20 (20.4%)</td><td>29 (29.6%)</td><td>13 (13.3%)</td><td>31 (31.6%)</td><td>13 (13.3%)</td></tr><tr><td rowspan="3">MAP-BE Lalagkas et al</td><td>Relative MPE, (%)</td><td>34.5 [29.8-39.2]</td><td>68.5 [64.4-72.5]</td><td>33.5 [29.4-37.8]</td><td>63.1 [58.8-67.5]</td><td>33.6 [29.1-38.1]</td><td>71.1 [66.6-75.5]</td></tr><tr><td>Relative RMSE, (%)</td><td>41.8</td><td>73.6</td><td>39.6</td><td>66.8</td><td>40.5</td><td>70.7</td></tr><tr><td>Number of MPE of the ±20% interval</td><td>67 (68.4%)</td><td>96 (98%)</td><td>68 (69.4%)</td><td>96 (98%)</td><td>67 (68.4%)</td><td>93 (94.9%)</td></tr><tr><td rowspan="4">450 mg/24 h of VGCV</td><td rowspan="3">XGBoost</td><td>Relative MPE, (%)</td><td>2 samples (C4 and C12)</td><td>3 samples (C3, C4 and C12)</td><td>3 samples (C0, C4 and C5)</td><td>3 samples (C0, C4 and C5)</td><td>3 samples (C0, C4 and C5)</td></tr><tr><td>Relative RMSE, (%)</td><td>0.95 [-1.12-3.01]</td><td>13.3 [11.6-14.9]</td><td>2.72 [1.12-4.33]</td><td>10.3 [9.01-11.6]</td><td>-6.76 [-8.76-4.75]</td><td>14.2 [11.9-16.6]</td></tr><tr><td>Number of MPE of the ±20% interval</td><td>10.4</td><td>15.6</td><td>8.50</td><td>12.2</td><td>12.1</td><td>18.5</td></tr><tr><td rowspan="3">MAP-BE Vezina et al</td><td>Relative MPE, (%)</td><td>-16.7 [-18.8-14.6]</td><td>1.88 [-0.63-4.40]</td><td>-14.6 [-16.4-12.8]</td><td>2 [-0.15-4.16]</td><td>-20.2 [-22.4-17.9]</td><td>3.81 [0.99-6.65]</td></tr><tr><td>Relative RMSE, (%)</td><td>15.6</td><td>12.8</td><td>12.2</td><td>11.0</td><td>23.0</td><td>14.7</td></tr><tr><td>Number of MPE of the ±20% interval</td><td>21 (21.4%)</td><td>9 (9.2%)</td><td>6 (6.1%)</td><td>8 (8.2%)</td><td>71 (72.4%)</td><td>10 (10.2%)</td></tr><tr><td rowspan="3">MAP-BE Lalagkas et al</td><td>Relative MPE, (%)</td><td>34.8 [29.9-39.8]</td><td>83.5 [77.4-89.6]</td><td>34.5 [30.0-38.9]</td><td>78.6 [73.1-84.1]</td><td>21.5 [17.1-26.0]</td><td>71.6 [65.9-77.3]</td></tr><tr><td>Relative RMSE, (%)</td><td>42.8</td><td>88.9</td><td>41.0</td><td>83.3</td><td>31.1</td><td>77.2</td></tr><tr><td>Number of MPE of the ±20% interval</td><td>71 (72.4%)</td><td>98 (100%)</td><td>71 (72.4%)</td><td>98 (100%)</td><td>42 (42.9%)</td><td>97 (99%)</td></tr></tbody></table>
<table><caption>**Table 5 (continued)**</caption><thead><tr><th rowspan="2">AUCss estimation method</th><th rowspan="2">Performances</th><th colspan="6">Patients from</th></tr><tr><th>Caldés et al. model (n=98)</th><th>Chen et al. model (n=98)</th><th>Caldés et al. model (n=98)</th><th>Chen et al. model (n=98)</th><th>Caldés et al. model (n=98)</th><th>Chen et al. model (n=98)</th></tr></thead><tbody><tr><td rowspan="3">450 mg/48 h