Deo Kumar Srivastava

Markers of dopamine metabolism in Parkinson's disease

We used two analytic methods (a multichannel coulometric electrode array with high-performance liquid chromatography, and gas chromatography-mass spectrophotometry) to measure CSF dopamine (DA) and its metabolites in mildly affected, unmedicated subjects with Parkinsons disease (PD). The mean (± SD) concentration of homovanillic acid (HVA), the most abundant product of DA turnover, was 164.57 ± 95.05 nM. As sequential aliquots of CSF were collected from the first to 23rd ml, CSF HVA concentration almost doubled. After HVA, 3-O-methyldopa (3-O-MD) was the next most abundant compound. The summed concentrations of 3-O-MD, 3,4-dihydroxyphenylacetic acid, 3-methoxytyramine, DA, DA-3-sulfate, homovanillol, and levodopa (LD) amounted to 12.6% of HVA. Concentrations of the DA metabolites did not correlate to a variety of indices of PD severity. The presence of LD and 3-O-MD may be indicators of DA synthesis and possibly could reflect compensatory processes among surviving dopaminergic neurons of the PD brain.

Ch. 24. Goodness-of-fit tests for univariate and multivariate normal models

The assumption of univariate and multivariate normality is implicit in most of the statistical procedures routinely used in the analysis of univariate and multivariate data. Now it is well recognized that, in general, the assumption of normality is at best suspect; e.g., see Geary (1947) , Pearson (1929) , Jeffreys (1961) , Mudholkar and Srivastava (2000a) and references therein. Furthermore, it is also well established that when the assumption of normality is violated most of the normal theory procedures lose validity, i.e., Type I error control, or become highly inefficient in terms of power. Numerous goodness-of-fit methods to test the assumption of univariate normality exist in the literature but no single test uniformly dominates all others. However, several theoretical and simulation justifications published in the literature indicate that the Shapiro-Wilk test is reasonable and appropriate in most situations of practical importance. The assumption of multivariate normality is harder to expect and justify since it implies joint normality, in addition to the marginal normality, of the components. This structural complexity may be a reason for a time lag in the development of goodness-of-fit tests for multivariate normality. However, the last two decades have seen advances leading to several competing tests of multivariate normality. In addition, it is seen that, as compared with the univariate methods, the multivariate data analysis methods are more prone to becoming invalid in terms of Type I error control and inefficient in terms of power when the normality assumption is violated. The purpose of this article is to present an overview of the methods for testing univariate and multivariate normality and to indicate their relative strengths and weaknesses.

Assessing the significance of difference between two quick estimates of location

Descriptive statistics such as means, standard deviations and quantiles are often the only records retained for long-term use from an exploratory, or otherwise, analyses of data. The problem of comparing locations of two populations with comparable dispersions on the basis of such records alone is addressed in this note. We construct analogues of the pooled t statistics by studentizing difference between two quick estimators such as trimeans, and Gastwirth estimators, using ranges of quantiles constituting the statistics. The null distributions of these statistics are then approximated by scaled Students t distributions, and examined for validity robustness and compared with competitors. It is seen that the operating characteristics of tests based on studentized differences of quick estimators are superior to those of pooled t tests, which can also be performed on the basis of summaries, and are comparable to those of Wilcoxon-Mann-Whitney rank sum tests which require the complete data rather than the su...

Ch. 25. Normal theory methods and their simple robust analogs for univariate and multivariate linear models

The assumptions of univariate and multivariate normality inherent in most of the statistical procedures in routine use are rarely verified in practice. Several robustness studies have shown that that the failure of the underlying assumption of normality leads to either failure of type I error control, or to conservative test procedures. In univariate case failure of normality assumption is not uncommon, and in practice multivariate normality is elusive enough to be considered illusory. Alternatives to the normal theory based methods are nonparametric and robust methods. It is generally recognized that the nonparametric methods, which involve minimal assumptions, can be less efficient, and although the nonparametric test procedures are well developed for the univariate setting, their development for the multivariate setting is unsatisfactory. On a similar note, the development of the robust procedures in the univariate setting is more advanced than in the multivariate setting. Also, the multivariate nonparametric and robust test procedures are asymptotic in nature with a few exceptions. In this manuscript we focus on a few cases of the univariate and multivariate linear models which are of practical importance and present an overview of some relevant robust test procedures, which can be reasonably used with moderate size samples.