Sivakrishna
☆    

India,
2020-10-07 08:15
(21 d 03:17 ago)

Posting: # 21973
Views: 426
 

 Treatment effect justification [General Sta­tis­tics]

Dear Members,

Good Morning!!

In the Bio equivalence study, the p value is < 0.05 for Treatment effect, i.e., Treatment effect was statistically significant at 5% level of significance and however the obtained 90% confidence intervals were with in 80.00% to 125.00% and power was >90%. Could you please provide your suggestions to justify the treatment effect.

Thanks in advance.

Thanks and Regards
G. Siva Krishna Teja.


Edit: Category changed; see also this post #1[Helmut]
ElMaestro
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Belgium?,
2020-10-07 10:19
(21 d 01:14 ago)

@ Sivakrishna
Posting: # 21974
Views: 394
 

 Treatment effect justification

Hi Siva Krishna,

something like this:

"The test producing a significant treatment effect is that log(y)T=log(y)R where y is the dependent variable (AUC or Cmax). This is not the hypothesis evaluated for the conclusion of bioequivalence. It is entirely expected that Test and Reference could be associated with different levels of (logarithmic) Cmax or AUC as they are truly two different formulations. What the evaluation for bioequivalence shows is that the difference in rate and extent and absorption does not differ by a clinically relevant margin, where clinical relevance is determined by the regulatory convention. Therefore the significant formulation effect does not translate, in this case, into inability to conclude bioequivalence."

Good luck.:-)

I could be wrong, but...

Best regards,
ElMaestro

No, of course you do not need to audit your CRO if it was inspected in 1968 by the agency of Crabongostan.
Helmut
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Vienna, Austria,
2020-10-07 11:07
(21 d 00:26 ago)

@ Sivakrishna
Posting: # 21975
Views: 387
 

 statistically significant ≠ clinically relevant

Hi Siva Krishna,

I guess 100% was not contained in the 90% CI, right?
If yes, you have a statistically significant difference which is clinically not relevant.1 We abandoned testing for a statistically significant difference (see ElMaestro’s post) 33 (‼) years ago with Schuirmann’s TOST.2 To quote Wasserstein et al.3

Don’t Say “Statistically Significant”


For which power did you plan the study? It might well be that
  • the T/R-ratio was closer to 100% than assumed and/or
  • the CV was lower than assumed and/or
  • the dropout-rate was lower than anticipated.
Any of those (and their combinations) will lead to higher power and increases the chance of a statistically significant treatment effect.
See also the second part of this post. If you are in the lower right quadrants, you have high power and a statistically significant treatment effect is likely.


  1. \(\small{\Delta}\) = clinically relevant difference. Commonly 0.20 (20%). For NTIDs (EMA and other jurisdicions) \(\small{\Delta}\) 0.10, for Cmax (Russian Federation, EEU, GCC) \(\small{\Delta}\) 0.25. For HVD(P)s, where CVwR >30%, \(\small{\Delta}\) >0.30 (scaled to the variability of the reference). The acceptance range for bioequivalence \(\small{\left \{\theta_1,\theta_2\right \}}\) is calculated by \(\small{\theta_1=1-\Delta}\), \(\small{\theta_2=(1-\Delta)^{-1}}\). If the 90% CI lies entirely within \(\small{\left \{\theta_1,\theta_2\right \}}\), the observed difference of the treatment effect is considered clinically not relevant – irrespective how wide the CI is or where the point estimate lies. A formulation with a PE of 100% (CI 80.00–125.00%) is as BE as another with a PE of 85% (CI 80.00–90.31%). In the former case you were extremely lucky and in the second you have a statistically significant difference (100% not contained in the CI).
  2. Schuirmann DJ. A comparison of the Two One-Sided Tests Procedure and the Power Approach for Assessing the Equivalence of Average Bioavailability. J Pharmacokin Biopharm. 1987; 15(6): 657–80. doi:10.1007/BF01068419.
  3. Wasserstein RL, Schirm AL, Lazar NA. Moving to a World Beyond “p < 0.05”. Am Stat. 2019; 73(sup1): 1–19. doi:10.1080/00031305.2019.1583913. [image] Open access.

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Sivakrishna
☆    

India,
2020-10-09 10:24
(19 d 01:08 ago)

@ Helmut
Posting: # 21985
Views: 282
 

 statistically significant ≠ clinically relevant

I would like to say Thank you sir for your valuable information. This may be helpful to my question.

Thanks and Regards
G. Siva Krishna Teja.
Helmut
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Vienna, Austria,
2020-10-09 15:04
(18 d 20:29 ago)

@ Sivakrishna
Posting: # 21986
Views: 249
 

 Problems with low variability

Hi Siva Krishna,

» I would like to say Thank you sir for your valuable information. This may be helpful to my question.

Welcome. Would you mind answering my previous questions:
» » I guess 100% was not contained in the 90% CI, right?
» » For which power did you plan the study?

Sometimes statistically significant differences are common, namely if the CV is low (say, <10%) and you plan for 80% power. Then you may end up with a sample size far below the regulatory minimum of twelve. Add more subjects to compensate for potential dropouts and…
In my protocols I state that extremely high power is expected and the CI might well contain not 100%.


[image] script:

library(PowerTOST)
balance <- function(x, seqs) { # gives complete sequences
  x <- ceiling(x) + ceiling(x) %% seqs
  return(x)
}
CV       <- 0.10    # assumed (here 10%)
theta0   <- 0.925   # assumed T/R-ratio
target   <- 0.80    # target (desired) power (here at least 80%)
do.rate  <- 0.10    # anticipated dropout rate (here 10%)
design   <- "2x2x2" # can be any one given by known.designs()
seqs     <- as.integer(substr(design, 3, 3)) # sequences
n        <- sampleN.TOST(CV = CV, theta0 = theta0, targetpower = target,
                         design = design, details = FALSE,
                         print = FALSE)[["Sample size"]]
if (n < 12) n <- 12 # force to minimum acc. to GLs
dosed    <- balance(n / (1 - do.rate), seqs) # adjust for dropout-rate & balance
eligible <- dosed:n; dropouts <- rev(eligible - n)
res      <- data.frame(dosed = dosed, dropouts = dropouts, eligible = eligible,
                       power = NA, CL.lo = NA, CL.hi = NA,
                       p.left = NA, p.right = NA)
for (j in seq_along(eligible)) {
  res$power[j] <- suppressMessages(
                    signif(power.TOST(CV = CV, theta0 = theta0,
                                      design = design, n = eligible[j]), 4))
  res[j, 5:6]  <- round(100*CI.BE(pe = theta0, CV = CV,
                                  design = design, n = eligible[j]), 2)
  res[j, 7:8]  <- suppressMessages(
                    signif(pvalues.TOST(pe = theta0, CV = CV,
                                        design = design, n = eligible[j]), 4))
}
print(res, row.names = FALSE)

Gives (if the assumptions about the CV and T/R-ratio are realized in the study):

 dosed dropouts eligible  power CL.lo CL.hi   p.left   p.right
    14        0       14 0.9760 86.49 98.93 0.001154 1.913e-06
    14        1       13 0.9652 86.22 99.23 0.001752 4.846e-06
    14        2       12 0.9521 85.92 99.59 0.002569 1.166e-05


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Helmut Schütz
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