of VGCV</td><td>XGBoost</td><td>Relative MPE, (%)</td><td>-3.48 [-5.69-1.26]</td><td>3.86 [-0.20-7.91]</td><td>-4.3 [-5.90-2.69]</td><td>16.5 [14.4-18.6]</td><td>-8.67 [-10.4-6.92]</td><td>27.5 [23.9-31.2]</td></tr><tr><td></td><td>Relative RMSE, (%)</td><td>8.16</td><td>20.76</td><td>9.14</td><td>19.65</td><td>10.2</td><td>33.0</td></tr><tr><td></td><td>Number of MPE of the ±20% interval</td><td>8 (8.2%)</td><td>29 (29.6%)</td><td>4 (4.1%)</td><td>33 (33.7%)</td><td>10 (10.2%)</td><td>73 (74.5%)</td></tr><tr><td rowspan="3">MAP-BE Vezina et al</td><td></td><td>Relative MPE, (%)</td><td>-26.5 [-28.6-24.5]</td><td>17.3 [13.1-21.5]</td><td>-24.7 [-26.4-22.9]</td><td>17.7 [13.8-21.6]</td><td>-27.6 [-29.5-25.7]</td><td>20.1 [16.3-23.9]</td></tr><tr><td></td><td>Relative RMSE, (%)</td><td>28.4</td><td>27.3</td><td>26.2</td><td>26.4</td><td>29.2</td><td>27.8</td></tr><tr><td></td><td>Number of MPE of the ±20% interval</td><td>78 (79.6%)</td><td>42 (42.9%)</td><td>74 (75.5%)</td><td>41 (41.8%)</td><td>82 (83.7%)</td><td>42 (42.9%)</td></tr><tr><td rowspan="3">MAP-BE Lalagkas et al</td><td></td><td>Relative MPE, (%)</td><td>24 [21.6-28.3]</td><td>117 [108-126]</td><td>-0.11 [-3.83-3.60]</td><td>115 [107-123]</td><td>17.8 [14.9-22.9]</td><td>120 [112-129]</td></tr><tr><td></td><td>Relative RMSE, (%)</td><td>34.6</td><td>125</td><td>18.7</td><td>122</td><td>30.0</td><td>127</td></tr><tr><td></td><td>Number of MPE of the ±20% interval</td><td>46 (46.9%)</td><td>98 (100%)</td><td>28 (28.6%)</td><td>98 (100%)</td><td>44 (44.9%)</td><td>98 (100%)</td></tr><tr><td rowspan="3">450 mg/72 h of VGCV</td><td>XGBoost</td><td></td><td>2 samples (C0 and C7)</td><td></td><td>3 samples (C0, C7 and C12)</td><td></td><td>3 samples (C0, C5 and C6)</td><td></td></tr><tr><td></td><td>Relative MPE, (%)</td><td>7.65 [6.14-9.16]</td><td>-</td><td>11.4 [9.59-13.2]</td><td>-</td><td>5.84 [4.31-7.38]</td><td>-</td></tr><tr><td></td><td>Relative RMSE, (%)</td><td>10.8</td><td>-</td><td>14.5</td><td>-</td><td>9.62</td><td>-</td></tr><tr><td rowspan="3">MAP-BE Lalagkas et al</td><td></td><td>Number of MPE of the ±20% interval</td><td>2 (2%)</td><td>-</td><td>15 (15.3%)</td><td>-</td><td>3 (3.1%)</td><td>-</td></tr><tr><td></td><td>Relative MPE, (%)</td><td>24.75 [20.3-29.2]</td><td>-</td><td>34.8 [30.5-39.1]</td><td>-</td><td>23.2 [19.0-27.4]</td><td>-</td></tr><tr><td></td><td>Relative RMSE, (%)</td><td>33.26</td><td>-</td><td>40.9</td><td>-</td><td>31.3</td><td>-</td></tr><tr><td></td><td></td><td>Number of MPE of the ±20% interval</td><td>51 (52%)</td><td>-</td><td>72 (73.5%)</td><td>-</td><td>51 (52%)</td><td>-</td></tr></tbody></table>

