Bioequivalence and Bioavailability Forum

Dear Eduardo,

the ‘classical’ algorithm uses a geometric progression in order to calculate sampling points based on:

• the number of samples
  
• the time points of the first and last sample

The algorithm is:

t_i = t_i-1 × (t_n/t₁)^1/(n–1)

where
i index of the respective time points (2, 3, …, n), n number of time points, t_i calculated time point at i, t_i–1 previous time point, t₁ first time point, and t_n last time point.

I prepared a little example based on following PK data:

• 1 compartment open model, no lag time
  
• F = 1
  
• Dose = 100 Units
  
• V = 10 L
  
• k_el = 0.25 h^-1
  
• k_a = 4 h^-1 (‘fastest’ subject), 0.4 h^-1 (‘slowest subject’)

With t₁ = 5 min (0.083 h), t_n = 12 h and 15 sampling points we get: 0.0833, 0.1188, 0.1695, 0.2417, 0.3447, 0.4917, 0.7012, 1.0000, 1.4262, 2.0339, 2.9007, 4.1369, 5.8999, 8.4142, and 12.0000.

Now you have to adapt these time points for practicability (e.g., sampling at 0.25 h instead of at 0.2417 h).

In the example you see another problem which may arise from mean curves (very often the only ones being published). The sampling scheme works fine for the ‘average’ subjects, and also for the ‘fastest’ ones, but the elimination phase may be insufficiently described for 'slow' subjects.

Therefore whenever possible try to get some ‘Spaghetti-Plots’ (overlays of all subjects in a previous study) in the planning phase.

Another problem are enteric coated formulations, which show a large variability in lag-times due to variability in gastric emptying.

The example to the right used PK parameters from the ‘fast’ subject with additonal lag-times of 0.5 and 1.5 h. The algorithm will simply fail if you are applying data from a mean curve only.

In such a case you will have to ‘pack’ as much time points as possible within the first 3 hours or so, in order to define the absorption phase and the peak properly; you should use the algorithm only for the elimination phase (with t₁ = 3 and t_n = 12).

Also note that the example is just illustrative; with ‘real world’ enteric coated formulations the t_max may be at 12 hours – or even later…

Conclusion: A simple algorithm may only serve you as an entry point; thorough knowledge of the drug’s (and formulation’s) PK is a prerequisite in study planning.