External Cross-validation Research Articles

Molecular classification of scrapie strains in mice using gene expression profiling

Transmissible spongiform encephalopathy strains demonstrate specific prion characteristics, each with specific incubation times, and strain-specific patterns of deposition of the misfolded isoform of prion, PrPSc, in the brains of infected individuals. Different biochemical properties, including glycosylation profiles and the degree of proteinase resistance, have been shown to be strain-specific. However, no relationship between these properties and the phenotypic differences in the subsequent diseases has as yet been determined. Here we explore the utility of gene expression profiles to identify differences in the host response to different strains of prion agent. We identify 114 genes that exhibit significantly different levels of expression in mice infected with three strains of scrapie. These genes represent a pool of genes involved in a strain-specific response to prion disease. We have identified the most discriminatory genes from this list utilizing a wrapper-based feature selection algorithm with external cross-validation.

Gene Selection for Sample Classifications in Microarray Experiments

DNA microarray technology provides useful tools for profiling global gene expression patterns in different cell/tissue samples. One major challenge is the large number of genes relative to the number of samples. The use of all genes can suppress or reduce the performance of a classification rule due to the noise of nondiscriminatory genes. Selection of an optimal subset from the original gene set becomes an important prestep in sample classification. In this study, we propose a family-wise error (FWE) rate approach to selection of discriminatory genes for two-sample or multiple-sample classification. The FWE approach controls the probability of the number of one or more false positives at a prespecified level. A public colon cancer data set is used to evaluate the performance of the proposed approach for the two classification methods: k nearest neighbors (k-NN) and support vector machine (SVM). The selected gene sets from the proposed procedure appears to perform better than or comparable to several results reported in the literature using the univariate analysis without performing multivariate search. In addition, we apply the FWE approach to a toxicogenomic data set with nine treatments (a control and eight metals, As, Cd, Ni, Cr, Sb, Pb, Cu, and AsV) for a total of 55 samples for a multisample classification. Two gene sets are considered: the gene set ΩF formed by the ANOVA F-test, and a gene set ΩT formed by the union of one-versus-all t-tests. The predicted accuracies are evaluated using the internal and external crossvalidation. Using the SVM classification, the overall accuracies to predict 55 samples into one of the nine treatments are above 80% for internal crossvalidation. ΩF has slightly higher accuracy rates than ΩT. The overall predicted accuracies are above 70% for the external crossvalidation; the two gene sets ΩT and ΩF performed equally well.

Gene Selection for Sample Classifications in Microarray Experiments

DNA microarray technology provides useful tools for profiling global gene expression patterns in different cell/tissue samples. One major challenge is the large number of genes relative to the number of samples. The use of all genes can suppress or reduce the performance of a classification rule due to the noise of nondiscriminatory genes. Selection of an optimal subset from the original gene set becomes an important prestep in sample classification. In this study, we propose a family-wise error (FWE) rate approach to selection of discriminatory genes for two-sample or multiple-sample classification. The FWE approach controls the probability of the number of one or more false positives at a prespecified level. A public colon cancer data set is used to evaluate the performance of the proposed approach for the two classification methods: k nearest neighbors (k-NN) and support vector machine (SVM). The selected gene sets from the proposed procedure appears to perform better than or comparable to several results reported in the literature using the univariate analysis without performing multivariate search. In addition, we apply the FWE approach to a toxicogenomic data set with nine treatments (a control and eight metals, As, Cd, Ni, Cr, Sb, Pb, Cu, and AsV) for a total of 55 samples for a multisample classification. Two gene sets are considered: the gene set omegaF formed by the ANOVA F-test, and a gene set omegaT formed by the union of one-versus-all t-tests. The predicted accuracies are evaluated using the internal and external crossvalidation. Using the SVM classification, the overall accuracies to predict 55 samples into one of the nine treatments are above 80% for internal crossvalidation. OmegaF has slightly higher accuracy rates than omegaT. The overall predicted accuracies are above 70% for the external crossvalidation; the two gene sets omegaT and omegaF performed equally well.

