Bootstrap analysis nonparametric

Figure 14-9 DoD plot for comparison of two drug assays nonparametric analysis. A histogram shows the relative frequency of N = 65 differences with demarcated 2.5 and 97.5 percentiles determined nonparametrleally.The 90% CIs of the percentiles are shown. These were derived by the bootstrap technique.

When a model is used for descriptive purposes, goodness-of-ht, reliability, and stability, the components of model evaluation must be assessed. Model evaluation should be done in a manner consistent with the intended application of the PM model. The reliability of the analysis results can be checked by carefully examining diagnostic plots, key parameter estimates, standard errors, case deletion diagnostics (7-9), and/or sensitivity analysis as may seem appropriate. Conhdence intervals (standard errors) for parameters may be checked using nonparametric techniques, such as the jackknife and bootstrapping, or the prohle likelihood method. Model stability to determine whether the covariates in the PM model are those that should be tested for inclusion in the model can be checked using the bootstrap (9). 

The quantile-BEAST algorithm is a nonparametric bootstrap method based upon the work of Efron. In the 1988 study, four individual benzoic acid derivatives were analyzed as were mixtures of the four derivatives. The active ingredient concentrations were varied between 0 and 25% of the sample, with aluminum oxide used as a diluent. The samples were ground and passed through a 100-mesh screen prior to analysis. Spectra were collected in triplicate at three wavelengths on an InfraAlyzer 400. 

Drennen and Fodder [116] published a paper in 1991 comparing the performance of the improved quantile-BEAST algorithm with that of the Mahalanobis distance in the qualitative analysis of carbamazepine tablets. While the Mahalanobis distance calculation assumes that spectral variations associated with both the calibration and test set are random, in complex pharmaceutical mixtures this may not be the case. The bootstrap algorithm, on the other hand, is a nonparametric test which can be used with nearly any spectral data distribution. 

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