Method for evaluating cardiotoxicity of medicine by using multiple in silico biomarkers-based logistic regression model

Abstract

A method for evaluating the cardiotoxicity of a drug by using a multiple in silico biomarkers-based logistic regression model, according to the present invention, comprises: generating a multi-input scenario for biomarkers and inputting same into ordinal logistic regression models (OLR) to predict a risk of arrhythmia (TdP) caused by a drug; and evaluating performance to rank and analyze the ordinal logistic regression models (OLR).

Description

A method for assessing the cardiotoxicity of pharmaceuticals using a logistic regression model based on multiple in silico biomarkers.

[0001] The present invention relates to a method for predicting the cardiotoxicity of a pharmaceutical product, and more particularly, to a method for evaluating the cardiotoxicity of a pharmaceutical product using a logical regression model based on multiple in silico biomarkers and a method for predicting the cardiotoxicity of a pharmaceutical product using multiple in silico biomarkers.

[0002] Drug-induced arrhythmia (Torsade de pointes, TdP) is a dangerous arrhythmia that can lead to sudden cardiac death. First described by Dessertenné in 1966, drug-induced arrhythmia (TdP) is primarily associated with a QT interval prolongation, whether congenital or acquired through drug therapy or electrolyte imbalance. TdP is characterized by a "long-short" onset sequence on the electrocardiogram, which aids in diagnosis and differentiation from other types of ventricular tachycardia. Furthermore, TdP can be caused by congenital (adrenergic-dependent) and acquired (pause-dependent) factors that contribute to QT prolongation. Given that QT prolongation can also be caused by drugs, researchers have focused on evaluating and alleviating drug-induced TdP. Some studies have attempted to identify predictors of drug-induced TdP, which are closely related to changes in action potential duration (APD) and repolarization, including early afterdepolarization and repolarization dispersion. Furthermore, clinical management and prevention strategies for TdP have been well described by Drew and Ackerman (2010) and Faber, Zehender, and Just (1994). They discussed the effective use of interventions such as magnesium sulfate and rate control in hospital settings. Studies by Glassman and Bigger (2001) and Kannankeril and Roden (2007) examined the pharmacogenetic aspects and broader implications of drug-induced long QT syndrome.

[0003] However, some studies have reported that QT prolongation is not the only cause of TdP. Drug inhibition of the hERG channel has been considered a key factor in inducing TdP. Therefore, hERG analysis has been integrated into cardiac safety assessments. Gintant et al. proposed hERG analysis as a surrogate marker for delayed cardiac repolarization and QT safety assessment. Furthermore, some studies have proposed incorporating hERG analysis into TdP assessment systems and combining it with other pharmacological factors, such as drug interactions with multiple ion channels, and physiological factors, such as patient-specific variables, to fully assess the TdP risk of a drug. Johanessenet et al. evaluated drug effects on multiple ion channels depicted in the electrocardiogram and highlighted that drug inhibition of multiple ion channels can either exacerbate or mitigate the risk of TdP. Kramer et al. also demonstrated the effectiveness of the proposed model in predicting the TdP risk of a compound by incorporating multichannel drug effects related to the TdP risk of a drug.

[0004] Despite efforts to assess the risk of TdP in drugs, focusing on hERG blockade and QT prolongation as surrogate markers, the current cardiac safety paradigm does not directly assess TdP. Sageret et al. identified several important limitations of the current approach, noting that blockade based solely on IKr does not adequately predict repolarization. They also observed that while QTc prolongation is a sensitive marker, it is not sufficiently specific to predict the risk of ventricular arrhythmias. They also noted that some drugs may block IKr despite not being arrhythmogenic. To address the limitations of the current paradigm, the researchers proposed a novel cardiac safety paradigm, the Comprehensive In Vitro Arrhythmia Assay (CiPA). CiPA consists of four components: in vitro assessment of drug-induced effects on multiple ionic currents, in silico evaluation using simulations in cardiac cell models, and in vitro drug effects and assessment in human induced pluripotent stem cell-derived ventricular cardiomyocytes (hiPSC-CMs).

[0005] Typically, most studies on the in silico assessment of TdP risk of drugs under the CiPA paradigm utilize the cardiac cell model (ORd model) proposed by O'Hara et al. This model generates in silico biomarkers, such as APD, calcium duration (CaD), and cumulative net charge (qNet). These in silico biomarkers then serve as inputs for analysis or training statistical tools or machine learning algorithms. The trained model predicts the TdP risk of the test drug. Previous computational studies utilizing CiPA to assess the TdP risk of drugs have shown promising performance.

[0006] Several studies have used a single biomarker as input for a two- or three-class classifier (low- or high-risk TdP). Other researchers have proposed two-biomarker inputs to the classifier, demonstrating significant classification performance for binary classification. One- and two-biomarker inputs are easily interpretable, as decision boundaries can be easily visualized. Furthermore, because more biomarkers can ideally capture a broader range of cellular physiological responses to a drug, several studies have built CiPA-based classifiers using two or more biomarkers as inputs. Another study has also used convolutional neural networks (CNNs) to predict TdP risk for drugs by leveraging in silico time-series signals.

[0007] Meanwhile, the qNet proposed by Li et al. has gained popularity among researchers over other complex TdP risk prediction models due to its high performance and simple interpretation of the classification model it provides using the input. However, some limitations require further improvement. First, the classifier's reliance on a single biomarker (qNet) may limit the physiological information captured in electrophysiological simulations of cardiac cells, thereby limiting its classification performance. Second, qNet measures the total net charge within the cell, which is difficult to observe and validate experimentally.

[0008] On the other hand, classification models utilizing multiple biomarkers lack interpretability, despite being able to capture more physiological responses in in silico simulations. Explainable artificial intelligence (XAI) algorithms, such as SHApley Additive exPlanation (SHAP), as suggested by Fuadah et al., can be used to explain model classification characteristics. Mahardhika et al.

[20] suggested that this approach can aid in model interpretation. However, it is significantly more complex than the Torsade metric score (TMS) threshold proposed by Li et al.

[21] . Furthermore, the overall classification performance of recent multi-biomarker classifiers is not significantly better than that of state-of-the-art classifiers using only qNet, making them undesirable for many researchers.

