Integrating Machine Learning Approaches and Topological Indices for Prediction of Electronic Properties in Anticancer Drugs

Abstract

In this study, machine learning was used to predict electronic properties of anticancer drugs using molecular descriptors. Four machine learning models were employed to understand and predict the relationship between molecular structure and properties of the molecules. The results showed that extreme gradient boosting (XGBoost) gave good prediction performance in handling complex and nonlinear patterns in the data. In all cases, the feature importance analysis showed a consistent ranking. It shows how molecular descriptors had an influence on property prediction. This study shows how molecular descriptors and machine learning may be used for predicting properties and computational drug design.

1. Introduction

Cancer continues to be a major global health challenge despite significant advancements in medical research and treatment. With more than 200 distinct types, cancer remains one of the leading causes of death in the 21st century. It is a complex disease influenced by many factors, including genetics and lifestyle. As one of the most challenging diseases of our time, cancer not only impacts individual health but also places a heavy burden on healthcare systems and economies. , According to the latest data from the International Agency for Research on Cancer for the year 2022, there were approximately 20 million new cancer cases worldwide and 9.7 million cancer-related deaths. These data show the urgent need for cancer prevention and treatment strategies worldwide, particularly in regions with limited resources. The study of the physicochemical properties of biomolecules and drugs plays an important role in understanding cancer mechanisms and developing therapies. These properties help in designing targeted drugs that can effectively interact with cancerous cells while minimizing toxicity to healthy tissues. In addition, molecular descriptors and topological indices are widely used to predict the behavior of anticancer drugs. These molecular descriptors provide information about the molecular structure and its relationship to biological activity.

Advancements in computational methods, particularly in machine learning and artificial intelligence, help in the accurate modeling and prediction of complex biological interactions. It significantly improves the efficiency in cancer research. Over the past three decades, machine learning has undergone a major transformation as an early 20th-century revolution. It has become a powerful tool for predicting material properties on a large scale. Recent progress extends the entire machine learning workflow, from developing mathematical descriptors that can represent material characteristics to selecting optimal algorithms for prediction. With the rise of testing technologies, large materials databases are now available that offer training data sets for data-driven models. These models help in the design and improvement of novel materials. It provides a novel approach to property calculation in areas like molecular docking, QSAR/QSPR modeling, genomic analysis, and network pharmacology. , Among various molecular properties, the polarizability prediction has been widely studied. Several studies employed quantum-chemical calculations and quantum-informed descriptors for its prediction. In contrast, graph-theoretical topological indices can be computed from molecular structures without requiring quantum chemical calculations. It provides an efficient basis for developing predictive models while maintaining prediction accuracy.

In the context of cancer drugs and treatment, machine learning has been widely applied to predict drug properties. Several studies have demonstrated the application of machine learning techniques in property prediction along with topological indices, which are used as molecular descriptors. Machine learning techniques such as Support Vector Regression, Random Forest, and XGBoost were employed to predict physicochemical properties of a diverse set of drugs. Various topological indices were used as input features to model complex and nonlinear relationships. Feature selection and hyperparameter tuning play an important role for better prediction accuracy. Xiaolong Shi et al. investigated the use of temperature-based topological indices in QSPR modeling of anticancer drugs for predicting properties. The results demonstrate that statistically significant regression and machine learning models can effectively estimate these properties, highlighting the potential of topological indices in drug design and optimization. Guoping Zhang et al. used degree-based topological indices and machine learning models for predicting physicochemical properties of antidepressant drugs. The findings show the superior performance of XGBoost and the First Zagreb index. It emphasizes their application in pharmaceutical property prediction and drug development. Jiang-Hua Tang et al. applied degree-based topological indices in QSPR modeling of arthritis drugs using linear regression, Random Forest, and XGBoost algorithms. The XGBoost model gave the best performance and confirmed the potential of topological descriptors as efficient tools for physicochemical property prediction. Uma Ramachandran et al. examined the use of topological indices within a QSPR framework to predict important physicochemical properties of cervical cancer drugs. The results show that XGBoost achieves superior predictive performance. Additionally, molecular descriptor-based machine learning frameworks have been used to predict electronic properties. Artificial neural networks achieved superior regression performance, and ensemble or kernel-based classifiers provided high classification accuracy. These studies demonstrate the use of topological indices in predicting various drug properties using machine learning. It highlights the growing importance of combining graph-theoretical descriptors with advanced machine learning techniques for reliable property prediction and drug design. Thus, the reviewed literature shows the importance of topological indices in drug property prediction and the continued focus on machine learning in upcoming research.