AUCss area under the curve at steady state obtained by trapezoidal method; MAP-BE maximum a posteriori Bayesian estimation; CX concentration at x hour after valganciclovir dose; the values in square brackets represent the 95% confidence intervals

Similarly, the performance of AUCss estimates by MAP-BE in the real patients was consistently worse than those obtained with the XGBoost algorithms. XGBoost consistently outperformed MAP-BE from the Vezina *et al.* model,

achieving lower relative RMSE values, smaller relative biases, and fewer MPEs outside the ±20% range. Likewise, for the Lalagkas *et al.* model, XGBoost demonstrated superior performance, with lower relative RMSE values and

<figure><img src="image_8.png" /></figure>
<figure><img src="image_9.png" /><figcaption>**Fig. 3** Scatterplots of ML predicted vs reference ganciclovir AUCs in the testing data sets</figcaption></figure>
<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /></figure>

<figure><img src="image_16.png" /><figcaption>Fig. 4 Ganciclovir AUCss prediction performance by MAP-BE and XGBoost algorithms</figcaption></figure>

<figure><img src="image_17.png" /></figure>
smaller relative biases, except in the scenario with three concentrations between C0 and C6. Additionally, XGBoost produced fewer MPEs outside the ±20% range, except in the three-concentration scenario between C0 and C12, where both methods performed similarly. Detailed results are available in Table 6.

## Influence of Deviation from Theoretical Sampling Times

The evaluation of deviations from theoretical sampling times indicates a notable degradation in XGBoost model performance, particularly in the Chen *et al.* model, where both relative bias and relative RMSE values increased significantly (from 3.86% to 29.7% and from 15.6% to 28.0% for the largest increase). Full results are available on supplemental data (Table S5).

## Discussion

In this work, we developed ML algorithms to estimate the inter-dose AUCss of GCV in adults' SOT prophylaxis. Our algorithms were trained on Monte Carlo simulations based on two models, using only two or three plasma concentrations and CrCL as predictive variables. As observed in some of our previous work, the XGBoost algorithm outperformed linear regression, linear SVM, MARS and random forest in predicting drug exposure (35–37). Interestingly, SVM also demonstrated very good performance, with differences that were not clinically significant. The performance in the training and testing sets was excellent, with bias close to zero and imprecision less than 8.50%.

For external validation, we generated new patients using two other popPK models. The results indicated a higher bias and greater imprecision for patients from the Chen model

compared to those from the Caldés model. We observed that the ML algorithms systematically overestimated AUCss in simulations from the Chen model. However, this decreased performance was anticipated, as the models by Vezina, Lalagkas, and Caldés were developed on European patients with kidney, liver, lung, or heart transplants, while the Chen model was developed from a Chinese population of solely kidney transplant patients. However, the MAP-BE approach using the Vezina model sometimes performed better in the Chen population than in the Caldés population, both of which are European-based models. This suggests that factors beyond population origin, such as structural model parameters, may also play a role. Specifically, we noted that while all models were based on two-compartment structures with Ka and lag time parameters, the clearance values in the Vezina and Chen models were similar and approximately twice as high as those in the Caldés model. This difference in clearance values may partially explain the observed differences in model performance, indicating that structural model characteristics are critical to consider when interpreting cross-population predictions.

The utility of developing an ML algorithm when popPK models are available for MAP-BE may be questioned. To answer that, we compared the performance of our ML algorithms with MAP-BE from the two popPK models used to train the ML algorithms, using an external dataset generated by simulation from two external popPK models. We found that the XGBoost algorithm performed better than MAP-BE based on the Lalagkas model. Although the MAP-BE performance of the Vezina model was close to that of the XGBoost algorithms for validation from the Chen population, it was poor for the Caldés population. This suggests greater generalizability and robustness of the estimates provided by the ML algorithms compared to those from MAP-BE. This superiority could be attributed to XGBoost's ability to handle complex, nonlinear relationships within the data,

