Internal cross-validation method

Unlike test set validation methods, cross-validation methods attempt to validate a model using the calibration data only, without requiring the preparation and analysis of an additional test set of samples. This involves the execution of one or more internal validation procedures (hereby called subvalidations), where each subvalidation involves three steps ... 

The selected subset cross-validation method is probably the closest internal validation method to external validation in that a single validation procedure is executed using a single split of subset calibration and validation data. Properly implemented, it can provide the least optimistic assessment of a model s prediction error. Its disadvantages are that it can be rather difficult and cumbersome to set it up so that it is properly implemented, and it is difficult to use effectively for a small number of calibration samples. It requires very careful selection of the validation samples such that not only are they sufficiently representative of the samples to be applied to the model during implementation, but also the remaining samples used for subset calibration are sufficiently representative as well. This is the case because there is only one chance given to test a model that is built from the data. 

To circumvent this issue, cross-validation methods have been proposed to evaluate the internal predictivity of the model by discarding one or several com-... 

An alternative approach to using traditional parametric statistical methods to calculate the significance of fitted correlations, would be to directly assess the model based on its ability to predict, rather than merely to assess how well the model fits the training set. When the quality of the model is assessed by the prediction of a test set, rather than the fit of the model to its training set, a statistic related to r or can be defined, and denoted q or q, to indicate that the quality measure is assessed in prediction. A q may be calculated by internal cross-validation techniques, or by the quality of predictions of an independent test set, in which case an upper-case is used. The equation to calculate q (or Q ) is shown in equation 9.3. 

The method of cross-validation is based on internal validation, which means that one predicts each element in the data set from the results of an analysis of the remaining ones. This can be done by leaving out each element in turn, which in the case of an nxp table would require nxp analyses. Wold [44] has implemented a scheme for leaving out groups of elements at the same time, which reduces the... 

Probably the most common internal validation method, cross-validation, involves the execution of one or more internal validation procedures (hereby called sub-validations), where each procedure involves the removal of a part of the calibration data, use of the remaining calibration data to build a subset calibration model, and subsequent application of the removed data to the subset calibration model. Unlike the Model fit evaluation method discussed earlier, the same data are not used for model building and model testing for each of the sub-validations. As a result, they can provide more realistic estimates of a model s prediction performance, as well as better assessments of the optimal complexity of a model. 

Although cross-validation is by far the most frequently used validation method in practice, it should be noted that there are other internal validation methods that have... 

A stereoselective GC method for determination of etodolac enantiomers in human plasma and urine was first reported as a preliminary method [35], and then as a validated method [36]. Sample preparation involved addition of (S)-(+)-naproxen (internal standard) and sodium hydroxide to diluted plasma or urine. The samples were washed with diethyl ether, acidified with hydrochloric acid, and extracted with toluene. ( )-(+)-naproxen was used as a derivatizing agent to form diastereomeric derivatives of etodolac. The gas chromatograph system used in this work was equipped with fused-silica capillary column (12 m x 0.2 mm i.d.) coated with high-performance cross-linked methylsilicone film (thickness 0.33 pm) and a nitrogen-phosphorous detector. The operating conditions were injector 250°C detector 300°C column 100-260°C (32 °C/min). 

Overtraining As with many other methods, decision trees are prone to overtraining if not monitored. The forecasting ability of the tree must be estimated by some, usually, internal validation method such as a validation set or through cross-validation. This will determine the depth and degree of branching of the derived tree. 

Very often a test population of data is not available or would be prohibitively expensive to obtain. When a test population of data is not possible to obtain, internal validation must be considered. The methods of internal PM model validation include data splitting, resampling techniques (cross-validation and bootstrapping) (9,26-30), and the posterior predictive check (PPC) (31-33). Of note, the jackknife is not considered a model validation technique. The jackknife technique may only be used to correct for bias in parameter estimates, and for the computation of the uncertainty associated with parameter estimation. Cross-validation, bootstrapping, and the posterior predictive check are addressed in detail in Chapter 15. 

Cross-validation is an internal resampling method much like the older Jackknife and Bootstrap methods [Efron 1982, Efron Gong 1983, Efron Tibshirani 1993, Wehrens et al. 2000]. The principle of cross-validation goes back to Stone [ 1974] and Geisser [ 1974] and the basic idea is simple ... 

Cross-validation estimates model robustness and predictivity to avoid overfitting in QSAR [27]. In 3D-QSAR models, PLS and NN model complexity are established by testing the significance of adding a new dimension to the current QSAR, i.e., a PLS component or a hidden neuron, respectively. The optimal number of PLS components or hidden neurons is usually chosen from the analysis with the highest q2 (cross-validated r2) value, Eq. (3). The most popular cross-validation technique is leave-one-out (LOO), where each compound is left out of the model once and only once, yielding reproducible results. An extremely fast LOO method, SAMPLS [42], which evaluates the covariance matrix only, allows the end user to rapidly estimate the robustness of 3D-QSAR models. Randomly repeated cross-validation rounds using leave 20% out (L5G), or leave 50% out (L2G), are routinely used to check internal... 

Kohavi, R. A. (1995). Study of cross-validation and bootstrap for accuracy estimation and model selection. In International joint conference on artificial intelligence (pp. 1137-1143). Schramm, S. (2011). Methode zur Berechnung der Feldeffektivitat integraler Fufigdnger-schutzsySterne. Dissertation, Technische Universitdt MUnchen. 

Most current studies report an internal validation accuracy without an independent validation set. When there are a sufficiently large number of samples, the whole dataset can be split into two, one for training and one for testing (validation) this method is called hold-out validation. When the number of samples is limited, leave-one-out cross validation (LOOCV) is a popular technique. Here, a procedure is repeated N times, and each time a different sample is left out and used for testing the model learned from the remaining (N - 1) samples. The accuracy of... 

Recently, the detechon of vancomycin resistant enterococci (VRE) using MALDI-TOF MS profiles and a support vector machine has been described [74]. Internal cross-vahdation of the optimal statishcal model resulted in a sensitivity of 92.4% and a specificity of 85.2%. A subsequent external validation study after incorporation of the algorithm into the rouhne laboratory workflow surprisingly showed an even higher sensihvity and specificity of 96.7% and 98.1%, respectively. A further advantage was the rehable differentiation from other, intrinsically vancomycin resistant species. These excellent results did lead to incorporation of the analysis into the authors rouhne laboratory workflow. The broad applicability of the method shU has to be shown. 

When two or more analytical methods are used to generate data within the same study, a cross validation study should incorporate calibration standards and a set of QC samples (N > 5 per QC concentration) and/or incurred samples run by both analytical methods. The mean values of a set of QC samples and/or incurred samples from one method to the other must not deviate by more than the predetermined acceptable bias for the method. Other statistical tests can be used to assess comparability between the methods, e.g. cross validation data evaluated by the client may follow acceptance criteria based upon their own internal SOPs. 

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