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.