<table><caption>**Table 6** Performances of the XGBoost Algorithms and MAP-BE in Real Patient Validation Dataset</caption><thead><tr><th>AUCss estimation method</th><th>Parameters</th><th>2 samples between C0 and C12</th><th>3 samples between C0 and C12</th><th>3 samples between C0 and C6</th></tr></thead><tbody><tr><td rowspan="3">XGBoost</td><td>Relative MPE, (%)</td><td>1.26</td><td>2.53</td><td>-18.0</td></tr><tr><td>Relative RMSE, (%)</td><td>12.7</td><td>14.1</td><td>19.4</td></tr><tr><td>Number of MPE of the ±20% interval</td><td>3 (16.7%)</td><td>4 (22.2%)</td><td>4 (22.2%)</td></tr><tr><td rowspan="3">MAP-BE<br>Vezina et al.</td><td>Relative MPE, (%)</td><td>-33.9</td><td>-34.5</td><td>-41.0</td></tr><tr><td>Relative RMSE, (%)</td><td>36.1</td><td>36.4</td><td>43.2</td></tr><tr><td>Number of MPE of the ±20% interval</td><td>16 (88.9%)</td><td>16 (88.9%)</td><td>17 (94.4%)</td></tr><tr><td rowspan="3">MAP-BE<br>Lalagkas et al.</td><td>Relative MPE, (%)</td><td>12.9</td><td>10.6</td><td>-4.19</td></tr><tr><td>Relative RMSE, (%)</td><td>37.2</td><td>33.8</td><td>31.7</td></tr><tr><td>Number of MPE of the ±20% interval</td><td>6 (33.3%)</td><td>4 (22.2%)</td><td>9 (50.0%)</td></tr></tbody></table>

AUCss area under the curve at steady state; MAP-BE maximum a posteriori Bayesian estimation
even though it was trained on simulated data. It also highlights that the residual error estimated using nonlinear mixed effects models' approach is probably overestimated.

We also evaluated our algorithms on real renal transplant patients. Algorithms using 2 or 3 samples between C0 and C12 performed excellently, while those restricted to 3 samples between C0 and C6 were less effective, showing a systematic underestimation of the inter-dose AUCss. This can be attributed to the fact that the reference inter-dose AUCss are determined using the trap ezoidal method, which lacks real data points between C5 and C24 or C48 and does not capture the bi-exponential decay described by the popPK models. Consequently, extrapolated concentrations at 12 h after the VGCV dose and inter-dose AUCss might be overestimated, and this overestimation might not be captured by algorithms using only three samples between C0 and C6. When comparing these predictions to those made by MAP-BE, XGBoost demonstrated superior performance in estimating AUCss. These findings emphasize the importance of consider ing all three evaluation criteria: rMPE, rRMSE, and the number of MPEs outside the ±20% range. A low rMPE combined with a high rRMSE indicates that, while the average error remains small (meaning predictions do not systematically deviate in one direction), individual errors exhibit high variability.

The XGBoost algorithm is not a simple formula. To enhance its usability, we developed a Shiny interface for real-time calculation of AUC0-24ss (38). The application, available at https://sayadi-h.shinyapps.io/AUC_GCV/, is currently for demonstration purposes. To use it, first select the appropriate GCV dosage from the four options: 900 mg/24 h, 450 mg/24 h, 450 mg/48 h, or 450 mg/72 h. Next, choose the model based on the number of possible blood samples. Finally, simply enter the eGFR and GCV plasma concentrations, and you're all set to obtain the results.

Interpretability remains a critical factor in the clinical acceptance of machine learning-based model-informed precision dosing (MIPD) tools. To enhance transparency, we generated variable importance plots (VIP) (Fig. 2), which explain the primary drivers of AUC predictions at the population level. Additionally, a future release of our algorithm will incorporate breakdown plots, providing deeper insights at the individual level and further enhancing the explainability of predictions.

Beyond interpretability, many MIPD tools struggle with clinical adoption due to a lack of user-centered design. In contrast, our approach prioritizes usability by validating the model through both external simulations and real patient data. The Shiny app was specifically developed to improve accessibility and ease of use for clinicians, addressing common barriers such as limited availability.

