In pharmaceutical development, a "dissolution test" refers to a test conducted in a test tube to examine how a drug behaves in the body.
For example, even if the active ingredients are the same in generic drugs, the formulation may change depending on the additives, manufacturing method, etc. In such cases, it is necessary to measure the dissolution rate (the percentage of the active ingredient dissolved) at regular intervals and compare the formulation before and after the change to show that the dissolution trends are similar.
The graph below shows what is called a dissolution curve, with the horizontal axis representing time (minutes) and the vertical axis representing dissolution rate. Using pH 4.5, pH 6.0, or water as the test solution, the dissolution rates of the test and reference products are plotted against time and connected by a broken line.
*The points plotted on the Y-axis are the average dissolution rates of multiple sample formulations.
Comparing the two curves for the three test solutions, the dissolution rate increases over time and approaches 100%, showing similar behavior. However, the two curves do not completely overlap, and differences can be seen at times.
Also, the curve for water appears more similar compared to the curves for pH 4.5 and pH 6.0.
So far, we have looked at how to interpret similarity when looking at graphs, but various indicators have been proposed to objectively determine the similarity of multiple dissolution curves .
In this article, we will introduce a method using a function called f2 , which is widely used as a judgment criterion, and how to calculate its value in JMP.
In addition to the f2 value, JMP can also calculate the confidence interval for f2. Rather than judging similarity based on the estimated value itself, you can determine similarity taking uncertainty into account by checking whether the lower limit of the calculated confidence interval is above the reference value (=50) .
F2 analysis
In F2 analysis, the value of f2 is calculated using the following formula from the dissolution rate values of the test formulation group and the reference formulation group at each time point.
In the formula, R_t^hat and T_t^hat represent the average dissolution rates of the test formulation group and the reference formulation group at time t, respectively.
The larger the f2 value calculated by this formula, the more similar the dissolution profiles are. If the difference in dissolution rate at all comparison points is 0 (zero), the denominator in the logarithm will be 1 and the logarithmic part on the right-hand side will be 2, so the f2 value will be 100 (= 50 x 2).
One standard for determining similarity is f2 = 50 , and JMP also uses this value as a standard.
However, caution is required as the "Guidelines for Bioequivalence Tests for Formulation Changes in Oral Solid Dosage Forms" and the "Guidelines for Bioequivalence Tests for Generic Drugs" state that the criteria for determining f2 differ depending on the time period and to what extent the reference formulation dissolves.
In JMP
To calculate the f2 value in JMP, use the options in the Curve Fitting platform. Here we will explain how to do this in JMP using an example.
The dissolution curves of the test formulation and the standard formulation are compared by calculating the f2 value for each type of test solution (pH 4.5, pH 6.0, Water).
The dissolution curve graph shown at the beginning was created from the following data. Six formulations (vessels) were used for each type of test solution (pH 4.5, pH 6.0, Water) and formulation (Test, Reference), and the dissolution rates were measured at 0, 5, 10, 15, ..., 240, and 360 minutes.
| Column names |
meaning |
| pH/Water |
Type of test solution (pH 4.5, pH 6.0, Water) |
| Drug |
Type of formulation (Test: test formulation, Reference: standard formulation) |
| Tablet sample |
Formulation sample number (1-6) |
| Minutes |
Hours (minutes) |
| % Release |
Dissolution rate (%) |
*This sample data can be downloaded from this blog (DissolutionData_Stacked.jmp).
operate
1. Select Analyze > Advanced Models > Fit Curve and specify the columns as follows: For Group By, specify the column that identifies the comparison target of the curves (in this example, "Drug"), and for By, specify the column that identifies the test solution (in this example, "pH/Water"), since you want to analyze each test solution separately.
2. A report will be displayed for each level of the By variable. Select the F2 Analysis option from the red triangle button next to "Curve Fit" in the upper left corner of the report.
3. In the "Dissolution curve estimation" window that appears, specify the column that identifies the individual formulation (vessel) (in this example, "Tablet sample") and the drug standard group (in this example, "Reference").
By performing the above steps, the "F2 Analysis" report for each test solution will be displayed.
F2 Analysis Report
■ In the case of "pH 4.5"
The report displays the dissolution curves for each group and time-dependent statistics (mean, standard deviation, coefficient of variation (CV)).
Areas highlighted in yellow meet the following criteria:
- There are two or more time points in the test group where the average dissolution is greater than 85%.
- The CV value at the first time point in the study group is greater than 20%.
- There are time points after the first time point in the test group where the CV value exceeds 10%.
Below this report, a report on the f2 value is displayed. The "Observed F2" (=45.081) is the f2 value calculated using the formula in the previous section. The bootstrap distribution of f2 was obtained by resampling the formulation using the bootstrap method, and the lower and upper limits of the 90% confidence interval were calculated using the BCa method (a bias correction method).
In this example, the estimated value of f2 is 45.081, with a 90% confidence interval of [43.638, 46.509].
JMP uses f2 = 50 as the standard, and if the lower limit of the 90% confidence interval is greater than 50, it will determine that f2 exceeds 50, even taking variability into account . In this example, the lower limit is 43.638, which is below 50, so we can conclude that the two curves are not similar.
■ In the case of "pH 6.0"
The estimated value of f2 is 50.208, with a 90% confidence interval of [48.103, 52.293].
The estimate for f2 itself is slightly over 50, but the lower limit of the confidence interval is below 50, so it is not comparable when you consider the uncertainty. The lower limit of the confidence interval is 48.103, which is not over 50.
■ In the case of "Water"
Looking at the dissolution curves, the curves for the test and reference formulations appear more similar than those at pH 4.5 and pH 6.0. The estimated value of f2 is 55.096 with a 90% confidence interval of [51.316, 60.548].
Since the lower limit of the 90% confidence interval is greater than 50, we can conclude that the two curves are similar in this case.
The results of the F2 analysis so far are summarized in a graph below. The dotted line on the vertical axis is drawn at the position where the F2 value is 50. As you can see from this graph, only Water has a lower limit of the 90% confidence interval that exceeds 50.
Other comparison methods
The F2 analysis introduced so far is a nonparametric method that does not assume a specific curve. There are several other methods for comparing dissolution curves besides F2 analysis, and JMP includes the F1 analysis, multivariate distance, and T2EQ methods.
Of these, T2EQ is a method that uses the statistic T2, which measures the difference in dissolution rate over multiple time points, to test whether that difference is within the range of equivalence (EQ).Rather than using confidence intervals to determine similarity, T2EQ calculates a p-value for the test statistic, and if this p-value is less than the specified significance level, the test formulation is considered similar to the reference tablet.
In this example, if we apply T2EQ to Water, the p-value is 1, which does not suggest that the two curves are similar, which is different from the conclusion of the F2 analysis.
by Naohiro Masukawa (JMP Japan)
Naohiro Masukawa - JMP User Community
