There are a number of different approaches to the assessment of doseproportionality, but most of these are directed toward hypothesis testing. The analysis of dose proportionality studies, however, requires estimation rather than significance testing in order that the pharmacokinetic and clinical significance of any nonproportionality can be assessed.The methods of statistical analysis of thesestudies have been reviewed. A n empirical model relating the log of thepharmacokineticparameter linearly to the log of the dose (the 'bower model") provides a readily interpreted measure of the degree of nonproportionality. The potential utility of this model has been demonstrated using a number of observed datasets from different drugs. If there is doubt over the goodness of f i t of the power model then analysis of variance (after log transformation), together with pairwise comparisons between doses, provides a suitable alternative approach.

Sumatriptan is classified as a vascular 5HT1 receptor agonist and is effective in the acute treatment of migraine and cluster headache. Sumatriptan is available as an injection for subcutaneous administration and as a tablet for oral administration. The pharmacokinetics of sumatriptan differ depending on the route of administration. The mean subcutaneous bioavailability is 96% compared to 14% for the oral tablet. The lower bioavailability following oral administration is due mainly to presystemic metabolism. The inter-subject variability in plasma sumatriptan concentrations is greater following oral administration and a faster rate of absorption of drug into the systemic circulation is achieved following subcutaneous dosing. The pharmacokinetics of sumatriptan are linear up to a subcutaneous dose of 16 mg. Following oral dosing up to 400 mg, the pharmacokinetics are also linear, with the exception of rate of absorption, as indicated by a dose dependent increase in time to peak concentration. Sumatriptan is a highly cleared compound that is eliminated from the body primarily by metabolism to the pharmacologically inactive indoleacetic acid analogue. Both sumatriptan and its metabolite are excreted in the urine. Although the renal clearance of sumatriptan is only 20% of the total clearance, it exceeds the glomerular filtration rate, indicating that sumatriptan undergoes active renal tubular secretion. Sumatriptan has a large apparent volume of distribution (170 l) and an elimination half-life of 2 h. Oral doses of sumatriptan were administered as a solution of dispersible tablets and subcutaneous dosing was by injection into the arm. In clinical practice, sumatriptan is administered as a film coated tablet or by subcutaneous injection into the thigh.

We investigated the hypothesis that distributions of continuous pharmacokinetic variables are positively skewed in nature and that logarithmic transformation of these variables restores normality. The distributions of common continuous noncompartmental pharmacokinetic variables were investigated for four different Glaxo Wellcome compounds, administered by three different routes of administration: ranitidine (po), sumatriptan (sc), ondansetron (iv), and bismuth, from ranitidine bismuth citrate (po). The distributions of all the investigated noncompartmental pharmacokinetic variables were adequately described by a log-normal distribution, whereas statistically significant departures from normality occurred in the majority of cases. Thus, unless there is strong and consistent evidence for a departure from log-normality, the parametric statistical analysis of common noncompartmental pharmacokinetic variables should be carried out after a priori log transformation.

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