Therapeutic drug monitoring (TDM) of GCV for SOT is not currently widespread. Nonetheless, as noted earlier, GCV demonstrates interindividual PK variability, especially among patients with reduced GFR. Moreover, a multicenter randomized study demonstrated that the increased exposure achieved with VGCV compared to oral GCV was associated with a lower incidence of CMV viremia (VGCV: 2.9% vs GCV: 10.4%, P = 0.001) and a reduction in the incidence of CMV viremia breakthroughs by day 100 post-SOT (incidence of 1.3% with an AUC0-24 h of 50 mg*h/L, while an AUC0-24 h of 25 mg*h/L increases the risk of viremia by 8 times) (12). Building on these results, another prospective, randomized, controlled study compared two groups: group A followed the manufacturer's dosing recommendations, while group B had their dosages adjusted based on target exposures. Group B showed faster viral clearance (12.5 vs. 17.6 days, P = 0.125), as well as significantly lower relapse rates (9.01% vs. 66.67%) and late infection rates (7.7% vs. 36.7%) compared to group A (13). Our ML algorithms could help to promote MIPD of VGCV, especially by using the one based on 2 sampled rending easier its use in routine practice.

This study has some limitations. One key limitation is that while Wiltshire *et al.* is often cited as the primary source defining AUC targets for GCV, other studies, such as Padulles *et al.*, have also demonstrated the relevance of these targets. However, the literature on GCV AUC targets remains limited. By simplifying GCV exposure estimation, our exposure prediction models could help fill this gap and facilitate future research on exposure-effect relationships.

While our ML models have shown promise in estimating AUC, they fundamentally differ from MAP-BE by directly estimating AUC without modeling the time-dependent PK dynamics. This difference represents a limitation, as ML models do not explicitly incorporate the evolving drug concentration over time, which limits their generalizability across varying dosing regimens or modified PK profiles.

Additionally, our findings on deviations from theoretical sampling times highlight a limitation of ML models, which are sensitive to precise sampling times. While these models have demonstrated promise in predicting drug exposure, our results suggest that their performance may be less robust when sampling times deviate from the theoretical. This issue is particularly evident in models like the Chen *et al.* model, where deviations resulted in a significant increase in error metrics. Although MAP-BE is generally more flexible regarding sampling time deviations, a recent study indicates that it, too, can be affected by such deviations (39). Future research should consider incorporating sampling time adjustments or exploring hybrid approaches that combine mechanistic modeling with ML techniques to enhance robustness.

Moreover, the validation of our algorithms was partially conducted on simulated patients. Our simulated AUCss
values are heavily dependent on the two popPK models used and the characteristics of the patient populations on which they were based. These models may not fully capture the variability and heterogeneity present in broader and more diverse patient populations, a fundamental limitation inherent to in silico approaches. Additionally, the renal transplant recipients had five blood samples and not a full PK profile, and no real patients with a dosing regimen of 450 mg every three days were investigated. Caution is warranted when applying the algorithm, particularly if their characteristics differ from those of the populations used to develop the popPK models. Future research should aim to include diverse patient populations with comprehensive PK profiles in external validation studies to improve the generalizability of our findings.

It is also essential to note that the ML algorithms were trained on two popPK models that eGFR differently: the Cockcroft-Gault formula for the Vezina model and the CKD-EPI formula for the Lalagkas model. The CKD-EPI formula includes race in its calculations of eGFR, which contradicts the current recommendations of European and American nephrology organizations advocating for race-neutral equations. This inclusion could potentially perpetuate health inequalities, particularly when developing AI-based models that might inadvertently incorporate such inductive bias. This raises the question of the generalizability of the ML algorithm when using various methods to estimate GFR. To address this, it is important to recall that eGFR is the least impactful predictive variable in terms of prediction accuracy. Additionally, in the testing data set, eGFR was estimated solely by the Cockcroft-Gault formula, yet the ML algorithms still yielded satisfactory results. To illustrate this discussion, let's consider a hypothetical scenario: A 50-year-old patient weighing 60 kg, with a plasma creatinine level of 70 µmol/L, who has ganciclovir concentrations of 5.20 mg/L at C4h and 1.14 mg/L at T12h while on a 900 mg/24 h VGCV regimen. CrCL is estimated at 94.9 ml/min using the Cockcroft-Gault formula and 104.8 ml/min/1.73 m² using the CKD-EPI formula. The AUCss estimated for this patient is 54.0 mg*h/L with Cockcroft-Gault and 53.0 mg*h/L with CKD-EPI. This example demonstrates that AUCss predictions remain consistent between the two methods of eGFR, confirming that the ML algorithm is robust and generalizable regardless of the method used to estimate GFR.

