Bioequivalence and Bioavailability Forum

Dear Sury,

❝ I have recently got an bioequivalence study with clinical endpoints for some drug

❝ In OGD it states that

❝

❝ “To establish bioequivalence, the 90% confidence interval of the test/reference ratio of the mean should be contained within [0.80, 1.25], using the per protocol (PP) population.”

For BE with PK endpoint, yes. Not with clinical endpoint.

❝ The scores of the clinical endpoint shall be as follows [...]

You're referring to the draft guidance on miconazole buccal tablets, right ? Would be easier for us if you could say so straight away and link the guidance...

❝ For the above, do we need to convert the grading (0,1,2,3) to log transformed data and conduct the statistical analysis?

❝

❝ As the above states that 20% difference is accepted, then in normal bioequivalence case (if untransformed data), it should be 80.00-120.00?

For the statistical analysis the draft guidance refers to another draft guidance, on adapalene + benzoyl peroxyde. Did you read it ? Did you see anywhere a mention of log-transformation ? And why are you changing acceptance limits of -0.20 to +0.20 into 80.00 - 120.00 ?

Hi Sury,

are you referring to buccal miconazole?

❝ For the above, do we need to convert the grading (0,1,2,3) to log transformed data and conduct the statistical analysis?

Grab you pocket calculator, fire up a spreadsheet or a statistical software.
Which result do you get for log(0)? Bonus question: Why?

❝ As the above states that 20% difference is accepted, then in normal bioequivalence case (if untransformed data), it should be 80.00-120.00?

Why? You claimed to quote from the OGD’s guidance:

❝ “To establish bioequivalence, the 90% confidence interval of the test/reference ratio of the mean should be contained within [0.80, 1.25], using the per protocol (PP) population.”

If you were referring to buccal miconazole, sorry, such a statement is not given there.

In Section 5 it is stated:

The recommended primary endpoint of this study is the proportion of subjects with a clinical cure at the test-of-cure (TOC) visit on Day 21 (i.e., 7 days after completion of 14 days of treatment) ± 4 days in the Per Protocol analysis population. A clinical cure is defined as complete resolution of all signs and symptoms of oropharyngeal candidiasis (oral lesion score = 0, signs and symptoms score = 0).

(my emphasis)

I must confess that this guidance leaves me confused. At a first look this smells of testing for equivalence of the ratio of two means with normality on the original scale (i.e., Fieller’s ‘fiducial’ confidence interval and the Sasabuchi test)^1,2 where the conventional limits are {0.80, 1.25}. But then I had some doubts. Before we perform statistics we have to consider the data-generating process. Scores are of an ordinal scale at its best. Quite often they are just nominal. Suitable tests for the former are nonparametric or proportional odds and for the latter the χ². Throwing away any data with scores > 0 sounds strange to me.

I didn’t run a test yet but consider these three cases:

1.         R      T
─────────────────────
        0      0
        0      0
        0      0
        0      0
        0      0
        0      0
        0      0
        0      0
        0      0
        0      3
        1      3
        1      3
─────────────────────
n(0)   10      9
n(0)/n  0.833  0.750
T/R            0.900
   Will it pass despite the fact that T obviously performs worse than R in ¼ of patients?
   
   
2.         R      T
─────────────────────
        0      0
        0      0
        0      0
        0      0
        0      0
        0      0
        1      3
        1      3
        1      3
        1      3
        1      3
        1      3
─────────────────────
n(0)    6      6
n(0)/n  0.500  0.500
T/R            1.000
   Hey, an equal proportion! Will it pass – with flying colors! – despite the fact that T performs worse than R in ½ of patients?
   
   
3.         R      T
─────────────────────
        0      0
        0      0
        0      0
        0      0
        0      0
        0      0
        0      do
        0      do
        0      do
        0      do
        0      do
        0      do
─────────────────────
n(0)   12      6
n(0)/n  1.000  1.000
T/R            1.000
   Say, in ½ of the patients after T their condition actually worsened to such a degree that they withdraw consent and dropped out from the study. If we perform the analysis on the per-protocol data set it looks soo_o nice though it isn’t.

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1. Hauschke D, Kieser M, Diletti E, Burke M. Sample size determination for proving equivalence based on the ratio of two means for normally distributed data. Stat Med. 1999;18(1):93–105.
   
2. Hauschke D, Steinijans V, Pigeot I. Bioequivalence Studies in Drug Development. Chichester: Wiley; 2007. Chapter 10.