[0009] The present invention has been proposed to solve the above technical problems, and provides a method for evaluating the cardiotoxicity of a drug using a multiple in silico biomarker-based logical regression model capable of classifying the TdP risk of a drug using a multiple biomarker input ordinal logistic regression model (OLR), and a method for predicting the cardiotoxicity of a drug using multiple in silico biomarkers.

[0010] Furthermore, the present invention addresses two key limitations of current in silico classification models for predicting TdP risk of drugs. A small number of biomarkers as inputs can limit classification performance, and while multi-biomarker input classifiers become more complex, classification models do not significantly outperform single-input models.

[0011] We propose a multi-biomarker input ordinal logistic regression (OLR) model to classify the risk of TdP for drugs. Similar to the Torsade Metric Score (TMS) threshold, we propose a novel Torsade Metric Score (TMS) derived from multiple biomarkers that may help explain the model's classification characteristics.

[0012] According to one embodiment of the present invention for solving the above problem, a method for evaluating the cardiotoxicity of a drug using a multiple in silico biomarker-based logical regression model is provided, which generates a multiple input scenario for a biomarker, inputs it into an ordinal logistic regression model (OLR), predicts the risk of torsade de pointes (TdP) due to a drug, evaluates the performance, and ranks and analyzes each ordinal logistic regression model (OLR).

[0013] In addition, the biomarkers are characterized by qNet (net ionic charge of six ion currents, ICaL, INaL, IKr, IKs, IK1, and Ito; net ionic charge entering the cell during depolarization), dvdtmax (maximum rate of change of membrane potential during AP rise; maximum value of membrane potential slope in action potential shape), vmax (maximum membrane potential), vrest (resting membrane potential), APD50 (action potential duration at 50% repolarization), APD90 (action potential duration at 90% repolarization), max_dv (maximum rate of change of membrane potential during repolarization), camax (maximum intracellular calcium concentration), caret (intracellular calcium concentration during resting), CaTD50 (calcium transient duration at 50% repolarization), CaTD90% (period of intracellular calcium concentration during 90% depolarization).

[0014] In addition, a method for predicting the cardiotoxicity of a drug using multiple in silico biomarkers is provided, characterized by using Caest (intracellular calcium concentration during resting period) and CaTD90 (period of intracellular calcium concentration during depolarization period) as in silico multiple biomarkers for drug cardiotoxicity evaluation.

[0015] In addition, a method for predicting the cardiotoxicity of a drug using multiple in silico biomarkers is provided, characterized by using qNet (net ionic charge influx into a cell during the depolarization period) and dVdtmax (maximum value of the membrane potential gradient in the action potential shape) as in silico multiple biomarkers for drug cardiotoxicity evaluation.

[0016]

[0017] In addition, a method for predicting the cardiotoxicity of a drug using multiple in silico biomarkers is provided, which utilizes a deep learning model that receives the variability of Caest (intracellular calcium concentration during resting state) and CaTD90 (period of intracellular calcium concentration during depolarization) as input to evaluate the proarrhythmic risk of the drug in the data processing unit.

[0018] In addition, a method for predicting the cardiac toxicity of a drug using multiple in silico biomarkers is provided, which uses a deep learning model that receives the variability of qNet (net ionic charge inflow into the cell during the depolarization period) and dVdtmax (maximum value of the membrane potential slope in the action potential shape) as input to evaluate the proarrhythmic risk of the drug in the data processing unit, and a CNN or ANN can be used as the deep learning model.

[0019]

[0020] The use of electrophysiological simulations and machine learning to predict drug cardiac toxicity is becoming popular and effective. Currently, the best in silico drug evaluation systems primarily use a single biomarker (qNet) to predict a drug's arrhythmia risk, which offers robust performance and simple model interpretation. However, more sophisticated classifiers that capture additional physiological biomarkers in cardiac cell simulations have been introduced, offering improved predictive capabilities but with reduced interpretability.

[0021] To address the limitations of using multiple biomarkers in drug cardiotoxicity assessment, the present invention improves upon the existing best model by incorporating additional physiological markers, significantly improving classifier performance. Furthermore, a common Tosad score for multi-biomarker approaches is introduced to facilitate the interpretation of model predictions when assessing arrhythmia risk. Furthermore, a novel ranking algorithm based on a simple multicriteria decision analysis method is applied to select various classifiers for standard cardiotoxicity assessment criteria.

[0022] The key tenet of the present invention is that combining well-established and quantifiable biomarkers achieves higher performance than qNet alone, providing a more viable alternative for cardiotoxicity assessment systems. In short, the present approach can help develop more effective classifiers that are easier to interpret.

[0023] Figure 1 is a diagram illustrating the overall workflow diagram of the present invention for obtaining an acceptable model for TdP risk assessment of a drug using multiple biomarkers.

[0024] Figure 2 is a diagram showing a TMS plot for the best OLR model using a single biomarker input.

[0025] Figure 3 shows the TMS plot and decision boundary and the best OLR model in two biomarker input methods using the manual data set.

[0026] Figure 4 shows the TMS plot and decision boundary for the best OLR model in two biomarker input methods using a hybrid data set.

[0027] Figure 5 is a diagram showing the overall results of all possible scenarios for all multi-biomarker input systems.

[0028] Figures 6a to 6k are diagrams showing overall statistics for biomarkers of the OLR model allowed for all scenarios of all multi-biomarker input systems.

[0029] Hereinafter, in order to explain in detail to a degree that a person having ordinary skill in the art to which the present invention pertains can easily practice the technical idea of ​​the present invention, an embodiment of the present invention will be described with reference to the attached drawings.

[0030]

[0031] FIG. 1 is a diagram illustrating the overall workflow of the present invention for obtaining an acceptable model for TdP risk assessment of a drug using multiple biomarkers.