In conclusion, we have developed and validated XGBoost ML algorithms for accurate estimation of GCV inter-dose AUCss. These algorithms were evaluated on both simulated patient data and real patient data. Although this tool requires further validation, it simplifies MIPD by requiring fewer samples than traditional methods. This advancement could facilitate the assessment of the relevance of GCV TDM in clinical studies and contribute to the development of future recommendations for its implementation in routine practice.

**Supplementary Information** The online version contains supplementary material available at https://doi.org/10.1208/s12248-025-01034-9.

**Author contributions** HS and JBW Substantially contributed to the conception and design of the study, performed data acquisition and analysis, and drafted the manuscript. Provided final approval of the version to be published and agrees to be accountable for all aspects of the work. YF, ML, PM: Played a key role in the interpretation of data, critically revised the manuscript for important intellectual content, and provided final approval of the version to be published. Agrees to be accountable for all aspects of the work. CC, SAZ and PAB Participated in the acquisition and analysis of data, contributed to drafting and revising the manuscript, and provided final approval of the manuscript. Agrees to accountability for the work's integrity.

**Funding** Open access funding provided by Université de Limoges. This work is part of the DIGPHAT project which was supported by a grant from the French government, managed by the National Research Agency (ANR), under the France 2030 program, with reference ANR-22-PESN-0017.

**Data Availability** The code used to generate the simulated data, along with the corresponding CSV files, is publicly available on GitHub at https://github.com/SAYADI-hamza/Estimation-of-Ganciclovir-Exposure-in-adults-transplant-patients-by-Machine-Learning. Due to privacy and ethical restrictions, the data from real patients cannot be made publicly available. However, these data can be provided by the corresponding authors upon reasonable request, subject to applicable data protection regulations and institutional guidelines.

## Declarations

**Conflict of Interest** No conflicts of interest to declare.

**Open Access** This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

## References

1. Zuhair M, Smit GSA, Wallis G, Jabbar F, Smith C, Devleesschauwer B, et al. Estimation of the worldwide seroprevalence of cytomegalovirus: A systematic review and meta-analysis. Rev Med Virol. 2019;29:e2034.

2. Kotton CN, Torre-Cisneros J, International CMV Symposium Faculty, Aguado JM, Alain S, Baldanti F, et al. Cytomegalovirus in the transplant setting: Where are we now and what happens next? A report from the International CMV Symposium 2021. Transpl Infect Dis. 2022;24:e13977.

3. Fishman JA. Infection in solid-organ transplant recipients. N Engl J Med. 2007;357:2601-14.

4. Ljungman P, Boeckh M, Hirsch HH, Josephson F, Lundgren J, Nichols G, et al. Definitions of cytomegalovirus infection
and disease in transplant patients for use in clinical trials. Clin Infect Dis. 2017;64:87–91.

5. Kotton CN, Kumar D, Caliendo AM, Huprikar S, Chou S, Danziger-Isakov L, et al. The Third International Consensus Guidelines on the management of cytomegalovirus in solid-organ transplantation. Transplantation. 2018;102:900–31.

6. Razonable RR, Humar A. Cytomegalovirus in solid organ transplant recipients-Guidelines of the American Society of Transplantation Infectious Diseases Community of Practice. Clin Transplant. 2019;33:e13512.

