Sheridan R P, Nachbar R B, Bush B L
Molecular Systems Department, Merck Research Laboratories, Rahway, NJ 07065.
J Comput Aided Mol Des. 1994 Jun;8(3):323-40. doi: 10.1007/BF00126749.
Trend vector analysis [Carhart, R.E. et al., J. Chem. Inf. Comput. Sci., 25 (1985) 64], in combination with topological descriptors such as atom pairs, has proved useful in drug discovery for ranking large collections of chemical compounds in order of predicted biological activity. The compounds with the highest predicted activities, upon being tested, often show a several-fold increase in the fraction of active compounds relative to a randomly selected set. A trend vector is simply the one-dimensional array of correlations between the biological activity of interest and a set of properties or 'descriptors' of compounds in a training set. This paper examines two methods for generalizing the trend vector to improve the predicted rank order. The trend matrix method finds the correlations between the residuals and the simultaneous occurrence of descriptors, which are stored in a two-dimensional analog of the trend vector. The SAMPLS method derives a linear model by partial least squares (PLS), using the 'sample-based' formulation of PLS [Bush, B.L. and Nachbar, R.B., J. Comput.-Aided Mol. Design, 7 (1993) 587] for efficiency in treating the large number of descriptors. PLS accumulates a predictive model as a sum of linear components. Expressed as a vector of prediction coefficients on properties, the first PLS component is proportional to the trend vector. Subsequent components adjust the model toward full least squares. For both methods the residuals decrease, while the risk of overfitting the training set increases. We therefore also describe statistical checks to prevent overfitting. These methods are applied to two data sets, a small homologous series of disubstituted piperidines, tested on the dopamine receptor, and a large set of diverse chemical structures, some of which are active at the muscarinic receptor. Each data set is split into a training set and a test set, and the activities in the test set are predicted from a fit on the training set. Both the trend matrix and the SAMPLS approach improve the predictions over the simple trend vector. The SAMPLS approach is superior to the trend matrix in that it requires much less storage and CPU time. It also provides a useful set of axes for visualizing properties of the compounds. We describe a randomization method to determine the optimum number of PLS components that is very much faster for large training sets than leave-one-out cross-validation.
趋势向量分析[卡哈特，R.E.等人，《化学信息与计算机科学杂志》，25(1985)64]，与诸如原子对之类的拓扑描述符相结合，已被证明在药物发现中对于按照预测的生物活性对大量化合物进行排序很有用。经测试，预测活性最高的化合物相对于随机选择的一组化合物，其活性化合物的比例通常会有几倍的增加。趋势向量简单来说就是感兴趣的生物活性与训练集中一组化合物的性质或“描述符”之间的一维相关数组。本文研究了两种用于推广趋势向量以改善预测排名顺序的方法。趋势矩阵法找到残差与描述符同时出现之间的相关性，并将其存储在趋势向量的二维类似物中。SAMPLS方法通过偏最小二乘法(PLS)推导线性模型，使用PLS的“基于样本”公式[布什，B.L.和纳赫巴，R.B.，《计算机辅助分子设计杂志》，7(1993)587]以提高处理大量描述符的效率。PLS将预测模型累积为线性分量的总和。表示为性质上的预测系数向量时，第一个PLS分量与趋势向量成比例。后续分量将模型调整为完全最小二乘法。对于这两种方法，残差都会减小，而过度拟合训练集的风险会增加。因此，我们还描述了防止过度拟合的统计检验。这些方法应用于两个数据集，一个是在多巴胺受体上测试的小的二取代哌啶同系物系列，另一个是大量不同化学结构的集合，其中一些对毒蕈碱受体有活性。每个数据集都被分成一个训练集和一个测试集，并根据对训练集的拟合来预测测试集中的活性。趋势矩阵法和SAMPLS方法都比简单的趋势向量改进了预测。SAMPLS方法优于趋势矩阵法，因为它所需的存储和CPU时间要少得多。它还提供了一组有用的轴来可视化化合物的性质。我们描述了一种随机化方法来确定PLS分量的最佳数量，对于大型训练集，该方法比留一法交叉验证要快得多。
