Bioequivalence and Bioavailability Forum

Dear Detlew!

❝ I'm not quite sure If I really understand what you attempt here.

In more detail now. The authors explored different methods for estimating t_lag. Clearly the one used in standard PK software (the last timepoint before the first measured concentration) performed worst – especially if k_a is high and few timepoints are available. We discussed that already (#1872, #4850). Csizmadia and Endrényi studied the methods in terms of RSME and bias; I’m also interested in setting up simulations of BE studies (formulations different in F, k_a, t_lag, or combinations). In other words: If we use a ‘bad’ method – is the BE outcome substantially affected? Some ideas:

• Reproduce the paper’s results for comparability.
  
• Explore t_lag as x of the last time point where C≤LLOQ and the first >LLOQ.
  
• Think about DR formulations. Is a shift in t_lag unbiased reflected in t_max? Would be nice because (already) frequent sampling around C_max would make additional frequent sampling around the expected t_lag unnecessary.

In my experience one- and two-compartment models with a lag-time cover the vast majority of IR and DR formulations. Even if in all subjects concentrations were measured at the first sampling time point PK models with a lag-time generally result in better fits (especially of the absorption phase and of C_max). Once I have a suitable setup I could try to answer questions only a few people dare to ask, like:

• AUC_t if t_last,R ≠ t_last,T (the wonderful missing value story). Explore the bias if the true ratio ≠ 1.
  
• AUC₇₂ or AUC_τ: Inter-/extrapolate to nominal time? Extrapolate a missing value?
  
• Missing values generally…
  
• C_last or estimated C_min at τ?¹
  
• Explore different algorithms in selecting the terminal phase in multicompartmental models.

BTW, Csizmadia and Endrényi refer in their models’ parameters to an earlier (and much quoted) publication by Bois et al (1994).² Interesting that there normal distributed data were assumed (why?) and a truncation of ±3 SD was used (though with the same CVs). Does anybody know an R package supporting the truncated log-normal?

The analytical error was already defined in a strange way in Bois’ paper:

Analytical assay errors were generated from truncated normal distributions with no bias (mean zero), a CV of 10%, truncation at ±3 CV, plus a fixed term equal to the product of the assay CV and the limit of quantification, LQ.

Also interesting that they also showed a large positive bias and terrible CV of AUC_∞, especially for two-compartment models. Of the extrapolation methods using the estimated C_last instead of the measured C_last performed slightly better. AUC_t performed best by far. The study was sponsored by the FDA – still requiring AUC_∞…

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1. Paixão P, Gouveia LF, Morais JGA. An alternative single dose parameter to avoid the need for steady-state studies on oral extended-release drug products. Eur J Pharm Biopharm. 2012;80(2):410–7. doi:10.1016/j.ejpb.2011.11.001
   
2. Bois FY, Tozer TN, Hauck WW, Chen M-L, Patnaik R, Williams RL. Bioequivalence: Performance of Several Measures of Extent of Absorption. Pharm Res. 1994;11(5):715–22. doi:10.1023/A:1018932430733