A Comparative Study of Statistical Methods to Assess Dilutional Similarity - The four parameter logistic model is a better control method than the dilution effect statistic - BioPharm International

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A Comparative Study of Statistical Methods to Assess Dilutional Similarity
The four parameter logistic model is a better control method than the dilution effect statistic


BioPharm International


DILUTION EFFECT (DE) MEASURE

The statistics used to compare sample and reference curves are not uniform across the industry. A statistic called dilution effect was introduced in the industry to assess dilution similarity.5,6 The dilution effect is a measure of the percent bias per 2-fold dilution in a test sample's value relative to that of the reference standard. It is the apparent change in a sample's dilution-adjusted concentration when it is diluted 2-fold.2,5 The dilution effect is calculated by Equation (2):









The estimated slopes of the test sample and reference standard respectively are obtained by fitting Equation (3):









Z =1 for the reference sample and Z = 0 for the test sample; xmid R is the EC50 of the reference sample and xmid S is the EC50 of the test sample. Perfect parallelism corresponds to 0% dilution effect. The absolute value of dilution effect less than 20% has been used in the industry to conclude dilutional similarity (parallelism) between the test sample and the reference standard.

TESTING FOR DILUTIONAL SIMILARITY

Dilutional similarity means that the reference and the test samples have common a, d, and b parameters. Thus, failure to share common a, d, and b parameters implies a failure of dilutional similarity. The DE statistic checks this only at one point (xmid) while the F-statistic checks the concentration range.

A standard F statistic for testing for parallelism (dilutional similarity) is obtained in the following way:

•Under the null hypothesis of parallel assays, use Equation (4):











•Fit equation 4 to the data to obtain the sum of squared errors (SSE), denoted as SSE ( Parallel).

•Under the alternative hypothesis that the curves are not parallel, i.e., asymptotes and slopes are not the same, use Equation (5):

















where the subscripts R and S denote parameters for the reference and sample logistics models, respectively. Z = 0 or 1 as shown earlier. Obtain SSE(Nonparallel) by fitting Equation (5) to the data.

Compute the F statistic for parallelism with Equation (6):










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