Bioequivalence and Bioavailability Forum

Dear DLabes!

First impressions from my side:
The authors compared results from the TTT-method to the ARS-algorithm and claimed ‘better performance’ in terms of bias (relative error RE% = 100×[estimate-true]/true).
M$ Excel’s pseudo-random number generator NORMINV(RAND(), mu, sigma) is known to be suboptimal. In generating 50 sets of 10000 random samples with different seeds each (i.e., 500000 samples), I got a maximum absolute bias of 2.3% (contrary to the 1% claimed by the authors). Therefore a significance limit of >2% difference between methods IMHO is too low (5% is more realistic).

However, in repeating their simulation ‘Study A’ (not only 10000 ‘profiles’, but 20 sets of 10000 each), I could confirm their results in terms of bias and precision (without setting my feet in the deep puddle of statistically comparing data sets):

lambda_z
         TTT-method
     mean    min     max
RE  -1.06%  -0.80%  -1.45%
CV  12.12%  11.97%  12.43%
       ARS-algorithm
     mean    min     max
RE  +5.08%  +4.58%  +5.59%
CV  20.89%  20.53%  21.28%

n (number of data points chosen)
         TTT-method
median   2.5% quant.  97.5% quant.
  8          5           10
       ARS-algorithm
median   2.5% quant.  97.5% quant.
  8          3           10

Scary histograms of number of sampling points selected by both methods clearly favors TTT.
For instance in my first data set ARS chose the last three data points in 23.73% of cases, whereas TTT suggested the same number in only 0.01%… In the upper range of data points ARS selected ≥10 data points in 40.40%, whereas TTT came up with the same n in just 2.78% of cases (≥11: ARS 19% – TTT 0%!).
According to the bias and precision seen in the simulations my personal reluctance against the automated ARS seems to be justified. I always suspected that the algorithm selects too many data points and was surprised to see that my prejudice was not only justified, but that the contrary (too little data points) also holds.

Lessons learned:

• Two-times t_max is a good starting point, but
  
• visual inspection is still suggested (not an automated procedure only).
  
• ARS leads to 'bad' results, both in terms of bias and precision.
  
• TTT not suitable for 2 distinctive phases (intersection suggested as 1^st value).

I’m considering to set up new simulations with a log-normal error model and also using either a better pseudo-random generator, or true random numbers obtained from www.random.org…
Another option I’m considering for testing is the method ‘lee’ in the package PK for R by Martin J. Wolfsegger and Thomas Jaki.^*

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• Wolfsegger MJ. The R Package PK for Basic Pharmacokinetics. Biometrie und Medizin 2006; 5: 61–8. online resource