Bioequivalence and Bioavailability Forum

Dear ElMaestro,

I agree with:

❝ Hmmmm

And also with:

❝ C_max etc varies from 0 and upwards …

… in ‘reality’ – since there is nothing like a negative concentration. But based on normal theory (parameters: mean, variance), we must accept the (small) probability of values <0 in the population. Example: two samples (1, 3), mean 2, variance 2, probability of a value of C≤0 in the population = 0.23%. If we log-transfom, the probability of a negative value is infinitesimaly small (nitpicking: it’s not defined, because log(0)=?, but if x→-∞, ℯ^x→0).

❝ Let's for simplicity consider the subject with the highest C_max in the dataset (log or not is not the important issue here). Now we do a parametric analysis of (log) C_min and we consider the (log) C_min residual e for the same subject and we disregard other factors for now (makes no difference but makes it less easy to grasp). We know something about e; the (log) C_max is higher than average (log) C_min so average (log) C_min plus e will be lower than (log) C_max for that subject.

Can you reword your simple statement for my even more simple mind? I did not get your point. From a PK point of view we are sure that C_max>C_min (by definition), but from a statistical POV I don’t see why this a priori knowledge should influence the distributional assumptions of either metric. If we build a statistical model for a metric we base it on distributional assumptions for that particular metric – and don't peek across the fence for another metric; e.g. we rely on a discrete distribution of t_max, not caring about the continous one of C_max.

❝ […] I meant nonparametric. Sorry about the meaning-disturbing typo.

Nonparametrics never disturb me.