[0032] Dose-response data were obtained from voltage patch-clamp experiments. Hill and hERG fitting were performed to estimate the IC_50, Hill coefficient, and dynamic hERG inhibition parameters of the drug samples, while bootstrapping was performed to augment these parameters for each drug, resulting in 2,000 samples for each drug. All parameters estimated by data fitting and bootstrapping were used as inputs to simulate drug effects during in silico AP simulations of cardiac myocytes to generate biomarkers. Biomarkers undergo data normalization (using a standard scaler normalization) to preserve physiological information and improve computational stability for training the OLR model using multiple biomarker inputs. All possible scenarios for the multi-biomarker input scheme were generated before the biomarker data were split into training and testing datasets. Each scenario of the multi-biomarker input was used to train the OLR model and tested 10,000 times using the test algorithm to obtain performance metrics. Finally, the performance metrics for all possible scenarios are evaluated using a ranking algorithm to select models based on acceptance criteria.

[0033]

[0034] The method for evaluating the cardiotoxicity of a drug using a logical regression model based on multiple in silico biomarkers of the present invention and the method for predicting the cardiotoxicity of a drug using multiple in silico biomarkers are processed in a data processing unit or a control unit.

[0035]

[0036] - Cardiac cell models and drug effects

[0037] The cardiac cell model used in in silico simulations is known as the CiPAORdv1.0 model, a modified version of the original ORd model proposed by Li et al., which was later improved by Dutta et al. The membrane potential (V_m) of the cardiac cell model is generally mathematically expressed as follows:

[0038] <Formula 1>

[0039] dVm / dt = (I ion + I stim )

[0040]

[0041] Here, I_ion is the transmembrane ionic current (μA / μF) composed of the fast sodium current (I_Na), the slow sodium current (I_NaL), the transient outward potassium current (I_to), the L-type calcium current (I_CaL), the sodium current through the L-type calcium channel (I_CaNa), the potassium current through the L-type calcium channel (I_CaK), the fast delayed rectifier potassium current (I_Kr), the slow delayed rectifier potassium current (I_Ks), the inward rectifier potassium current (I_Kl), the sodium-calcium exchange current (I_NaCa), the sodium ATPase current (I_NaK), the sarcolemma calcium pump current (I_pCa), and the background currents (I_Nab, I_Cab, and I_Kb). I_stim is the membrane stimulus current.

[0042]

[0043] A key change made to the original ORd model is the reconstruction of IKr by a dynamic inhibition model of the hERG channel. The model was then modified by recalculating the maximum conductances of the five major ion currents (I_Kr, I_Ks, I_K1, I_CaL, and I_NaL) to match experimental data on the APD rate dependence for the control (no drug) and five channel blockers presented by Dutta et al. Furthermore, the inhibitory effects of the drugs on ion channels other than hERG are assumed to follow the conduction blocking mechanism proposed by Mirams et al. Inspired by Hill, as follows:

[0044]

[0045] <Formula 2>

[0046] inhibition effect = 1 / 1+(IC 50 / D) h

[0047]

[0048] Here, D represents the drug concentration (in nM), IC_50 represents the 50% inhibitory concentration (in nM), and h represents the Hill coefficient. The inhibitory effect is assumed to readjust the maximum conductance of the ion channel as follows.

[0049]

[0050] <Formula 3>

[0051] g i = g control,i (1 - inhibition effect)

[0052]

[0053] Here, g_i represents the maximum conductance of ion channel i under the drug effect, and g_(control,i) represents the maximum conductance of ion channel i in the absence of the drug. In the present invention, as suggested in previous studies, it is assumed that the inhibitory effect of the drug applies only to four ion channels, namely, hERG, CaL, Na, and NaL channels.

[0054]

[0055]

[0056]

[0057]

[0058]

[0059]

[0060]

[0061]

[0062]

[0063] - Drug data

[0064] TdP riskTraining datasetTesting datasetDrugCmax (nM)DrugCmax (nM)HighBepridil33Azimilide70Dofetilide2Disopyramide742Quinidine3237Ibutilide100Sotalol14690Vandetanib255IntermediateChlorpromazine38Astemizole0.26Cisapride2.6Clarithromycin1206Ondansetron139Cloza pine71Terfenadine4Domperidone19Droperidol6.3Pimozide0.431Risperidone1.81LowDiltiazem122Loratadine0.45Mexiletine4129Metoprolol1800Ranolazine1948.2Nifedipine7.7Verapamil81Nitrendipine3.02Tamoxifen21

[0065] Table 2 shows the drug dataset for training and testing the OLR model.

[0066]

[0067] As shown in Table 2, 12 training drugs and 16 test drugs were used in the study of the present invention. Furthermore, two key drug data sets are required to perform in silico simulations using the CiPAORdv1.0 cell model.

[0068] First, to simulate the dynamic inhibition of hERG channels, several dynamic hERG parameters must be obtained, such as the maximum drug effect at saturating concentration (K_max), the unbound reaction rate (K_u), the Hill coefficient (n), the 50% maximal effect concentration (EC_50), and the membrane potential when half of the drug-bound channel is open. The dynamic hERG parameters can be obtained by fitting patch-clamp recording data to a dynamic inhibition model of the hERG channel. Bootstrapping is then performed to estimate the uncertainty of each parameter. Bootstrapping and data fitting generated 2,000 samples of dynamic hERG parameters for each drug. The Rscript and experimental data for hERG fitting are available online at https: / / github.com / FDA / CiPA / tree / Lab_Specific_Validation_Calibration_2020 / hERG_fitting.

[0069]

[0070] Second, to simulate the inhibitory effects of drugs on the channels CaL, NaL, and Na, IC_50 and h values, as shown in Equation 2, are required. Hill fitting, which fits the dose-response data from voltage patch clamp experiments for the three ion channels to the Hill equation, as shown in Equation 2, is performed to obtain the best estimates of the IC_50 and h values ​​of the corresponding ion channels. Markov Chain Monte Carlo (MCMC) can then be performed to estimate the uncertainty of the two parameters. MCMC generates 2,000 IC_50 and h samples for each channel per drug. In the present invention, two drug data sets are used: a manual and a hybrid data set. The dose-response data for the manual dataset can be found online at https: / / github.com / FDA / CiPA / tree / Model-Validation-2018 / Hill_Fitting / data, while the hybrid dataset is available at https: / / github.com / FDA / CiPA / tree / Lab_Specific_Validation_Calibration_2020 / chantest_Hill_fitting / data. Finally, the Rscripts for performing Hill fitting and Markov Chain Monte Carlo (MCMC) can be found at https: / / github.com / FDA / CiPA / tree / Lab_Specific_Validation_Calibration_2020 / chantest_Hill_Fitting.

