Bioequivalence and Bioavailability Forum • To test or not to test…

To test or not to test… [🇷 for BE/BA]

posted by Helmut – Vienna, Austria, 2015-08-11 03:21 (3512 d 03:04 ago) – Posting: # 15218
Views: 17,183

Hi BE-proff,

interesting paper. So I stick with Shapiro-Wilk for my home brewed stuff.

❝ But one thing worries: the article concludes that all tests are rather weak if sample size is below 30. :-(

❝ What to think about BE-studies with samples 18, 24? :confused:

Don’t test for normality. The multiplicative model we are using in BE is based on

The basic equation of PK:
  AUC = FD/CL,
which can be linearized by taking the logarithms to
  ln(AUC) = ln(F) + ln(D) – ln(CL).
Now we can apply an ANOVA, which requires additive effects.
OK, we are interested in comparing the Fs of product (assuming equal doses and clearances). So,
  BA = AUC_T/AUC_R or ln(BA) = ln(AUC_T) – ln(AUC_R). Nice.
Multiplicative errors in bioanalytics due to serial dilution of stock / spiking solutions.

Have a look at this example (slides 4–6): Pooled AUC-data of 437 subjects. Shapiro-Wilk rejects the normality assumption for raw data with p 1.35·10^–14 (‼), but not for ln(AUC) with p 0.293. In the next slide we have one of the studies (n=12). The normality assumption is neither rejected for AUC nor for ln(AUC). The former p-value is smaller than the latter, but still n.s. Normality tests are not built to decide between two distributions. That’s not their job, but ours.

Nitpicking:

Strictly speaking the distribution of PK metrics is irrelevant (as long as they are identical). In the BE-context only the within-subject residuals of the model should be normal. It might well be that residuals of two extremely skewed (not normal, but identical) distributions still give nomal residuals.
If these residuals are not normal, one could opt for a nonparametric method. Well, cough…

How is your R-learning curve doing? Try this:

x1 <- rweibull(40, 1, 1) # Weibull distribution x2 <- rweibull(40, 1, 1) d <- x1-x2 op <- par(no.readonly=T) par(mfrow=c(3, 1)) hist(x1, freq=F, xlim=c(0, 8), xlab="", las=1, main="x1") legend("topright", bty="n", legend=paste("p =", signif(shapiro.test(x1)$p.value, 3))) hist(x2, freq=F, xlim=c(0, 8), xlab="", las=1, main="x2") legend("topright", bty="n", legend=paste("p =", signif(shapiro.test(x2)$p.value, 3))) hist(d, freq=F, xlim=c(-6, 6), xlab="", las=1, main="x1 \u2012 x2") legend("topright", bty="n", legend=paste("p =", signif(shapiro.test(d)$p.value, 3))) par(op)

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Complete thread:

Comparison of normality tests BE-proff 2015-08-10 09:07 [🇷 for BE/BA]
- To test or not to test…Helmut 2015-08-11 01:21
  - To test or not to test… BE-proff 2015-08-11 10:06
    - R packages/libraries Helmut 2015-08-11 12:07
      - R packages/libraries BE-proff 2015-08-11 12:29
        
        R packages/libraries Helmut 2015-08-11 13:18
        
        R packages/libraries BE-proff 2015-08-11 22:15
        
        R packages/libraries Helmut 2015-08-11 22:28
        
        R packages/libraries BE-proff 2015-08-11 22:39
        
        R packages/libraries d_labes 2015-08-12 09:07
        
        R packages/libraries BE-proff 2015-08-12 10:36
        
        R packages/libraries install d_labes 2015-08-12 11:13
        
        install package(s) from a local zip file? yjlee168 2015-08-12 11:43
        
        install package(s) from a local zip file? BE-proff 2015-08-12 12:06
        install package(s) d_labes 2015-08-12 13:02
        
        Packages attached by default Helmut 2015-08-12 13:13
        install package(s) yjlee168 2015-08-12 14:58
        
        suggested package(s) d_labes 2015-08-12 16:33
        
        R packages/libraries install BE-proff 2015-08-12 11:57
        
        I don't believe!!! BE-proff 2015-08-12 18:26
        
        Congratulation d_labes 2015-08-13 08:36