## Leave-One-Out (IBD) [Design Issues]

❝ After I tried to run the SAS code (Example 4.5), I got the CI, but there is only one Residual value. I guess I suppose to calculate the intra-subject CV from this value, right? So, My question is, Do we only get one Intra-subject CV from three-comparison of the treatment (T-R, S-T, S-R) while we got three CI (T-R, S-T, S-R)?

I’m not equipped with … Hence, my understanding of the code is limited.

You are right, in the model you get only

*one*(pooled) estimate of the variance. That’s not a good idea, since it will “work” only if intra-subject variances would be identical and the treatment differences at least very similar. Otherwise, the treatment estimates will be biased and the type I error is not controlled. See also this post.

At the 2

^{nd}Workshop of the Global Bioequivalence Harmonisation Initiative (Rockville, September 2016) Pina D’Angelo gave a presentation

*“Testing for Bioequivalence in Higher‐Order Crossover Designs: Two‐at‐a‐Time Principle Versus Pooled ANOVA”*showing exactly that. Here some of her slides:

Purpose

- To determine which method of statistical analysis

is more appropriate to conclude bioequivalence in

higher‐order crossover studies:- The
**two‐at‐a‐time**principle using two separate

incomplete block design ANOVAs

- A
**pooled**approach using one ANOVA and a common

error term for the two contrasts

- The

Introduction

Statistical Concerns:

- Different means (point estimates) between formulations

- Different variances between formulations

- If either situations exist, which method of analysis

reduces bias the most:**two‐at‐a‐time**principle or

**pooled**ANOVA?

Simulated Data: Summary

- When all three treatments have similar means and there is

homogeneity of variances, both methods give very similar

results.

- When treatment means differ but there is homogeneity of

variances, both methods give very similar results. With higher

variability, the power is slightly increased when using the pooled

ANOVA method.

- When treatment means are similar but variances are not

homogeneous, the two‐at‐a‐time method gives higher power to

detect BE for the treatment with lower variability

- When treatment means differ and variances are not

homogeneous, the two‐at‐a‐time method increases power to

detect BE for the treatment with lower variability. Moreover,

type I error is higher when using the pooled ANOVA method.

Closing Remarks

- Using a two‐at‐a‐time principle for statistical analysis of a

higher‐order pilot study will have more value for decision-

making on which multiple tests lots will be selected for use

in a pivotal study based on the pilot study results. The

intra‐subject variability of a specific test‐to‐reference

comparison can be determined using the two‐at‐a‐time

principle, which may be an important factor in selecting a

test product considering test products are generally

formulated to show different characteristics for testing in a

pilot study.

If you are interested in all pairwise comparisons, generate three data sets (values or T&R, S&R, T&S,

*i.e.*, exclude all values of the respective other treatment S, T, R) whilst keeping the codes for sequence and period. This will give you data sets which represent an IBD (incomplete block design). Run the usual model on them.

This approach is also recommended in the EMA’s BE-GL:

In studies with more than two treatment arms (e.g. a three period study including two references, one from EU and another from USA […], the analysis for each comparison should be conducted excluding the data from the treatments that are not relevant for the comparison in question.

(my emphasis)Example 4.5 (Phoenix/WinNonlin 8, mixed effects, Satterthwaite’s degrees of freedom):

` PE (%) 90% CI (%) s²`_{w} CV_{w} (%)

pooled model T vs. R AUC 116.15 (108.97, 123.81) 0.043954 21.20

T vs. R Cmax 129.65 (118.84, 141.45) 0.084569 29.71

S vs. R AUC 140.63 (131.93, 149.90) 0.043954 21.20

S vs. R Cmax 159.75 (146.42, 174.30) 0.084569 29.71

T vs. S AUC 82.60 ( 77.46, 88.07) 0.043954 21.20

T vs. S Cmax 81.16 ( 74.35, 88.56) 0.084569 29.71

IBD models T vs. R AUC 116.05 (108.92, 123.65) 0.042525 20.84

T vs. R Cmax 129.54 (119.26, 140.71) 0.074744 27.86

S vs. R AUC 141.09 (131.39, 151.51) 0.053706 23.49

S vs. R Cmax 160.48 (145.20, 177.36) 0.109492 34.02

T vs. S AUC 83.12 ( 78.37, 88.15) 0.035788 19.09

T vs. S Cmax 81.63 ( 75.33, 88.46) 0.069372 26.80

Evidently variances are not identical. The ones of T/R are smaller than the ones of S/R. If we apply the pooled model the CIs of T/R will be wider than in the IBD model and the CIs of S/R narrower.

BTW, I don’t understand what the purpose of the

`carry`

variable in Byron’s code is.*Dif-tor heh smusma*🖖🏼 Довге життя Україна!

_{}

Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮

Science Quotes

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