[0071]

[0072] - In silico simulation of action potential (AP) and biomarker extracts

[0073] During in silico simulations of the action potential (AP), hERG and Hill parameters derived from data bootstrapping and Markov Chain Monte Carlo (MCMC) were used. The simulation protocol generally followed that proposed by Chang et al. For each drug sample, the first 1,000 bits of the AP were simulated under drug-free conditions. Then, drug inhibition effects were induced for the next 1,000 bits.

[0074] Additionally, the action potential (AP) selection procedure for the last 250 beats is performed by extracting the most drug-affected AP with the highest maximum repolarization rate (max_dv) among the last 250 beats. The max_dv is extracted between 30% and 90% for a fully repolarized AP. For APs that can repolarize by 30% but not 90%, the max_dv is found between 30% repolarization and the beat end. Finally, when the AP does not depolarize by 30%, the max_dv is obtained between the peak of the AP and the beat end.

[0075] In silico simulations of action potentials (APs) assume a cycle length of 2,000 ms. Note that the full analysis is not performed on APs that fail to depolarize beyond 0 mV. AP simulations and AP selection are performed for four different drug concentrations ranging from 1 to 4x cmax (maximum blood drug concentration).

[0076] An Rscript to perform action potential (AP) simulations is available online at https: / / github.com / FDA / CiPA / tree / Lab_Specific_Validation_Calibration_2020 / chantest_AP_simulation.

[0077]

[0078] Eleven biomarkers are extracted from the action potential (AP), which is most affected by drugs. These biomarkers include qNet (net ionic charge of six ionic currents, ICaL, INaL, IKr, IKs, IK1, and Ito; net ionic charge entering the cell during depolarization), dvdtmax (maximum rate of change of membrane potential during AP rise; maximum value of membrane potential slope in the action potential shape), vmax (maximum membrane potential), vrest (resting membrane potential), APD50 (action potential duration at 50% repolarization), APD90 (action potential duration at 90% repolarization), max_dv (maximum rate of change of membrane potential during repolarization), camax (maximum intracellular calcium concentration), caret (intracellular calcium concentration at rest), CaTD50 (calcium transient at 50% repolarization), and CaTD90% (calcium transient at 90% repolarization; duration of intracellular calcium concentration during 90% depolarization). Biomarkers serve as inputs for the OLR model to predict the TdP risk of a drug.

[0079]

[0080] - Data preprocessing

[0081] The raw biomarker data undergoes filtering and normalization. Drug samples with NaN values ​​for at least one biomarker are omitted from the analysis. To facilitate fitting the ordinal logistic regression (OLR) model, each biomarker is then normalized using a simple standard scaling algorithm. First, each biomarker data in the training data is subtracted by its mean and divided by its standard deviation. The test data set is then rescaled using the mean and standard deviation values ​​of the original training data set before scaling. This simple rescaling approach allows the OLR model to converge more easily when fitting the training data while preserving the physiological information of the biomarkers.

[0082]

[0083] - Generate input scenarios for each multi-biomarker input method

[0084] Each multi-biomarker input scheme has multiple input scenarios. The total number of unique input scenarios for each multi-biomarker scheme can be expressed using the following combination formula:

[0085]

[0086] <Formula 4>

[0087] Number of input scenarios = M! / r!(M - r)!

[0088]

[0089] Here, M is the total number of biomarkers (11 biomarkers), and r is the number of biomarkers in the input scheme. For example, when using a two-biomarker input scheme, the total number of unique input scenarios is 11! / 2!(11-2)!=55. Each input scenario has training and testing data that are fed to the ordinal logistic regression model (OLR) for training and testing procedures.

[0090]

[0091] - Training and testing of ordinal logistic regression models (OLR)

[0092] The general formula of the OLR model using N biomarkers can be expressed as follows.

[0093]

[0094] <Equation 5, Equation 6>

[0095]

[0096]

[0097] Here, z_1 and z_2 represent the logit function, α_1 and α_2 are the intercepts, and β_i is the slope of biomarker i. The training data is fitted to the OLR model to obtain the model parameters α_1, α_2, and β_i during the training process.

[0098] Additionally, the trained OLR model is tested 10,000 times on the test dataset proposed by Li et al. In each test, 16 drug sample sets of 16 different test drugs are sampled with replacement. The TdP risk prediction for each drug sample is then calculated and compared with the true label. Classification performance measures are captured in each test, generating 10,000 samples for each performance measure. Performance measures used to evaluate the OLR model include the area under the curve (AUC) of the receiver operating characteristic (ROC) curve, positive and negative likelihood ratios (LR), classification error, and pairwise comparison accuracy. The formulas for LR+ and LR- are as follows:

[0099]

[0100] <Equation 7, Equation 8>

[0101] LR + = sensitivity / 1 - specificity

[0102] LR - = 1 - sensitivity / specificity

[0103]

[0104] Here, sensitivity is defined as TP / (TP+FN), and specificity is defined as TN / (TN+FP) (TP is true positive, TN is true negative, FP is false positive, and FN is false negative). Furthermore, classification error is defined as the absolute difference between the actual and predicted risk labels, and pairwise comparisons describe the ranked pairs of drug samples based on the Torsade metric score (TMS). For an OLR model using multiple biomarker inputs according to Equation 5 and Figures 6a to 6k, the TMS of a drug sample can be defined as follows.

[0105] <Formula 9>

[0106] TMS = (Z1+ Z2) / 2

[0107] Each performance indicator has a different usage pattern. Some performance measures, such as the area under the curve (AUC) of the ROC, LR+, and LR-, are used to evaluate binary classification performance, while others (classification error and pairwise accuracy) are used to evaluate three-class classification. Binary classification divides low-risk drugs into intermediate / high-risk drugs, and high-risk drugs into intermediate / low-risk drugs. Meanwhile, three-class TdP risk classification directly separates low-, intermediate-, and high-risk drugs. Therefore, the eight performance measures quantify the classification performance of the OLR model.