7. Pescovitz MD, Rabkin J, Merion RM, Paya CV, Pirsch J, Freeman RB, et al. Valganciclovir results in improved oral absorption of ganciclovir in liver transplant recipients. Antimicrob Agents Chemother. 2000;44:2811–5.

8. Grayson ML, Cosgrove S, Crowe S, Hope W, McCarthy J, Mills J, et al. Kucers' The Use of Antibiotics: A Clinical Review of Antibacterial, Antifungal, Antiparasitic, and Antiviral Drugs, Seventh Edition - Three Volume Set. CRC Press; 2017.

9. Wiltshire H, Hirankarn S, Farrell C, Paya C, Pescovitz MD, Humar A, et al. Pharmacokinetic profile of ganciclovir after its oral administration and from its prodrug, valganciclovir, in solid organ transplant recipients. Clin Pharmacokinet. 2005;44:495–507.

10. 021304s008,022257s003lbl.pdf. Available from: https://www.accessdata.fda.gov/drugsatfda_docs/label/2010/021304s008,022257s003lbl.pdf. Accessed 2024 Apr 2024.

11. Manuel O, Pascual M, Perrottet N, Lamoth F, Venetz J-P, Decosterd LA, et al. Ganciclovir exposure under a 450 mg daily dosage of valganciclovir for cytomegalovirus prevention in kidney transplantation: a prospective study. Clin Transplant. 2010;24:794–800.

12. Wiltshire H, Paya CV, Pescovitz MD, Humar A, Dominguez E, Washburn K, et al. Pharmacodynamics of oral ganciclovir and valganciclovir in solid organ transplant recipients. Transplantation. 2005;79:1477–83.

13. Padullés A, Colom H, Bestard O, Melilli E, Sabé N, Rigo R, et al. Contribution of population pharmacokinetics to dose optimization of ganciclovir-valganciclovir in solid-organ transplant patients. Antimicrob Agents Chemother. 2016;60:1992–2002.

14. Mártsan A-G, Edwina AE, Burgerhof JGM, Berger SP, de Joode A, Damman K, et al. Ganciclovir therapeutic drug monitoring in transplant recipients. J Antimicrob Chemother. 2021;76:2356–63.

15. Wong DD, Ho SA, Domazetovska A, Yong MK, Rawlinson WD. Evidence supporting the use of therapeutic drug monitoring of ganciclovir in transplantation. Curr Opin Infect Dis. 2023;36:505–13.

16. Tängdén T, Cojutti PG, Roberts JA, Pea F. Valganciclovir pharmacokinetics in patients receiving oral prophylaxis following kidney transplantation and model-based predictions of optimal dosing regimens. Clin Pharmacokinet. 2018;57:1399–405.

17. Abdul-Aziz MH, Alfenaar J-WC, Bassetti M, Bracht H, Dimopoulos G, Marriott D, et al. Antimicrobial therapeutic drug monitoring in critically ill adult patients: a Position Paper. Intensive Care Med. 2020;46:1127–53.

18. Sheiner LB, Rosenberg B, Melmon KL. Modelling of individual pharmacokinetics for computer-aided drug dosage. Comput Biomed Res. 1972;5:411–59.

19. Le Loudec F, Puisset F, Thomas F, Chatelut É, White-Koning M. Easy and reliable maximum a posteriori Bayesian estimation of pharmacokinetic parameters with the open-source R package mapbayr. CPT Pharmacometrics Syst Pharmacol. 2021;10:1208–20.

20. Woillard J-B, Labriffe M, Prémaud A, Marquet P. Estimation of drug exposure by machine learning based on simulations from published pharmacokinetic models: the example of tacrolimus. Pharmacol Res. 2021;167:105578.

21. Destere A, Marquet P, Gandonnière CS, Åsberg A, Loustaud-Ratti V, Carrier P, et al. A hybrid model associating population pharmacokinetics with machine learning: a case study with iohexol clearance estimation. Clin Pharmacokinet. 2022;61:1157–65.

22. Destere A, Marquet P, Labriffe M, Drici M-D, Woillard J-B. A hybrid algorithm combining population pharmacokinetic and machine learning for isavuconazole exposure prediction. Pharm Res. 2023;40:951–9.