The main objective of this study is to develop, evaluate, and compare machine learning models that predict electronic properties, molar refractivity, and polarizability. These properties were specifically chosen based on previous research on anticancer drugs. A strong correlation was observed between them and molecular descriptors. , Molar refractivity and polarizability play important roles in drug design. They influence molecular interactions, drug binding affinity, and cell permeability, which are important factors for the efficacy of anticancer drugs. Accurate prediction of molar refractivity and polarizability can facilitate the characterization of anticancer drugs by enabling efficient assessment of molecular properties linked with intermolecular interactions, molecular recognition, and drug-like behavior. It further supports compound characterization, virtual screening, and lead optimization of cancer drugs. Additionally, we aim to identify the best prediction model by evaluating and comparing the performance of the machine learning models. These models will help in making accurate predictions and better understanding of the relationship between these properties and descriptors.

2. Computational Details

2.1. Data Set

In this study, a data set consisting of 500 anticancer drugs are sourced from ChemSpider and PubChem databases. The corresponding physicochemical properties, including molar refractivity (cm³·mol^–1) and polarizability (ų), were collected from the databases and used as target variables. A fundamental requirement for a reliable QSPR model is understanding and characterization of the data set. For molar refractivity, the values ranged from 9.1 to 432.8, with a mean of 109.85 and a standard deviation of 58.50, indicating considerable variation among the molecules. For polarizability, the values ranged from 3.6 to 171.6, with a mean of 43.48 and a standard deviation of 23.15, also showing noticeable variation. Both properties exhibited a positive skew of about 1.7, meaning that most molecules had lower values, while a few had much higher values. This non-normal and uneven distribution suggests that nonlinear machine learning models are more suitable, as they can better capture complex relationships between molecular structure and properties than simple linear models.

The corresponding SMILES representations of these drugs were also retrieved, which will be used as the basis for molecular structure analysis. These SMILES strings were used as inputs for Python-based cheminformatics tools to compute molecular descriptors. Specifically, RDKit was used to convert SMILES into molecular graph objects and compute descriptors with all hydrogens added via Chem.AddHs­(mol), which is used for better representation. NetworkX was used to construct adjacency and distance matrices, which are important for calculating descriptors, while NumPy handled numerical operations.

In this study, the molecular descriptors considered are topological indices that capture structural and connectivity information on molecules in numerical values. Distance-based indices are based on the shortest and longest path lengths between pairs of vertices. It helps capture the overall molecular size within the molecular graph. In terms of chemistry, these indices show how far atoms are positioned from other atoms and how they are connected. It is related to molecular properties that are influenced by electron cloud distribution across the entire structure. Degree-based indices are derived from the degrees of vertices. They are defined as the number of bonds connected to each atom. These indices help us understand local branching and atomic connectivity within the molecule. In terms of chemistry, it shows molecular branching and bonding. They influence reactivity and physicochemical behavior. These indices help in understanding the overall chemical structure and encoding it into numerical values. It makes these indices suitable for QSPR modeling and helps in the prediction of physicochemical properties. Table represents the various molecular descriptors that serve as features. ,, Here, d(m,n) is the distance between the vertices m and n, D(m,n) denotes the maximum length of a path between the vertices m and n, and d _p and d _q represent the degrees of the vertices p and q.