[0108]

[0109] - Rank of ordinal logistic regression model (OLR)

[0110] Given the numerous OLR models evaluated and the eight performance metrics captured across 10,000 tests, a simple and systematic ranking procedure is needed to quantify the overall performance of OLR models. Due to its simplicity and interpretability, we propose a simple additive weighting method to rank OLR models. The ranking algorithm is as follows.

[0111] First, the performance level criteria for each performance indicator (a total of eight indicators) follow the criteria proposed by Li et al., which categorize performance levels into excellent, good, and minimal performance. However, the previous performance level criteria utilized continuous and approximate performance measures to establish the performance levels of OLR models, making it difficult to quickly evaluate numerous ORL models. Therefore, we propose utilizing specific value ranges for each performance indicator to indicate excellent, good, minimal, and rejected performance.

[0112] Second, weights are assigned to each performance criterion. The weight values ​​are assumed to increase linearly from 0 (reject) to 3 (excellent). Finally, the weights are normalized using min-max normalization.

[0113] Third, each performance measure is weighted based on the difficulty of the classification prediction. Performance measures used for binary classification, such as ROC, AUC for LR+, and LR-, are assumed to be less weighted than those used for three-class classification (classification error and pairwise comparison accuracy).

[0114] Finally, the normalized weights are calculated by dividing the weight of each performance indicator by the overall weight. The overall performance score of the OLR model can be calculated by multiplying the normalized weights of the performance measures by the normalized weights of the performance level criteria, as follows:

[0115]

[0116] <Formula 10>

[0117]

[0118]

[0119] Here, w is the normalized weight value, i is the performance measure, and j is the performance level. Finally, the OLR model is rejected if it fails to meet the minimum acceptance criteria for all performance measures. Additionally, Rscripts for training, testing, and ranking the OLR model are available online at https: / / github.com / kit-cml / cml_olr.

[0120]

[0121]

[0122]

[0123]

[0124]

[0125]

[0126]

[0127]

[0128]

[0129]

[0130]

[0131]

[0132]

[0133]

[0134]

[0135]

[0136]

[0137] - result

[0138] DatasetBiomarkerPerformance measuresperformancescoreAUC of ROCLR+LR-classificationerrorpairwisecomparisonaccuracyLowHighLowHighLowHighManualqNet*0.840.922.34.52.3E-013.00E-010.19750.920.7qNet0.872727270.895833336.59993842.9999920.440000620.333334220.2720122460.9146919430.7APD900.890909090.916666672.19999675.999970.314286791.20E-060.3742015580.8720379150.666667APD500.890909090.916666672.19999673.9999880.314286791.33E-060.371104880.8767772510.633333max_dv0.872727270.916666671.759998335.999970.366667831.20E-060.3762929790.8483412320.633333CaTD500.781818180.833333331.31999932.9999920.733333820.333334220.5723996220.7393364930.3vmax0.690909090.541666674.39996260.5000010.660000371.4999990.6708967230.6777251180.1vrest0.454545450.31252.19998681.7143E-060.880000132.399996640.8768111880.5165876780.1carest0.50.3752.19999344.00E-060.733333661.333332890.6571539080.5450236970.1CaTD900.627272730.791666671.31999931.50E+000.733333820.750000370.7101944510.6682464450.1camax0.490909090.3751.099999723.00E-060.942857231.499999250.7442090860.540284360.066667dvdtmax0.309090910.229166670.60000041.20E-05400001.2451.090908991.050187010.4312796210.

[0139]

[0140] DatasetBiomarkerPerformance measuresperformancescoreAUC of ROCLR+LR-classificationerrorpairwisecomparisonaccuracyLowHighLowHighLowHighHybridqNet*0.930.887.30E+0530.270.330.25810.920.766667qNet0.945454550.864583335.499975252.9999920.244445370.333334220.2456869620.9146919430.733333APD900.909090910.916666672.19999675.999970.314286791.20E-060.3318576850.8815165880.7max_dv0.890909090.916666672.19999675.999970.314286791.20E-060.3446571620.8720379150.666667APD500.927272730.916666672.749995193.9999880.2750013.00E-010.3196816310.8957345970.6CaTD500.718181820.770833331.466664962.249996250.825000240.375000940.4961637470.7203791470.333333carest0.772727270.447916672.199996710.4400006210.4807719470.6682464450.233333CaTD900.636363640.760416671.099999732.249996250.942857230.375000940.5565889390.7251184830.233333camax0.745454550.479166672.19999561.50E+000.550000620.900000120.3971003390.6824644550.2vmax0.745454550.52.19998686.00E-010.880000132.9999880.907478060.6824644550.133333dvdtmax0.436363640.541666670.80000021.00E+00200001.01410.8474324080.4502369670.066667vrest0.563 636360.31251.099999453.00E-010.97777784.4999790.9675394130.540284360.066667.

[0141]

[0142] Tables 3 and 4 present the performance metrics and performance scores of the OLR model on the test dataset using a single biomarker input scheme. Gray, red, blue, and green represent criteria for failure, minimally acceptable, good, and excellent performance, respectively.

[0143]

[0144] The results of the single biomarker input method are consistent with previous studies.

[0145] The best biomarker for TdP risk classification for a single biomarker input scheme on both the manual and hybrid datasets is qNet, as shown in Table 2, confirming the results reported by Li et al. Accepted OLR models on the manual dataset utilized qNet, APD90, and APD50 as inputs, while OLR models using the hybrid dataset utilized qNet, APD90, max_dv, and APD50. Other biomarkers, such as CaTD50, CaTD90, carest, climax, vmax, Rest, and dvdtmax, performed relatively poorly, as not all performance measures met the minimum acceptance criteria. In particular, the OLR model utilizing dvdtmax showed significantly lower performance on both the manual and hybrid datasets.

[0146] Additionally, the TMS plots of the best models for the single biomarker input scheme are shown in Figure 2. For the manual dataset (panels A1 and A2), the TMS thresholds are Threshold_1=15.8129 and Threshold_2=-15.8129, whereas for the hybrid dataset (panels B1 and B2), the thresholds are Threshold_1=8.7226 and Threshold_2=-8.7226. Most of the training drugs (panels A1 and B1) are correctly classified for the manual and hybrid datasets. However, some test drugs in panels A2 and B2 are misclassified. For example, in the manual dataset, most of the pimozide and domperidone samples are classified as high-risk (originally intermediate-risk), whereas most of the metoprolol samples are considered intermediate-risk (originally low-risk). Additionally, in the hybrid dataset, most of the disopyramide samples are classified as intermediate-risk (originally high-risk). In contrast, most samples of pimozide and domperidone are considered high-risk (originally intermediate-risk) drugs.

