The normal distribution

The normal distribution, often referred to as the Gaussian distribution, and at other times, the bell curve, takes its name from the prodigious German mathematician Carl Friedrich Gauss (1777-1855), who discovered it while studying the distribution of measurement errors in astronomy.

It is something we take very much for granted in clinical and biomedical research. It is certainly something inherently useful in being able to group our observable data, and to be able to describe a central tendency that can be used to represent groups of subjects or patients. Another way of looking at the normal distribution of data is to do a probit analysis. Here is an example of the apparent normality in the frequency distribution as applied to the CYP1A2 metabolic ratio in a Chinese population. Under these circumstances, the probit plot approximates linearity.

Frequency and probit distribution of CYP1A2 activity in a Chinese population as indicated by plasma log-transformed 1,7-dimethylxanthine/caffeine [lg(17X/137X)] ratios (n = 419).Chen et al, Clinical Pharmacology & Therapeutics 78, 249-259 (September 2005)

In this instance however, the normality of the distribution hides a plethora of heterogeneity as the CYP1A2 gene is highly polymorphic, and the authors in this study reports that the G–3113A polymorphism is associated with decreased CYP1A2 activity, haplotype pairs 10 and 13 are responsible for high CYP1A2 activity, and haplotype pairs 5, 8, 9, 12, and 15 are responsible for low CYP1A2 activity in Chinese subjects.

In understanding diversity of human drug response, understanding 'normality' is an important starting point, but we need to look beyond this. Normality can work against us.