## 2 QSAR--A Brief Overview
### Chemical Space  
The process of drug discovery is an extremely costly and time-consuming endeavor aimed at ensuring the safety and quality of new chemical entities entering the market. It is estimated that developing a novel molecule can take up to 14 years and cost more than USD one billion from target identification to regulatory approval [36].  
One significant challenge in the medical field is the vast chemical space, forming what is known as the \"drug-like\" environment. An estimated 10\({}^{200}\) drug-like molecules could theoretically be synthesized. Screening all of them would take approximately 2 \(\times\) 10\({}^{193}\) years if one molecule were tested every second [37]. This highlights the necessity of employing smarter methods such as Statistical Molecular Design (SMD) [38]. SMD is an approach used to intelligently select chemical features, effectively expanding the chemical space and increasing the informational content of a chemical library. All available compounds or chemical structural blocks (n) are described using (p) descriptors, forming an n \(\times\) p data matrix X, where each row represents a compound from the library and each column corresponds to the value of a specific descriptor. The matrix X is then subjected to Principal Component Analysis (PCA) [39; 40], offering two key options: (1) summarizing the information from \(p\) descriptors into m \(<\) p principal components that explain most of the variance in the X matrix; (2) using orthogonal (uncorrelated) principal components for fractional factorial designs. The basic workflow for SMD is presented in Figure 2.  
PCA reduces the complexity of original variables by transforming them into principal component scores--linear combinations of the original data--making them easier to interpret. These scores, referred to as principal properties (PPs), represent key chemical characteristics and are mathematically independent. The values of each principal component score vector reflect changes in chemical properties when transitioning between compounds or substituents. The PPs are systematically varied across the entire dataset, ensuring that each PP is explored at all levels of the others. In full and fractional factorial designs, PPs are typically evaluated at two levels: a low level (minus) and a high level (plus), although some designs may include three to five levels. This results in a table of plus and minus signs that defines the optimal combinations of PPs,  
Figure 1: Workflow of QSAR modeling. Initially, a set of chemical compounds needs to be evaluated for their biological activity (BA). Next, the chemical structure of the compounds is described using various chemical descriptors, followed by the application of appropriate chemometric techniques to correlate the measured activity with the chemical descriptors, leading to a QSAR model. The derived model needs to be further validated for accurate predictions and interpretations. The model, along with the associated statistical parameters and graph, is arbitrary.  
chemical properties for a subset of representative compounds. This approach enables the selection of a subset of compounds or substituents that are both representative and diverse. The combination of full or fractional factorial design with PCA results is referred to as Statistical Molecular Design (Figure 2). By selecting a training set based on SMD principles, the degree of multicollinearity in the latent variables (PPs) is automatically reduced, thereby improving subsequent regression analysis [38; 41; 42; 43].