Bioequivalence and Bioavailability Forum • Misinterpretation

Misinterpretation [Software]

posted by Helmut – Vienna, Austria, 2025-11-15 10:38 (201 d 11:43 ago) – Posting: # 24499
Views: 4,217

Hi Shuanghe,

❝ I still cannot believe that I had the false memory for so many years, and I still think I must've have read it somewhere else about the step-wise regression approach

You are not alone. Perhaps in this post?

An indirect^a quote of WinNonlin (1.1 of 1996 ‼):

Linear regressions are repeated using the last three points, the last four points, the last five points etc. For each regression, an adjusted R² is computed:$$\small{Adjusted\,R^2=1-\frac{\left(1-R^2\right)\cdot(n-1)}{n-2}}$$where n is the number of data points in the regression and R² is the square of the correlation coefficient. The regression with the largest adjusted R² is selected to estimate the terminal half-life, with one caveat: if the adjusted R² does not improve, but is within .0001 of the largest value, the regression with the larger number of points is used.

Yet another approach.^b

One problem is to find an algorithm that identifies an appropriate range over which the linear regression should be done. One such algorithm, which has long served this author well, but always needs to be supplemented by a sanity check, goes as follows:

Use the last three points to make a linear regression on and compute the R² to this linear regression.
Successively add earlier time points and make the linear regression of these data points until R² decreases (i.e., degree of explanation decreases).
When a point for which a R² decrease is encountered, remove that point and add the preceding one. Repeat the analysis. If R² still decreases, the process is stopped and the data are included in the linear regression up to the first decrease in R². If however R² increases, we consider the removed point an outlier and continue the process with that individual point removed.

This is not a fool-proof method but it usually represents a good starting point. However, sometimes one needs to use only the last two points in the estimate of the terminal slope, which this method does not allow for (no R² can be computed in that cases). Data must therefore always be inspected in order to allow for manual modification of the time interval over which the regression should be made.

Gieschke R. Half-life. In: Cawello W, editor. Parameters for Compartment-free Pharmacokinetics. Aachen: Shaker Verlag; 2003. p. 55.
Källén A. Computational Pharmacokinetics. Boca Raton: Chapman & Hall/CRC; 2008. p. 43

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Helmut Schütz

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Complete thread:

new regression rule for lambda_z in Phoenix: bug or new feature? Shuanghe 2025-11-10 15:55 [Software]
- new regression rule for lambda_z in Phoenix: bug or new feature? Helmut 2025-11-11 08:42
- new regression rule for lambda_z in Phoenix: no change in implementation SDavis 2025-11-11 14:24
  - new regression rule for lambda_z in Phoenix: no change in implementation Shuanghe 2025-11-11 22:38
    - Old User’s Guides Helmut 2025-11-11 23:20
    - Misinterpretation Helmut 2025-11-12 12:16
      - Misinterpretation Shuanghe 2025-11-12 21:24
        
        MisinterpretationHelmut 2025-11-15 09:38
        Misinterpretation billdenney 2026-02-27 14:20
        
        Clarification Helmut 2026-02-27 15:29
  - Rewording appreciated Helmut 2025-11-12 10:30
    - Reason for failing to calculate lambda and Kel in Phoenix jag009 2026-01-29 04:20
      - Reason for failing to estimate λz Helmut 2026-01-29 11:04