1. Molecular Descriptors Used as Input Features.

molecular descriptors (features)	formula
Wiener Index (W)	∑d(m, n)
Hyper-Wiener Index(WW)	$$\sum \frac{d(m,n)+d^2(m,n)}{2}$$
Harary Index (H)	$$\sum \frac{1}{d(m,n)}$$
Detour Index (D)	∑D(m, n)
Detour Harary Index (DH)	$$\sum \frac{1}{D(m,n)}$$
First Zagreb Index (MA)	∑(d p + d q )
Second Zagreb Index (MB)	∑(d p .d q )
First Hyper Zagreb Index (HMA)	$$\sum {(d_p+d_q)}^2$$
Second Hyper Zagreb Index (HMB)	$$\sum {(d_p.d_q)}^2$$
Redefined First Zagreb Index (RMA)	$$\sum \frac{d_p+d_q}{d_p.d_q}$$
Redefined Second Zagreb Index (RMB)	$$\sum \frac{d_p.d_q}{d_p+d_q}$$
Atom Bond Connectivity Index (ABC)	$$\sum \sqrt{\frac{d_p+d_q-2}{d_p.d_q}}$$
Sum Connectivity Index (SCI)	$$\sum \sqrt{\frac{1}{d_p+d_q}}$$
Randić Index (R)	$$\sum \frac{1}{\sqrt{d_p.d_q}}$$
Reciprocal Randić Index (RR)	$$\sum \sqrt{d_p.d_q}$$
Geometric Arithmetic Index (GA)	$$\sum \frac{2\sqrt{d_p.d_q}}{d_p+d_q}$$
Arithmetic Geometric Index (AG)	$$\sum \frac{d_p+d_q}{2\sqrt{d_p.d_q}}$$
Sombor Index (SO)	$$\sum \sqrt{{(d_p)}^2+{(d_q)}^2}$$
Modified Sombor Index (MSO)	$$\sum \frac{1}{\sqrt{{(d_p)}^2+{(d_q)}^2}}$$
Harmonic Index (HA)	$$\sum \frac{2}{d_p+d_q}$$

2.2. Machine Learning Workflow

The machine learning models used include extreme gradient boosting (XGBoost), Random Forest, categorical boosting (CatBoost), and light gradient boosting machine (LightGBM). The XGBoost model is known for its gradient boosting technique and high predictive performance, and the Random Forest model is valued for its ensemble of decision trees and ability to avoid overfitting. , Along with these, the CatBoost model and LightGBM model are used for their efficiency in processing large data sets. These models use a consistent and well-structured methodology for the regression analysis.

Figure presents the workflow diagram, outlining the key steps involved in the machine learning process used in the study.

1.

Machine learning workflow for electronic property prediction.

2.3. Model Training and Validation

The data set was divided into a 70–30 train-test split to maintain reproducibility and avoid sampling bias. The model was trained using only the training set, and the test set was used for independent performance evaluation. A 5-fold cross-validation was conducted during training. It is used to maintain statistical stability. This ensures that all data subsets contribute to validation and reduces the dependency on any single split. It also helps in minimizing evaluation variance. While both models follow the same workflow, they differ in algorithm choice, tuning scope, parameter grid design, and visualization refinements. Hyperparameter optimization was performed only on the training data to maximize the model’s performance. This process employed RandomizedSearchCV to broadly explore parameter spaces and then was followed by a refined GridSearchCV based on the initial results. The optimized hyperparameters varied depending on the model architecture. The specific hyperparameters optimized for each model are summarized in Table .

2. Optimized Hyperparameters for the Machine Learning Model.

model	optimized hyperparameters
Random Forest	n_estimators, max_depth, min_samples_split, min_samples_leaf, max_features, bootstrap, criterion
XGBoost	n_estimators, max_depth, learning_rate, subsample, colsample_bytree, min_child_weight, gamma, alpha, lambda
LightGBM	n_estimators, max_depth, learning_rate, num_leaves, subsample, colsample_bytree, min_child_samples, reg_alpha, reg_lambda
CatBoost	iterations, depth, learning_rate, subsample, colsample_bylevel, min_data_in_leaf, reg_lambda, random_strength, bagging_temperature, border_count

3. Results

3.1. Correlation Analysis

A Pearson correlation analysis was conducted to understand the linear relationship between the molecular descriptors and target properties. The correlation coefficients (r) were calculated between each descriptor and both properties and are presented in Table .

