2 of the MRTD for antiretroviral type compounds would be particularly useful in formulation studies so that clinically relevant extrapolations on drug dissolution and permeability can be made earlier in the drug development process [17– 20]. Several recent studies have been conducted to deﬁne a relationship between the dose and physicochemical prop- erties of the drug [20, 21], or to investigate the underlying mechanisms of drug toxicity and bioaccumulation [20, 22]. Still, the prediction of optimal dose continues to challenge pharmaceutical scientists because of its complexity and variability between diﬀerent organisms. Artiﬁcial neural net- works (ANNs) have emerged as a powerful tool suitable for processing complex relationships between molecular stimuli and biological system responses [23]. Examples include prediction of warfarin maintenance dose [24], gentamicin steady-state plasma concentrations [25], skin permeability [26], and prediction of HIV drug resistance [27]; supporting data for these and other studies suggest the utility of neural network modeling for predicting maximum therapeutic doses. We believed that since the MRTD estimates are derived from human data, they would provide a more relevant, accurate, and speciﬁc estimate for toxic dose levels compared to risk assessment models based on animal data alone. In this article, we predict the MRTD of antiretroviral drugs from their molecular structures using relevant molecular property descriptors and neural network software as a data mining tool. Predictive performance of the models were evaluated and statistically compared with the results obtained clinically or reported in the literature. The application of predictive models in the design of safe, eﬀective antiretroviral drug delivery systems is discussed. 2. Materials and Methods 2.1. Chemoinformatic Software and Modeling Tools. The physicochemical descriptors, molecular weight (MW), aque- ous solubility (ASol), and lipophilicity (AlogP) were deter- mined using ALOGPS 2.1. Virtual Computational Chemistry Laboratory, (http://www.vcclab.org/) [28, 29]. Bioaccumu- lation descriptors, log biotransformation half life (log- BioHL), oxidation half life (OxidHL), and biodegrada- tion probability (P[BD]) were determined using EPI Suite v.410 (http://www.epa.gov/oppt/sf/tools/methods.htm) [30, 31]. All inferential statistics and MRTD data analysis was performed using MedCalc v.12 (MedCalc Software bvba, Belgium). Artiﬁcial neural network analysis was performed using Tiberius Data Mining Software v.6.1.9 (Tiberius Data Mining Software Ltd. Pty, UK). 2.2. MRTD Training and Validation Datasets. The MRTD of 31 structurally diverse antiretroviral drugs were taken from the FDA MRTD database or package inserts. This “clinical MRTD” dataset was randomly split into training and validation subsets as shown in Table 1. Subsequently, each of the calculated descriptors and clinical MRTD values were correlated by multiple linear regression analysis and the results used to identify statistically signiﬁcant property descriptors. An error back propagation algorithm was used Bias MW ASol AlogP logBioHL P[BD] OxidHL Clinical MRTD Computational and Mathematical Methods in Medicine Figure 1: A neural network model was constructed with (2) hidden neuron, (1) output variable that is Clinical MRTD, and (6) input variables that is, OxidHL, P[BD], logBioHL, AlogP, ASol, MW. Total number of patterns (23) were loaded in the data of which 23 were complete and available for training. Two nonlinear neurons were used and the model error minimization was stable for 20 minutes. for network training, with learning rate set at 0.7. A tangent sigmoid transfer function on the ﬁrst layer and two neurons with a nonlinear transfer function on the hidden layer were minimalistic structures used to reduce over-ﬁtting. Results of MRTD versus molecular property descriptors with multiple correlation coeﬃcients are listed in Table 2. For the neural network model training, correlation and error statistics are listed in Table 3. 2.3. Model Validation and Statistical Comparisons. The pre- dictability of each of the multiple linear regression (MLR) and neural network (TNN) models was evaluated by a cross- validation procedure [32]. Each model was constructed on the basis of the same training dataset and was subsequently used to predict the excluded test data. Statistical comparisons were performed between the clinical MRTD and predicted MRTD values using the root mean squared error (RMSE), Kendall’s correlation coeﬃcient (tau), P-value, and Bland Altman plots for methods comparisons. 3. Results 3.1. Model Predicted versus Actual MRTD Estimates. In this multivariable system, a quantitative relationship between certain molecular property descriptors and maximum rec- ommended therapeutic dose was characterized using two datasets (i.e., MRTD and TEST). A multiple linear regression (Table 2) and a 6-2-1-neural network model (Figure 1) for the prediction ARVs maximum dose were constructed. Table 1 lists summary statistics for the molecular property descriptors and corresponding MRTD values in each dataset. The ARVs in this study, although few in number, covered a broad range (CV equal to 40% or greater) in terms of the physicochemical (MW, ASol, AlogP) and bioaccumu- lation properties (logBioHL, OxidHL, P[BD]) included. A signiﬁcant diﬀerence in mean ASol between training set (6.1489 g/L) and TEST set (0.436 g/L) was noted although corresponding changes in lipophilic character were not as great. Multiple linear regression analysis was performed with results listed in Table 2. A statistically signiﬁcant but modest correlation between two of the six descriptors, that is, P[BD]