The not so normal distribution

The normal distribution is a convenient tool when you need to describe your data. Unfortunately it introduces a blind spot when it comes to interpreting the data.

When we look at the distribution, our eye intuitively focuses on the centre of the distribution. We see the central tendency of the distribution and the variance around it. This is fine when you are describing the data. But averages don't really help you if you are the storeman who's responsible for purchasing clothes for a bunch of factory workers.

This is the odd thing about studying variability in therapeutic response to drugs. We all know variability exists. We see this in every sphere of human activity, from buying clothes and cosmetics to the ability to complete a physical fitness test. Yet inexplicably, when it comes to dosing patients, people imagine that a dosage regiment based on the mean of a relatively small unrepresentative study sample will somehow represent the dosage requirement for everyone on this planet.

Here is a series of distributions of the clearances of CYP3A5 substrates midazolam and alfentanil (Kharasch et al, Clinical Pharmacology & Therapeutics (2007) 82, 410–426). The distributions are skewed to the right and so are clearly log-normally distributed.

Here is a frequency distribution of the log-metabolic ratio for midazolam in a Chinese population (Zhu et al, Br J Clin Pharmacol. 2003 March; 55(3): 264–269).

Notice from these plots just how variable the clearances and the metabolic ratios (more about this later) are. How do we, under these conditions determine the correct doses for each patient? Clearly applying population averages will not work. Are we able to do it?

The earlier posting on wafarin show how it can be done for warfarin.More on dosage optimization issues later.

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.