Discriminating Different Classes of Toxicants by Transcript Profiling

Male rats were treated with various model compounds or the appropriate vehicle controls. Most substances were either well-known hepatotoxicants or showed hepatotoxicity during preclinical testing. The aim of the present study was to determine if biological samples from rats treated with various compounds can be classified based on gene expression profiles. In addition to gene expression analysis using microarrays, a complete serum chemistry profile and liver and kidney histopathology were performed. We analyzed hepatic gene expression profiles using a supervised learning method (support vector machines; SVMs) to generate classification rules and combined this with recursive feature elimination to improve classification performance and to identify a compact subset of probe sets with potential use as biomarkers. Two different SVM algorithms were tested, and the models obtained were validated with a compound-based external cross-validation approach. Our predictive models were able to discriminate between hepatotoxic and nonhepatotoxic compounds. Furthermore, they predicted the correct class of hepatotoxicant in most cases. We provide an example showing that a predictive model built on transcript profiles from one rat strain can successfully classify profiles from another rat strain. In addition, we demonstrate that the predictive models identify nonresponders and are able to discriminate between gene changes related to pharmacology and toxicity. This work confirms the hypothesis that compound classification based on gene expression data is feasible.

Discriminating different classes of toxicants by transcript profiling.

Male rats were treated with various model compounds or the appropriate vehicle controls. Most substances were either well-known hepatotoxicants or showed hepatotoxicity during preclinical testing. The aim of the present study was to determine if biological samples from rats treated with various compounds can be classified based on gene expression profiles. In addition to gene expression analysis using microarrays, a complete serum chemistry profile and liver and kidney histopathology were performed. We analyzed hepatic gene expression profiles using a supervised learning method (support vector machines; SVMs) to generate classification rules and combined this with recursive feature elimination to improve classification performance and to identify a compact subset of probe sets with potential use as biomarkers. Two different SVM algorithms were tested, and the models obtained were validated with a compound-based external cross-validation approach. Our predictive models were able to discriminate between hepatotoxic and nonhepatotoxic compounds. Furthermore, they predicted the correct class of hepatotoxicant in most cases. We provide an example showing that a predictive model built on transcript profiles from one rat strain can successfully classify profiles from another rat strain. In addition, we demonstrate that the predictive models identify nonresponders and are able to discriminate between gene changes related to pharmacology and toxicity. This work confirms the hypothesis that compound classification based on gene expression data is feasible.

Total and Local Quadratic Indices of the Molecular Pseudograph's Atom Adjacency Matrix: Applications to the Prediction of Physical Properties of Organic Compounds

A novel topological approach for obtaining a family of new molecular descriptors is proposed. In this connection, a vector space E (molecular vector space), whose elements are organic molecules, is defined as a “direct sum” of different ℜi spaces. In this way we can represent molecules having a total of i atoms as elements (vectors) of the vector spaces ℜi (i=1, 2, 3,..., n; where n is number of atoms in the molecule). In these spaces the components of the vectors are atomic properties that characterize each kind of atom in particular. The total quadratic indices are based on the calculation of mathematical quadratic forms. These forms are functions of the k-th power of the molecular pseudograph’s atom adjacency matrix (M). For simplicity, canonical bases are selected as the quadratic forms’ bases. These indices were generalized to “higher analogues” as number sequences. In addition, this paper also introduces a local approach (local invariant) for molecular quadratic indices. This approach is based mainly on the use of a local matrix [Mk(G, FR)]. This local matrix is obtained from the k-th power (Mk(G)) of the atom adjacency matrix M. Mk(G, FR) includes the elements of the fragment of interest and those that are connected with it, through paths of length k. Finally, total (and local) quadratic indices have been used in QSPR studies of four series of organic compounds. The quantitative models found are significant from a statistical point of view and permit a clear interpretation of the studied properties in terms of the structural features of molecules. External prediction series and cross-validation procedures (leave-one-out and leave-group-out) assessed model predictability. The reported method has shown similar results, compared with other topological approaches. The results obtained were the following: a) Seven physical properties of 74 normal and branched alkanes (boiling points, molar volumes, molar refractions, heats of vaporization, critical temperatures, critical pressures and surface tensions) were well modeled (R>0.98, q2>0.95) by the total quadratic indices. The overall MAE of 5-fold cross-validation were of 2.11 oC, 0.53 cm3, 0.032 cm3, 0.32 KJ/mol, 5.34 oC, 0.64 atm, 0.23 dyn/cm for each property, respectively; b) boiling points of 58 alkyl alcohols also were well described by the present approach; in this sense, two QSPR models were obtained; the first one was developed using the complete set of 58 alcohols [R=0.9938, q2=0.986, s=4.006oC, overall MAE of 5-fold cross-validation=3.824 oC] and the second one was developed using 29 compounds as a training set [R=0.9979, q2=0.992, s=2.97 oC, overall MAE of 5-fold cross-validation=2.580 oC] and 29 compounds as a test set [R=0.9938, s=3.17 oC]; c) good relationships were obtained for the boiling points property (using 80 and 26 cycloalkanes in the training and test sets, respectively) using 2 and 5 total quadratic indices: [Training set: R=0.9823 (q2=0.961 and overall MAE of 5-fold cross-validation=6.429 oC) and R=0.9927 (q2=0.977 and overall MAE of 5-fold cross-validation=4.801 oC); Test set: R=0.9726 and R=0.9927] and d) the linear model developed to describe the boiling points of 70 organic compounds containing aromatic rings has shown good statistical features, with a squared correlation coefficient (R2) of 0.981 (s=7.61 oC). Internal validation procedures (q2=0.9763 and overall MAE of 5-fold cross-validation=7.34 oC) allowed the predictability and robustness of the model found to be assessed. The predictive performance of the obtained QSPR model also was tested on an extra set of 20 aromatic organic compounds (R=0.9930 and s=7.8280 oC). The results obtained are valid to establish that these new indices fulfill some of the ideal requirements proposed by Randić for a new molecular descriptor.