3. Correlation Coefficients Between Molecular Descriptors and Target Properties.

descriptor	MR (cm3·mol–1)	P (Å3)
W	0.8525	0.8545
WW	0.7934	0.7955
H	0.9390	0.9403
D	0.8464	0.8484
DH	0.8882	0.8896
MA	0.9589	0.9598
MB	0.9468	0.9476
HMA	0.9413	0.9421
HMB	0.8893	0.8899
RMA	0.9680	0.9690
RMB	0.9656	0.9664
ABC	0.9679	0.9688
SCI	0.9743	0.9753
R	0.9730	0.9740
RR	0.9627	0.9636
GA	0.9741	0.9751
AG	0.9658	0.9668
SO	0.9560	0.9568
MSO	0.9785	0.9795
HA	0.9768	0.9778

The analysis shows that all descriptors have strong positive correlations with both target properties. W, D and DH show strong correlations (r ≈ 0.84–0.89). H, MA, MB, HMA, and HMB demonstrate even stronger correlations (r > 0.93). Among all descriptors, MSO (r = 0.9785 for MR, r = 0.9795 for P) and HA (r = 0.9768 for MR, r = 0.9778 for P) gave the highest correlation values. Descriptors such as SCI, R, GA, ABC, AG, RMB, and RMA also show very high correlation values (r > 0.96), which confirms their strong prediction for molecular refractivity and polarizability. Overall, the correlation coefficients range from approximately 0.79 to 0.98. This shows a statistically significant and strong linear relationship between the selected molecular descriptors and the target properties.

3.2. Model Performance Summary

Table presents the regression metrics for all models that were evaluated on the training and testing sets for molar refractivity and polarizability. The regression metrics provide a quantitative assessment of model accuracy and error distribution.

4. Regression Performance Metrics Used for Model Evaluation.

model	target property	data set	R 2	RMSE	MAE
XGBoost	molar refractivity (cm3·mol–1)	Train	0.9704	9.7319	3.6820
		Test	0.9497	13.9963	7.5931
	polarizability (Å3)	Train	0.9802	3.1513	0.9654
		Test	0.9452	5.7672	2.9334
Random Forest	molar refractivity (cm3·mol–1)	Train	0.9909	5.3947	3.1556
		Test	0.9382	15.5171	7.9157
	polarizability (Å3)	Train	0.9923	1.9700	1.0298
		Test	0.9422	5.9227	2.9973
CatBoost	molar refractivity (cm3·mol–1)	Train	0.9688	9.9945	6.1016
		Test	0.9358	15.8158	8.6753
	polarizability (Å3)	Train	0.9698	3.8928	2.3552
		Test	0.9411	5.9771	3.2605
LightGBM	molar refractivity (cm3·mol–1)	Train	0.9335	14.5891	5.9308
		Test	0.9074	18.9914	9.0109
	polarizability (Å3)	Train	0.9339	5.7621	2.1668
		Test	0.9132	7.2595	3.2652

From the regression metrics, XGBoost showed a strong balance between the training and testing performance for both properties. It achieved testing R ² values of 0.9497 for molar refractivity and 0.9452 for polarizability, with lower RMSE and MAE values. Random Forest also achieved the highest training R ², but it also showed overfitting. CatBoost performed reasonably well. However, LightGBM had the lowest test R ², especially for molar refractivity, which shows weaker generalization.

3.3. Visual Evaluation of Predictions

To further evaluate model predictions. Scatter plots of actual vs predicted values for both models are plotted in Figure for molar refractivity and Figure for polarizability. In the case of molar refractivity, XGBoost demonstrates the closed fit to the diagonal line, which shows high prediction accuracy and generalization. Random Forest also performs well but shows more scattered points, which indicate overfitting. CatBoost performs moderately with small deviations and remains consistent with its lower R ². LightGBM shows the widest spread, particularly at higher values, which matches its lowest test performance. Overall, XGBoost is the most reliable model for predicting the molar refractivity.

2.

Actual versus predicted molar refractivity (cm³·mol^–1) values obtained using machine learning models: (a) XGBoost, (b) Random Forest, (c) CatBoost, and (d) LightGBM.

3.

Actual versus predicted polarizability (ų) values obtained using four machine learning models: (a) XGBoost, (b) Random Forest, (c) CatBoost, and (d) LightGBM.

In the case of polarizability, the XGBoost model gives the best results with most points close to the line, which means its predictions are very accurate. Random Forest also performs well but has a few more scattered points. CatBoost shows slightly more errors, especially for high values. LightGBM has the most spread-out points, particularly for large values, which shows that it is less accurate. Again, XGBoost is the most reliable model for predicting the polarizability.