23. Elmokadem A, Riggs MM, Baron KT. Quantitative systems pharmacology and physiologically-based pharmacokinetic modeling with mrgsolve: a hands-on tutorial. CPT Pharmacometrics Syst Pharmacol. 2019;8:883–93.

24. Vezina HE, Brundage RC, Balfour HH. Population pharmacokinetics of valganciclovir prophylaxis in paediatric and adult solid organ transplant recipients. Br J Clin Pharmacol. 2014;78:343–52.

25. Lalagkas PN, Iliou J, Rigo R, Miarons M, Fernández-Alarcon B, Bestard O, et al. Comparison of three renal function formulas for ganciclovir/valganciclovir dose individualization in CMV-infected solid organ transplantation patients using a population approach. Clin Pharmacokinet. 2023;62:861–80.

26. Labriffe M, Woillard J-B, Debord J, Marquet P. Machine learning algorithms to estimate everolimus exposure trained on simulated and patient pharmacokinetic profiles. CPT Pharmacometrics Syst Pharmacol. 2022;11:1018–28.

27. Caldés A, Colom H, Armendariz Y, Garrido MJ, Troconiz IF, Gil-Vernet S, et al. Population pharmacokinetics of ganciclovir after intravenous ganciclovir and oral valganciclovir administration in solid organ transplant patients infected with cytomegalovirus. Antimicrob Agents Chemother. 2009;53:4816–24.

28. Chen B, Hu S-S, Rui W-B, An H-M, Zhai X-H, Wang X-H, et al. Population pharmacokinetics and Bayesian estimation of the area under the concentration-time curve for ganciclovir in adult Chinese renal allograft recipients after valganciclovir administration. J Clin Pharmacol. 2021;61:328–38.

29. Billat P-A, Woillard J-B, Essig M, Sauvage F-L, Picard N, Alain S, et al. Plasma and intracellular exposure to ganciclovir in adult renal transplant recipients: is there an association with haematological toxicity? J Antimicrob Chemother. 2016;71:484–9.

30. Chen T, Guestrin C. XGBoost: A scalable tree boosting system. Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. New York, NY, USA: Association for Computing Machinery; 2016. p. 785–94. Available from: https://doi.org/10.1145/2939672.2939785. Accessed 3 Oct 2024.

31. Breiman L. Random Forests. Machine Learning. 2001 [cited 2024 Oct 3];45:5–32. https://doi.org/10.1023/A:1010933404324.

32. Friedman J, Hastie T, Tibshirani R. Regularization paths for generalized linear models via coordinate descent. J Stat Softw. 2010;33:1–22.

33. Cortes C, Vapnik V. Support-vector networks. Mach Learn [Internet]. 1995 [cited 2024 Oct 3];20:273–97. https://doi.org/10.1007/BF00994018.

34. Friedman JH, Roosen CB. An introduction to multivariate adaptive regression splines. Stat Methods Med Res. 1995;4:197–217.

35. Ponthier L, Ensuque P, Destere A, Marquet P, Labriffe M, Jacqz-Aigrain E, et al. Optimization of vancomycin initial dose in term and preterm neonates by machine learning. Pharm Res. 2022;39:2497–506.

36. Codde C, Rivals F, Destere A, Fromage Y, Labriffe M, Marquet P, et al. A machine learning approach to predict daptomycin exposure from two concentrations based on Monte Carlo simulations. Antimicrob Agents Chemother. 2024;68:e0141523.

37. Ponthier L, Autmizguine J, Franck B, Åsberg A, Ovetchkine P, Destere A, et al. Optimization of ganciclovir and valganciclovir starting dose in children by machine learning. Clin Pharmacokinet. 2024;63:539–50.
38. Shiny. Shiny. Available from: https://shiny.posit.co/. Accessed 25 Apr 2024.

39. Hovd M, Robertsen I, Woillard J-B, Åsberg A. A method for evaluating robustness of limited sampling strategies-exemplified by serum iohexol clearance for determination of measured glomerular filtration rate. Pharmaceutics. 2023;15:1073.

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