[0147] Figure 2 is a diagram showing a TMS plot for the best OLR model using a single biomarker input.

[0148] Panels A1 and A2 show the OLR training and testing results using the manual dataset, while panels B1 and B2 show the results for the hybrid dataset. qNet was found to be the optimal biomarker for the OLR model using a single biomarker input for both the manual and hybrid datasets. Red, blue, and green represent high-risk, intermediate-risk, and low-risk drugs, respectively. The red and blue dotted lines represent the TMS thresholds. The blue dotted line represents TMS threshold_1, which distinguishes drugs into low-risk and intermediate-low risk TdP, and the red dotted line represents TMS threshold_2, which distinguishes drugs into high-risk and intermediate-low risk TdP. For panels A1 and A2, the value of TMS threshold_1 is 15.8129 and threshold_2 is -15.8129, whereas for panels B1 and B2, threshold_1 is 8.7226 and threshold_2 is -8.7226.

[0149]

[0150] - Multi-biomarker input can significantly improve TdP risk classification performance and increase the number of acceptable OLR models.

[0151]

[0152] Figure 3 is a diagram showing the TMS plot and decision boundary and the best OLR model in two biomarker input methods using the manual data set.

[0153] Panels A1 and A2 show TMS plots of the OLR model using 12 training drugs and 16 test drugs. The color coding for the three TdP risk classes is the same as in Figure 2. The decision boundaries for the best models for the two biomarker input methods are shown in the scatterplots in panels B1 and B2. Here, the blue and red dashed lines distinguish drugs in the same way as TMS threshold_1 and threshold_2 mentioned in Figure 2. The value of TMS threshold_1 is 2.5240, and threshold_2 is -2.5240.

[0154]

[0155] Figure 4 is a diagram showing the TMS plot and decision boundary for the best OLR model in two biomarker input methods using a hybrid data set.

[0156] The information presented in the figure is similar to that in Figure 3, except that the data used for training and testing the OLR model is a hybrid dataset. The value of TMS Threshold_1 is 10.9585, and the value of Threshold_2 is -10.9585.

[0157]

[0158] Figure 5 is a diagram showing the overall results of all possible scenarios for all multi-biomarker input systems.

[0159] Panel A shows the performance scores of the best OLR models for each input scheme. The blue line represents the results using the manual dataset, and the red line represents the results using the hybrid dataset. Black triangles indicate OLR models that failed to meet the acceptance criteria. Panel B shows the distribution of accepted OLR models across various multi-biomarker input schemes. The color coding is the same as in Panel A.

[0160]

[0161] Increasing the number of biomarkers input to the OLR model can improve classification performance. As shown in Figure 5, Panel A, incorporating up to five (for the manual dataset) or six (for the hybrid dataset) biomarkers as input can improve the overall performance score of the OLR model, reaching maximum values ​​of 0.9 and 0.77, respectively. However, the overall classification performance can be reduced when adding 10 biomarkers (best performance score of 0.7) or 11 biomarkers (best performance score of 0.57) for the OLR model using the hybrid dataset, which performs worse than the OLR model using only qNet.

[0162] Similarly, for the OLR model using the manual dataset, the best performance score drops significantly when using all biomarkers (11 biomarkers), but the score (0.73) is still better than when using only qNet input (performance score 0.7).

[0163] Additionally, the number of accepted models varies depending on the multiple biomarker input scheme, as shown in Figure 5 Panel B. The highest number of accepted models occurs when five biomarkers are utilized in the manual and hybrid datasets, followed by four and six biomarker inputs. Furthermore, the manual dataset produces more accepted models than the hybrid dataset in all multiple biomarker input schemes. In fact, for the 7-, 8-, 9-, and 10-biomarker input schemes, the manual dataset produces more than twice as many accepted models as the hybrid dataset. Finally, comparing the results shown in Figure 5 Panels A and B, we see that the maximum number of biomarkers that simultaneously generates the highest performance scores and the most accepted models is five.

[0164]

[0165] - Biomarker statistics: Alternative biomarkers other than qNet play a significant role in predicting TdP risk of drugs.

[0166] Figures 6a to 6k are diagrams showing the overall statistics for biomarkers of the OLR model allowed for all scenarios of all multi-biomarker input systems.

[0167] There are three main panels: Occurrence, Impact, and Performance Score. Blue represents results using the manual dataset, while red represents results using the hybrid dataset. The solid gray line in the Occurrence panel represents 50% occurrence, while the solid gray line in the Impact panel represents 0.5 impact. The solid black lines in the Impact and Performance Score panels represent the average impact and performance score values ​​for the biomarker. The dotted lines represent the minimum and maximum scores.

[0168]

[0169] Figure 6 shows how frequently a biomarker is used, how influential it is, and how the performance scores of accepted models differ across all possible input scenarios for various multi-biomarker input schemes. The occurrence of a biomarker is defined as how often the biomarker is included in accepted models. For example, a biomarker has an occurrence of α% for an n-biomarker input scheme, which means that the biomarker is used by α% of all accepted models using n-biomarker inputs. An occurrence of 100% indicates that all accepted models for that multi-biomarker input scheme use the biomarker. Similarly, a zero occurrence indicates that no accepted models include the biomarker as an input. Furthermore, the influence of a biomarker is defined as the absolute weight (β value) of the biomarker relative to the maximum weight available in the OLR model. For example, an influence of 1 indicates that the biomarker has the highest weight among all biomarkers used in the OLR model. In contrast, an impact score of 0 indicates that the biomarker is not included in the OLR model. The impact score can also help determine whether altering the biomarker can significantly change the TMS threshold of the OLR model. Furthermore, the performance score of a biomarker shown in Figure 6 represents the corresponding performance score of an approved model that includes that biomarker. Since a biomarker can be included in multiple approved models within the same multi-biomarker scheme, its impact and performance scores may vary.

