Bhattacharya Modeling

Abstract

In 1967 Bhattacharya, a biologist from India, presented a method for identifying juvenile-fish subgroups from random samples (Bhattacharya 1967). By now this test, based on Gaussian curves, has become a key-method for the analysis and sustainability of this important resource in the eco-system, and is recommended by the Food and Agricultural Organization of the United Nations Guidelines (FAO 2011). As Gaussian curves are the mainstream not only with fish population research, but also with clinical data, it is peculiar that, so far, this method has not been widely applied in clinical research. When searching Pub Med we only found a few clinical-laboratory studies (Guerin et al. 1992; Watson et al. 1999; Pottel et al. 2008; Baadenhuijsen and Smit 1985), epidemiological (Metz et al. 2002; Zhang et al. 2004) and genetic studies (Miescke and Musea 1994; Evans et al. 1983), and not a single cardiovascular study. In clinical research data-files are, usually, summarized by their means and standards deviations (SDs). Standard deviations are a convenient way of estimating the spread in your data, but they are only valid if your data can be assumed to follow a clock-like Gaussian curve. Under this assumption the mean ± 1.96 × SDs covers 95% of the data. Of course, many cardiovascular data samples are not perfectly Gaussian-like. Mean and SDs are, therefore, just approximations. There may be better methods to find the best fit Gaussian curves for your data. Instead of the mean, the mode or median can be used, and instead of histograms consistent of bins, more refined Kernel histograms consistent of multiple similarly sized small Gaussian curves can be drawn (Metz et al. 2002). Also, distribution-free statistical methods like non-parametric tests can be applied to “quasi-gaussianize” the data. However, all of these methods massage the data. Bhattacharya modeling does not massage the data, but, instead, unmasks Gaussian curves, as truly present in the data, and removes outlier frequencies. In clinical research it could be used (1) for unmasking normal values of diagnostic tests, (2) for improving the p-values of data testing, and (3) for objectively searching subsets in your data. The current chapter uses as examples simulated vascular lab scores to investigate the performance of Bhattacharya modeling as compared to standards methods, and was written to acquaint the clinical research community with this novel method.