3.4. Feature Importance

Feature importance analysis was conducted using model-derived and permutation importance. It evaluated the contribution of each molecular descriptor for property prediction. The results presented in Tables and show how different machine learning models depend on various molecular descriptors to predict properties. The corresponding bar plots shown in Figures and represent the change in feature importance for each property. They highlight which descriptors stand out in the specific models. Model-derived importance reflects the internal decision-making mechanism of the trained model. Permutation importance provides an independent and performance-based evaluation by observing how prediction accuracy changes when feature values are randomly shuffled. The use of these two analyses for feature importance provides an unbiased and robust evaluation of the descriptors.

5. Feature Importance for Molar Refractivity (cm³·mol^–1).

feature	XGBoost	Random Forest	CatBoost	LightGBM
W	0.5758	8.1515	8.1547	3.3333
WW	0.6601	4.7352	13.8680	1.0814
H	0.1378	2.5029	1.0437	0.2123
D	0.5619	3.1233	3.3183	1.7078
DH	0.0269	0.5566	2.5501	1.1086
MA	1.4013	1.0215	5.4291	0.0360
MB	0.0159	0.6969	2.3516	0.1382
HMA	0.0201	0.3855	3.4191	0.4073
HMB	0.1079	0.3333	5.2304	0.3503
RMA	0.0182	2.4510	4.1278	0.0515
RMB	0.9172	2.1000	4.0976	0.4998
ABC	2.9736	1.3489	8.3074	22.1520
SCI	7.0780	5.9835	2.5372	6.7760
R	0.0454	2.5767	1.7903	0.6645
RR	0.0308	0.4265	10.1568	0.0083
GA	56.0051	10.7827	4.4056	2.1967
AG	0.0064	3.3758	1.6073	0.7229
SO	0.0151	2.0286	6.5065	0.0156
MSO	29.0621	38.9423	2.6227	25.8624
HA	0.3060	8.2911	3.5461	32.5117

6. Feature Importance for Polarizability (ų).

feature	XGBoost	Random Forest	CatBoost	LightGBM
W	0.8262	7.3851	8.5342	3.5634
WW	0.7086	4.8883	13.8711	0.8849
H	0.1473	1.0205	1.0768	0.1810
D	0.6496	2.4795	3.4897	1.6480
DH	0.1350	0.4079	2.5122	1.1148
MA	2.0910	0.4883	5.2408	0.0307
MB	0.0295	0.1975	2.1645	0.1297
HMA	0.0359	0.3138	3.4355	0.3862
HMB	0.1465	0.3398	5.5285	0.4757
RMA	0.0007	1.5349	3.8829	0.0971
RMB	0.0791	1.7425	1.5907	0.4261
ABC	3.9826	3.4601	9.0261	22.1991
SCI	6.4132	2.0794	2.2667	7.1977
R	0.0455	3.2053	2.3084	0.5877
RR	0.0259	1.2444	10.4100	0.0097
GA	47.9990	10.4544	4.2958	2.1192
AG	0.0038	2.3212	1.7834	0.8857
SO	0.0377	0.2404	7.4384	0.0128
MSO	36.5351	46.9735	2.4829	26.2084
HA	0.0817	7.1567	3.6014	31.6902

4.

Feature importance comparison for molar refractivity (cm³·mol^–1).

5.

Feature importance comparison for polarizability (ų).

For molar refractivity, Geometric Arithmetic Index is the most significant descriptor for the XGBoost model, while the Modified Sombor Index was dominant in the Random Forest model. For CatBoost, the Hyper-Wiener Index showed high importance, while the Harmonic Index was the most important descriptor for LightGBM. In all the models, Atom Bond Connectivity Index, Sum Connectivity Index, and Modified Sombor Index consistently appeared as important features, which indicate their influence on molar refractivity prediction. Some features like Redefined First Zagreb Index and Reciprocal Randić Index showed low importance across all models, which suggests a weaker correlation.

For polarizability, a few features have a strong influence across all four models, such as Geometric Arithmetic Index and Modified Sombor Index. In the XGBoost and Random Forest models, these two descriptors were the top contributors. In LightGBM, Harmonic Index and Atom Bond Connectivity Index show high influence, while CatBoost gives more balanced importance across features like Hyper-Wiener Index, Zagreb Index, Hyper Second Zagreb Index, Randić Index, and Atom Bond Connectivity Index. On the other hand, descriptors such as Second Zagreb Index and Sombor Index show low importance, which means they contribute less to the model’s prediction.