[0170] The occurrence scores of biomarkers vary depending on the multiple biomarker input method. For the 1-biomarker input method, qNet is the only biomarker with a 100% occurrence, as the OLR model with qNet input is the baseline for the acceptance criterion. Therefore, other biomarkers have an occurrence rate of 0. Furthermore, all biomarkers show 0 occurrences for 10- and 11-biomarker inputs using the hybrid dataset, as no models are accepted due to this scheme. Furthermore, APD90 is not utilized in the acceptance models of the 9-biomarker input method using the hybrid dataset, whereas in contrast, all accepted models with the same 9-biomarker input use APD90 when using the manual dataset.

[0171]

[0172] Furthermore, while qNet has previously been a prominent biomarker for classifying TdP risk of drugs, it is not always used in accepted models using multiple biomarker inputs. qNet's lowest incidence was observed after 3 biomarker inputs (18%) for the manual dataset and after 4 biomarker inputs (59%) for the hybrid dataset, with increasing impact scores. Consistent with qNet, biomarker incidence increases as more biomarkers are incorporated into the input, except for vrest, which exhibits a decreasing trend when the hybrid dataset is used.

[0173] Furthermore, the influence of biomarkers, as shown in Figure 6, can provide insight into how strongly they influence the prediction of TdP risk in the accepted OLR model. Some biomarkers, such as qNet, vmax, and carest, show decreasing influence (in terms of the average influence score) as more biomarkers are incorporated as inputs into the OLR model using the manual dataset. Similarly, other biomarkers, such as dvtmax, camax, and CaTD50, generally have an average influence score below 0.5 when the number of input biomarkers is ≥2. Interestingly, the average influence scores of vrest, APD50, APD90, and CaTD90 are mostly ≥0.5.

[0174] For the accepted models using the hybrid dataset, qNet is the only biomarker that exhibits a negative influence trend, while CaTD90 demonstrates a positive influence trend. Other biomarkers show varying influence trends across different input schemes. However, qNet is the only biomarker with a minimum influence score higher than 0.2 (except for the 10- and 11-biomarker input schemes). Furthermore, the average influence scores of dvtmax, vmax, maxdv, camax, carest, and CaTD50 are mostly below 0.5. Furthermore, the maximum influence score of vmax does not reach 1, indicating that vmax is not the most influential biomarker in the accepted OLR model. In contrast, other biomarkers, such as APD50 and APD90, mostly exhibit average influence scores above 0.5.

[0175] The performance scores of the accepted OLR models that integrate specific biomarkers are also shown in Figure 6. In general, the performance scores of the accepted OLR models using the hybrid dataset are very close to those of qNet alone (performance score 0.73). Furthermore, when APD50 is used in the accepted OLR models, the performance scores plateau at 0.73 for some biomarker inputs ranging from 2 to 9. In contrast, when using the manual dataset, the performance scores of the accepted models range from a minimum of 0.7 (qNet alone) to 0.9. Interestingly, the performance scores of the accepted models using qNet can only reach a maximum of 0.9 when 7-biomarker inputs are applied, whereas the accepted OLR models can achieve the same maximum performance score with a smaller number of biomarker inputs when using other biomarkers.

[0176]

[0177] - Discussion

[0178] Simple yet powerful: Ordinal logistic regression (OLR) models with multiple biomarker inputs can outperform other machine learning algorithms.

[0179] We demonstrate that the best OLR model using a multi-biomarker input scheme can outperform the existing state-of-the-art CiPA-based classifier proposed by Li et al. The authors of the prior art proposed a classifier with a performance score of 0.7 when using a manual dataset and 0.76 when using a hybrid dataset.

[0180] In contrast, the best OLR model we propose in this study achieved a higher performance score of 0.9 when using the manual dataset and 0.767 when using the hybrid dataset, as shown in Figure 5. Furthermore, although the two-biomarker input classifier proposed by Lancaster and Sobie showed a similarly superior AUC of the ROC score for binary classification as the best OLR model, our model can predict three-class TdP risk at once, achieving better overall performance than the model proposed by Lancaster and Sobie.23

[0181] Furthermore, more complex TdP risk classifiers utilizing ANNs and CNN-based classifiers only achieve performance equivalent to or lower than the best proposed OLR model. The ANN models proposed by Yedam et al. and Mahardika et al. fail to meet the minimum acceptance criteria for LR-, whereas the classifier proposed by Fuadah et al. meets good criteria for AUC of ROC, similar to the best proposed OLR model. Furthermore, the CNN model utilizing qInward variability proposed by Jeong et al. fails to meet the minimum acceptance criteria for AUC of ROC and LR-, whereas the CNN-based classifier using the dVm / dt shape of Jeong et al. fails only on the LR- performance measure. Other classifiers proposed by Jeong et al. show overall lower performance than the best OLR model, which yields good performance for both low-risk and high-risk classifications for LR-, but not for the best model, yielding good performance for the minimum acceptance criteria for LR+. In contrast, the best OLR model meets the minimum and good criteria for LR+, which corresponds to the good performance of the model of Jeong et al.

[0182] Another important aspect of in silico classifiers is interpretability. In silico evaluation procedures utilizing multiple biomarker inputs and the Torsade Metric Score (TMS) can enable simpler and more clear interpretation of TdP risk prediction results. TMS thresholds for systems with two or more biomarkers can be presented similarly to those for systems with one or two biomarkers, thanks to the general properties of TMS defined in Equation 9. Previous advanced classifiers based on ANN and CNN architectures, despite their significant TdP risk prediction performance, did not provide quantitative TMS values ​​for drug samples, making model predictions difficult to interpret.

[0183]

[0184] - What can be done if there are a large number of acceptable OLR models?

[0185] Our proposed in silico evaluation of the TdP risk of drugs using a multi-biomarker ordinal logistic regression (OLR) model can also reveal a variety of OLR models that meet the performance criteria based on the CiPA paradigm, as shown in Panel B of Figure 5 . Excluding the results using the biomarker input scheme (the OLR model with qNet as input is the reference model), the number of accepted models using the manual dataset is 781 in total, while the number of accepted models using the hybrid dataset is 622. Together with the results shown in Figure 6 , our proposed in silico approach demonstrates that qNet is not the only biomarker that can effectively predict the TdP risk of a compound, providing a valuable alternative.

