Testing for bimodality in frequency distributions of data suggesting polymorphisms of drug metabolism‐histograms and probit plots.

Abstract

1. The shape of histograms used to illustrate density distributions of indices of polymorphic drug metabolism was shown to be sensitive to the position of the cell divisions. 2. Non‐linearity of the probit plot was shown not to indicate bimodality of the original density distribution. Computer simulation was used to generate examples of unimodal density distributions with curvilinear probit plots. 3. Using the same technique probit plots for bimodal density distributions were constructed. Some were shown to differ less from the probit plots of certain unimodal distributions than did the original density distributions. 4. The position of the antimode was shown not to coincide with inflections seen in the probit plots. 5. A new method for determining the linearity of probit plots is suggested.

Phenotypic debrisoquine 4‐hydroxylase activity among extensive metabolizers is unrelated to genotype as determined by the Xba‐I restriction fragment length polymorphism.

“…However, non-linearity in a a 3.0 0 normit plot is a necessary but not sufficient criterion for the presence of bimodality since normit plots obtained either from the mixture of two normal distributions or from a distribution having a low degree of kurtosis result in similar S-shaped curves (Everitt & Hand, 1981;Jackson et al, 1989a). The theoretical frequencies of dominant homozygotes and of heterozygotes for an autosomal recessive defect were then calculated according to the Hardy-Weinberg law.…”

“…In contrast, graphical or statistical analysis (maximum likelihood, kernel distributions) of metabolic ratios does not differentiate the two genotypes within the EM group (Caporaso et al, 1989a;Jackson et al, 1986Jackson et al, , 1988Jackson et al, , 1989aLennard et al, 1986;Price-Evans et al, 1983;Steiner et al, 1985) despite highly variable cytochrome P4501ID6-mediated metabolism of a number of substrates among subjects with the EM phenotype. Skoda et al (1988) have reported that Southern blotting of genomic DNA digested with Xba I can identify mutant alleles of the responsible gene and can therefore be used to definitively assign the heterozygous genotype to some Caucasian subjects.…”

Testing for bimodality in frequency distributions of data suggesting polymorphisms of drug metabolism‐hypothesis testing.

“…In an attempt to overcome the limitations of using only normal distributions (Jackson et al, 1989) Maclean (1976 performed a power transformation on the index prior to fitting the data with normal distributions. This has the effect of providing good fits of normal distributions to unimodal but skewed data sets.…”

“…We have previously considered the use of graphical methods to detect polymorphisms of drug metabolism from in vivo data (Jackson et al, 1989). Although these techniques can be used as an initial screen to identify the presence of bimodality in frequency distributions they cannot be used to test the strength of the hypothesis that two or more populations are present.…”

“…The chi-square test is then used to show whether the differences between the observed and predicted numbers in each cell could have arisen by chance. However, as suggested previously (Jackson et al, 1989), the form of the histogram may be sensitive to the Correspondence: Dr P. R. Jackson, University Department of Pharmacology and Therapeutics, Royal Hallamshire Hospital, Sheffield S10 2JF positioning of the data cells and the distribution is invariably assumed to be normal or log-normal. The first of these problems is overcome by using the Kolmogoroff-Smimov test (Kolmogoroff, 1941), which checks goodness-of-fit of the cumulative distribution to that of the predetermined distribution over a given range.…”