4. Discussion

Among all of the models that have been considered, XGBoost emerged as the most effective model. It is reliable for predicting electronic properties from the molecular descriptors. Its performance strength shows its ability to model complex and nonlinear structure–property relationships. It maintains generalization across diverse chemical compounds. It gradually improves errors through gradient boosting and captures high-order interactions among descriptors that are important for better property prediction. Although a few compounds showed deviations in the prediction plots, it still remains acceptable within the error limits. It did not affect the overall model performance. These deviations are expected chemically. Compounds with irregular branching may affect the electron distribution, which can lead to errors during prediction.

A key outcome of this study is that topological indices can be considered for the prediction of the electronic properties. This highlights their chemical significance. Both the molar refractivity and polarizability are bulk electronic properties. It depends on molecular size, molecular volume, and electron cloud distribution, instead of conformational or energetic features. These characteristics are fundamentally linked to the molecular connectivity and position of the atoms. It can be fully captured by using these molecular descriptors, which encode molecular information from a chemical graph. In terms of computational methodology, these descriptors encode molecular structural information in a compact form by using numbers. It helps in avoiding three-dimensional geometries or quantum chemical calculations.

Indices like Geometric Arithmetic Index, Modified Sombor Index, Sum Connectivity Index, Atom Bond Connectivity, and First Zagreb Index play an important role in prediction. They effectively capture the structural and connectivity patterns of the molecules. The Geometric Arithmetic index balances geometric and arithmetic means of vertex degrees. It makes it sensitive to degree heterogeneity and molecular branching. The Atom–Bond Connectivity Index emphasizes the inverse relationship between bond connectivity and branching. In chemical terms, it shows how bond environments influence electron density under an external electric field. Similarly, the Sum Connectivity Index captures cumulative degree interactions. It effectively encodes the overall bonding density of the molecule, which directly impacts polarizability. The First Zagreb Index, which sums squared vertex degrees, shows the overall degree concentration in the molecular graph. The Modified Sombor Index also helps in degree-based information by weighting squared degree contributions.

Recent studies have demonstrated the growing importance of machine learning for molecular property prediction through automated descriptor generation and advanced deep learning architectures. However, many of these approaches rely on sophisticated electronic or geometric representations. In contrast, the present work investigates whether computationally inexpensive topological indices can effectively predict the molecular electronic properties.

The scientific novelty of the study also shows that molecular descriptors based on simple chemical graphs can be used with gradient boosting models. It can be helpful in predicting electronic properties for large and diverse drug data sets. This highlights that the prediction of electronic properties does not necessarily require extensive computational or experimental work. Instead, the structure–property relationship, along with a nonlinear modeling framework, can play a significant role.

5. Conclusion

This study shows how machine learning can be used for effective property predictions. In all of the models that have been considered, XGBoost consistently outperformed others. It showed the best balance between training and testing performance, along with high R ² values and low prediction errors. Furthermore, feature importance analysis also validated its robustness. It shows that the Geometric Arithmetic Index and the Modified Sombor Index had a strong influence on the prediction performance. While Random Forest, CatBoost, and LightGBM showed reasonable accuracy, they either overfitted or did not generalize well. Overall, XGBoost was the most reliable model, as it provides accurate predictions without overfitting. The study shows that machine-learning models with selected molecular descriptors may be useful for predicting molecular properties. Furthermore, these findings suggest that this method can be extended to other molecular descriptors, different property types, and advanced modeling techniques. However, the present study relies on two-dimensional topological descriptors and does not consider three-dimensional representations or parameters. Additionally, a more diverse data set may help in better generalization of the proposed method. Future research may focus on investigating three-dimensional molecular and quantum chemical descriptors to capture more structural information. The application of advanced deep learning techniques may further improve prediction performance for larger and diverse data sets. The proposed framework may also be used for different classes of chemical compounds and combined with recent AI-driven approaches to molecular property prediction. It contributes to the development of AI-driven methods in molecular property prediction.

The raw data, trained machine learning models, and Python code for finding molecular descriptors and applying the raw data to the models and computing error estimates are available at the following link: https://github.com/simran2410/cancer_drugs.

S.K.: Conceptualization, methodology, software, validation, formal analysis, and writingoriginal draft. R.S.J.: Conceptualization, supervision, writingreviewing and editing, visualisation.

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

The authors declare no competing financial interest.