[0186] Incorporating more experimentally measurable biomarkers, such as action potential (AP) and calcium-related biomarkers, is also a feasible and important approach to provide physiological understanding and possible further experimental validation of in silico experimental results. Several studies utilizing multi-biomarker inputs without qNet have demonstrated that measurable biomarkers can be used to predict TdP risk for drugs19,22,23,26,30,31, but their prediction performance is superior to state-of-the-art classifiers using qNet alone. Our proposed approach demonstrates that some measurable biomarkers, such as the combination of APD and CaD, can outperform state-of-the-art classifiers based on qNet alone. Based on the manual dataset, 34 accepted models do not include qNet as a biomarker, whereas 119 models do not include qNet as an input for the hybrid dataset. Therefore, utilizing various accepted models that do not include qNet may be more advantageous, as they may provide physiological insights into TdP risk prediction.

[0187]

[0188] - Concerns about the performance of in silico TdP risk assessment of drugs using hybrid datasets.

[0189] The relatively similar performance and performance scores of the accepted models using the hybrid dataset (Figure 6), as well as the relatively high incidence and impact of qNet, may highlight the limitations of using hybrid datasets for in silico TdP risk assessment of drugs. The high incidence and impact of qNet indicate that similar OLR models that rely heavily on qNet are generated and exhibit similar classification performance. Furthermore, the effect of the high reliance on qNet using the hybrid dataset is also evident in the significantly lower number of accepted models (622 accepted models) compared to the manual dataset (781 accepted models). Furthermore, the maximum TdP risk prediction performance of models using the hybrid dataset is significantly lower than that of the manual dataset, as shown in Panel A of Figure 5, highlighting the lower quality of hybrid data for TdP risk assessment compared to the manual dataset. Furthermore, one could argue that manual experimental protocols for assessing the pharmacodynamic inhibition effects of drugs are significantly superior to data from automated high-throughput systems (HTS) used in "hybrid" protocols. That is, it is also possible to leverage dynamic inhibition data from 'hybrid' channels from one laboratory to another, with different experimental protocols to examine drug inhibition effects on CalL, Na, and NaL channels20,41. The significant differences in silico results between passive and hybrid datasets may prompt future studies to reconsider the use of 'hybrid' approaches when constructing in silico classifiers to maximize TdP risk prediction using multi-biomarker inputs.

[0190]

[0191] - The multi-biomarker OLR model is extended for various cardiotoxicity assessment protocols.

[0192] The general characteristics of TMS in multi-biomarker OLR models can be extended to incorporate in silico biomarkers generated from cardiac electrophysiological simulations at the tissue or organ level. Tissue- or organ-level simulations can capture cell-cell interactions within the electric field that cannot be revealed in single-cell simulations. Furthermore, excitation-contraction coupling can be implemented in cardiac tissue- or organ-level simulations, which can generate more realistic electrophysiological states of the heart. Furthermore, incorporating some biomarkers associated with QT prolongation, such as pseudo-ECG signals, may help improve the model's prediction of TdP risk, as QT prolongation is a well-known symptom of TdP. Finally, retaining the physiological information of biomarkers through simple normalization is still necessary to provide more interpretable results and valuable information on important biomarkers for TdP risk prediction in future studies.

[0193]

[0194] As such, those skilled in the art will appreciate that the present invention can be implemented in other specific forms without altering its technical spirit or essential characteristics. Therefore, the embodiments described above should be understood as illustrative in all respects and not restrictive. The scope of the present invention is indicated by the claims below rather than the detailed description above, and all changes or modifications derived from the meaning and scope of the claims and their equivalents should be construed as being included within the scope of the present invention.

Claims

1. A method for evaluating the cardiotoxicity of a drug using a multiple in silico biomarker-based logistic regression model, which generates multiple input scenarios for biomarkers and inputs them into an ordinal logistic regression model (OLR) to predict the risk of drug-induced arrhythmia (TdP), evaluates performance, and ranks each ordinal logistic regression model (OLR) and analyzes them.

2. In paragraph 1, The above biomarkers are, A multi-in silico biomarker-based logistic regression model for drug therapy characterized by qNet (net ionic charge of six ionic currents, ICaL, INaL, IKr, IKs, IK1, and Ito; net ionic charge entering the cell during depolarization), dvdtmax (maximum rate of change of membrane potential during AP rise; maximum value of membrane potential slope in the action potential shape), vmax (maximum membrane potential), vrest (resting membrane potential), APD50 (action potential duration at 50% repolarization), APD90 (action potential duration at 90% repolarization), max_dv (maximum rate of change of membrane potential during repolarization), camax (maximum intracellular calcium concentration), caret (intracellular calcium concentration during resting), CaTD50 (calcium transient duration at 50% repolarization), CaTD90% (period of intracellular calcium concentration during 90% depolarization) Cardiotoxicity assessment method.

3. A method for predicting drug cardiotoxicity using multiple in silico biomarkers, characterized by using Carest (intracellular calcium concentration during resting period) and CaTD90 (period of intracellular calcium concentration during depolarization period) as in silico multiple biomarkers for drug cardiotoxicity evaluation.

4. A method for predicting drug cardiotoxicity using multiple in silico biomarkers, characterized by using qNet (net ionic charge influx into cells during depolarization) and dVdtmax (maximum value of membrane potential gradient in action potential shape) as in silico multiple biomarkers for drug cardiotoxicity evaluation.

5. A method for predicting the cardiac toxicity of a drug using multiple in silico biomarkers, which utilizes a deep learning model that receives the variability of Caest (intracellular calcium concentration during resting state) and CaTD90 (period of intracellular calcium concentration during depolarization) as input to evaluate the proarrhythmic risk of the drug in the data processing unit.

6. A method for predicting the cardiotoxicity of a drug using multiple in silico biomarkers, which utilizes a deep learning model that receives the variability of qNet (net ionic charge inflow into the cell during the depolarization period) and dVdtmax (maximum value of the membrane potential gradient in the action potential shape) as input to evaluate the proarrhythmic risk of the drug in the data processing unit.

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