Body mass index as a measure of body fatness: age- and sex-specific prediction formulas

In 1229 subjects, 521 males and 708 females, with a wide range in body mass index (BMI; 13.9-40.9 kg/m2), and an age range of 7-83 years, body composition was determined by densitometry and anthropometry. The relationship between densitometrically-determined body fat percentage (BF%) and BMI, taking age and sex (males = 1, females = 0) into account, was analysed. For children aged 15 years and younger, the relationship differed from that in adults, due to the height-related increase in BMI in children. In children the BF% could be predicted by the formula BF% = 1.51 x BMI-0.70 x age - 3.6 x sex + 1.4 (R2 0.38, SE of estimate (SEE) 4.4% BF%). In adults the prediction formula was: BF% = 1.20 x BMI + 0.23 x age - 10.8 x sex - 5.4 (R2 0.79, SEE = 4.1% BF%). Internal and external cross-validation of the prediction formulas showed that they gave valid estimates of body fat in males and females at all ages. In obese subjects however, the prediction formulas slightly overestimated the BF%. The prediction error is comparable to the prediction error obtained with other methods of estimating BF%, such as skinfold thickness measurements or bioelectrical impedance.

Accurate prediction of &OV0312;O2max in cycle ergometry

Numerous equations exist for predicting VO2max from the duration (an analog of maximal work rate, Wmax) of a treadmill graded exercise test (GXT). Since a similar equation for cycle ergometry (CE) was not available, we saw the need to develop such an equation, hypothesizing that CE VO2max could be accurately predicted due to its more direct relationship with W. Thus, healthy, sedentary males (N = 115) and females (N = 116), aged 20-70 yr, were given a 15 W.min-1 CE GXT. The following multiple linear regression equations which predict VO2max (ml.min-1) from the independent variables of Wmax (W), body weight (kg), and age (yr) were derived from our subjects: Males: Y = 10.51 (W) + 6.35 (kg) - 10.49 (yr) + 519.3 ml.min-1; R = 0.939, SEE = 212 ml.min-1. Females: Y = 9.39 (W) + 7.7 (kg) - 5.88 (yr) + 136.7 ml.min-1; R = 0.932, SEE = 147 ml.min-1 Using the 95% confidence limits as examples of worst case errors, our equations predict VO2max to within 10% of its true value. Internal (double cross-validation) and external cross-validation analyses yielded r values ranging between 0.920 and 0.950 for the male and female regression equations. These results indicate that use of the equations generated in this study for a 15 W.min-1 CE GXT provides accurate estimates of VO2max.