Non-parametric alternative to bioequivalence analysis

[JoakimE]

Hi,

I am working with a DDI clinical study in which a standard linear mixed model has been used to assess bioequivalence between the victim drug alone and the victim drug+perpetrator drug on a number of PK parameters. Unfortunately, model diagnostics are particularly poor. The residual term is not at all normally distributed and there are signs of heteroscedasticity in the residual variance. I have tried transforming the data, but this is difficult without loosing the interpretability of the model results.

I am thinking of an alternative non-parametric approach to asses equivalence. My idea is to derive a new variable as the ratio of PK parameter victim drug / PK parameter victim+perpetrator drug. Then calculating the median of this variable as a point estimate and constructing distribution-free CIs for the median using Hahn and Meeker's method available in proc univariate. Something like this:

proc univariate data=ratios cipctldf alpha=0.1;
var ratio_var;
output out=pctl pctlpts=50 pctlpre=p cipctldf=(lowerpre=LCL upperpre=UCL);
run;

Question is, does this sound like a viable non-parametric alternative to my problem? Are there better alternatives? I know I could, for example, use two one sided Wilcoxon signed rank tests. However, it is more informative and appealing in my opinion to answer the bioequivalence-question using CIs.

Thanks in advance for any assistance.

[SteveDenham]

With a little jiggering, you can get the bioequivalence boundaries from the two one-sided Wilcoxon tests.  And interestingly enough, at least to me, these boundaries are dependent only on the number of observations involved, i.e. for any given sample size, there is one Wilcoxon value for the not greater than and one for the not less than tests. If your Wilcoxon value falls between these, then you have some indication of equivalence.

All this comes with a BIG caveat. If your raw data  has one or more "outlier" value(s), converting to ranks throws that valuable information away.  Since most equivalence trials are somewhat restricted in sample size, those extreme values are telling you that the distributions are likely not the same.

So, rather than rank (or any other) transformation, you might look into resampling methods to calculate the difference in means, the variance of that difference, and the resulting confidence interval.

SteveDenham

[JoakimE]

Thank you Steve! But would say that a Wilcoxon CI has any benefits compared to a Hahn and Meeker CI, which is already readily available through proc univariate?

[SteveDenham]

The Hahn and Meeker CI is based on the assumption that the data are normally distributed. If that were the case, there would be no need to consider using a non-parametric approach to BE.

SteveDenham

[JoakimE]

Not sure what you are referring to now. The Hahn&Meeker CI that you get through cipctldf in proc univariate is distribution free based on ranks.Hence, my question if it could be used in my current BE scenario with non-normally distributed data.

[SteveDenham]

Not quite. In one case the H&M method assumes normality around the percentiles (reference to Section 4.4.1). It involves the CIPCTNORMAL option. There is second method in H&M (Section 5.2) that is completely distribution-free for the confidence intervals around the percentiles, though. This uses the CIPCTLDF option. This may be the one you are referring to, as it accepts three variations using the  TYPE= option - asymmetric two tailed, one sided lower and one sided upper. So in the end you could do two one-sided intervals as an approach to bioequivalence. I apologize for the miscommunication.

SteveDenham

[JoakimE]

Ok, thanks for the clarification. It would seem my initial idea might work then. Thanks for the input!