JMP를 활용한 Biological Assays - 개념 및 PLA(Parallel Line Assay) 분석방법

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Biological Assay refers to an analysis method that determines the concentration or efficacy of a substance by its effect on living cells or tissues. The European Pharmacopoeia provides detailed information related to design/analysis/feasibility testing, etc. in Section 5.3, which is the same as the United States Pharmacopoeia (USP 1032-1034) and ICH Q2R.

In bioassay analysis, there are several analysis designs as shown below, but this paper will only describe PLA (Parallel Line Assays).

One.Parallel Line Model

2.Slope-Ratio Model

3.Quantal Responses

4.Extended Sigmoid Dose-Response Curves

First, in bioassays, experimental result data is only available when the following three conditions are met: Statistically Valid “It is said.

One. The linear regression coefficient must be statistically significant. That is, the linear regression coefficient p-value must be less than 0.05 .

2. Parallelism between straight lines must be satisfied. In other words, a protest expressing non-parallelism p-value must be greater than 0.05 .

3. All straight lines must satisfy linearity. In other words, the quadratic regression coefficient p-value must be greater than 0.05 .

Let's first learn the above dictionary concepts and then do a case analysis using the example provided in EP 5.3.

The sample data below is an example of “Two-Dose Multiple Assay with Completely Randomized Design”.

The above data is imported into JMP Data Table as shown below. 

Before analyzing, draw the two pictures below. The picture on the left is the regression fitting result for each of the three preparations, and the picture on the right is a plot that overlays the three preparations. Looking at the picture on the right, you can see that it may be difficult to satisfy parallelism with Standard and T in Preparation U.

  

  

In the analysis, we will first check whether the three conditions mentioned above (significance / parallelism / linearity of the regression coefficient) are satisfied, and when the three conditions are satisfied, we will calculate the Relative Potency.

One. Significance of the regression coefficient: Since the p-value of the linear regression coefficient for each preparation is less than 0.05, it can be judged that the significance of the regression coefficient is satisfied.

2. Parallelism: The p-value of the term related to the parallelism of the three straight lines is less than 0.05, so it cannot be considered that parallelism is satisfied.

However, when Preparation U is excluded, it can be said that parallelism is satisfied.

  

Note: The above results can be interpreted as follows: The term representing parallelism above is the term representing two-factor interaction in design of experiments. In other words, the existence of a two-factor interaction as shown in the figure below means that the term is statistically significant (p-value is less than 0.05). In other words, as shown above, the fact that the relevant term is not statistically significant (p-value is greater than 0.05) can be judged as No Interaction, meaning that the two straight lines are parallel, as shown in the picture below.

 

 

3. Linearity: In this case, there are two dose levels, so there is no need to test the curve. However, if there are three or more Dose Levels, linearity can be checked by fitting a quadratic term and testing whether the regression coefficients of the linear term and the regression coefficient of the quadratic term are statistically significant (p-value greater than or equal to 0.05). .

[How to find Relative Potency]

In the dialog box below, click Red Triangle and then click Estimate >> Expanded Estimates.

If the result is as follows, the Relative Potency of Preparation T compared to the Standard (of course, the natural logarithm is used here) is

(Slope of Preparation T-Standard Preparation Slope) ÷ Common Slope

It is obtained by the formula.

 

 

In other words, (-3.125-3.125)/(-58.97016) = 0.1060 is the Relative Potency of Preparation T.