# Bioequivalence and Bioavailability Forum 02:59 CEST

verstc
Junior

China,
2018-06-12 02:23

Posting: # 18885
Views: 2,641

## how to calculate MSEw and MSEb [General Sta­tis­tics]

Dear All，

I am a fresher to BE analysis. As I known, for inter-CV and intra-CV calculation, CVintra%=100√(e^(MSE_W)-1), CVinter%=100√(e^((MSE_B-MSE_W)/2-1) ). Now, I am confused how to calculate the MSE_w and MSE_B for 2 X 2 crossover design and fully replicated design (TRT|RTR or TRTR|RTRT). Could anyone tell me the detail of calculation for these different designs?

Shawn

Edit: Category changed; see also this post #1. Relax; see also this post #9 (I deleted another post of yours 13 hours after this one). [Helmut]
Helmut
Hero

Vienna, Austria,
2018-06-12 16:54

@ verstc
Posting: # 18891
Views: 2,480

## Get software!

Hi Shawn,

» I am a fresher to BE analysis.

Welcome to the club!

» […] how to calculate the MSE_w and MSE_B for 2 X 2 crossover design and fully replicated design (TRT|RTR or TRTR|RTRT).

Thanks for not mentioning the lousy partial replicate (TRR|RTR|RRT).

» Could anyone tell me the detail of calculation for these different designs?

Do you want to calculate it manually (paper, pencil, brain)? A nice morning exercise as long as you have only fixed effects in the model (ANOVA).*
If you are interested in full-blown mixed-effects models (e.g., the FDA’s or the CFDA’s for reference-scaling), forget it. This would require restricted maximum likelihood estimation, which is – practically – impossible without software.

Given all that, get suitable software, validate it, and be happy. The residual mean squares are part of the standard output (example of a 2×2 design).

• Chow S-C, Liu J-p. Design and Analysis of Bioavailability and Bioequivalence Studies.
Boca Raton: CRC Press; 3rd edition 2009. ISBN: 978-1-58488-668-6.

Cheers,
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. ☼
Science Quotes
verstc
Junior

China,
2018-06-17 14:55

@ Helmut
Posting: # 18910
Views: 2,369

## Get software!

Dear Helmut,

It is clear to me for your explain.

I am wondering if there is a way to reduce the intra-subject CV. I think intra-subject CV is an inherent characteristic of a drug. is it right? If it not, does anyone can reduce it by any ways?

Thanks,

best,
Shawn

Helmut
Hero

Vienna, Austria,
2018-06-17 16:10

@ verstc
Posting: # 18912
Views: 2,372

## Within-subject variability: Property of the drug (& formulation)

Hi Shawn,

» I think intra-subject CV is an inherent characteristic of a drug. is it right?

Only if you are talking about an intravenous dose. Otherwise, it is mixture of the properties of the drug (influenced by transporters, pre-systemic and first-pass metabolism, clearance) and the formulation / physiology (absorption, lag-time due to gastric emptying). See my nitpicking paragraph in this post.

» If it not, does anyone can reduce it by any ways?

I can’t imagine how.1,2 In a crossover design every subject acts as its own control. Imagine you have a very high between-subject variability (e.g., extensive and poor metabolizers or one is stupid enough to include only ballerinas and sumo-wrestlers in a study). The within-subject variability will not be affected.
Try it: Use the data of any study and multiply results of half of the subjects by two (mimicking the ballerinas with low volumes of distribution) and divide the other half by two (mimicking the sumo-wrest­lers). What do you get?

In a simple crossover CVintra is pooled from CVwT and CVwR (i.e., one common variance is assumed in the model). If CVwT < CVwR (the reference is a lousy product), the CI is inflated and we are punished by a higher sample size. All too bad that we don’t know the CVs in a simple 2×2 crossover. We need one the full replicate designs (see also this post) and reference-scaling for a potential incentive in the sample size.
An example: CVwT and CVwR 0.3–0.5, theta0 0.95, targetpower 0.8. `sampleN.TOST()` does not support different CVs. Makes sense, since only CVw is part of the model. We can misuse the function `sampleN.scABEL()` after ‘switching off’ all scaling conditions. Does it help? Not at all. Only ABEL can be nice.

```library(PowerTOST) CV.lo     <- 0.30 CV.mid    <- 0.40 CV.hi     <- 0.50 CVwR      <- CVwT <- seq(CV.lo, CV.hi, 0.1) res       <- data.frame(CVwT=rep(CVwT, each=length(CVwR)),                         CVwR=rep(CVwR, length(CVwT)), CVw=NA,                         n.ABE=NA, n.ABE.sim=NA, n.ABEL=NA) res\$CVw   <- mse2CV((CV2mse(res\$CVwT)+CV2mse(res\$CVwR))/2) # remove all scaling conditions reg       <- reg_const("USER", r_const=log(1.25)/CV2se(0.3),                        CVswitch=0.3, CVcap=0.3, pe_constr=FALSE) for (j in 1:nrow(res)) {   res\$n.ABE[j] <- sampleN.TOST(CV=res\$CVw[j], theta0=0.95, design="2x2x4",                                print=FALSE, details=FALSE)[["Sample size"]]   res\$n.ABE.sim[j] <- sampleN.scABEL(CV=c(res\$CVwT[j], res\$CVwR[j]),                                      theta0=0.95, design="2x2x4",                                      regulator=reg, print=FALSE,                                      details=FALSE)[["Sample size"]]   res\$n.ABEL[j] <- sampleN.scABEL(CV=c(res\$CVwT[j], res\$CVwR[j]),                                   theta0=0.95, design="2x2x4",                                   regulator="EMA", print=FALSE,                                   details=FALSE)[["Sample size"]] } print(res[with(res, order(CVw, CVwT)), ], row.names=FALSE)  CVwT CVwR       CVw n.ABE n.ABE.sim n.ABEL   0.3  0.3 0.3000000    20        20     18   0.3  0.4 0.3527824    26        26     16   0.4  0.3 0.3527824    26        26     24   0.4  0.4 0.4000000    34        34     20   0.3  0.5 0.4089765    34        34     16   0.5  0.3 0.4089765    34        34     32   0.4  0.5 0.4518401    42        42     18   0.5  0.4 0.4518401    42        42     24   0.5  0.5 0.5000000    50        50     22```

Lesson learned: Even if we would know that the reference is a lousy product, in ABE we suffer.

1. I once heard about a Russian CRO claiming that “our volunteers have a lower CVintra and studies at our site can be smaller than usual”. What the heck are they doing? Include mo­no­zycotic twins or have access to human clones? Would violate the assumption of independence in the model. I guess, they are just fabricating data.
2. Some people claim that extreme standardization (BMI, …) will also help to reduce CVintra. I strongly doubt that since the between- and within-variance components are mutually independent.

Cheers,
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. ☼
Science Quotes
nobody
Senior

2018-06-19 10:20

@ Helmut
Posting: # 18919
Views: 2,259

## Within-subject variability: Property of the drug (& formulation)

» 2. Some people claim that extreme standardization (BMI, …) will also help to reduce CVintra. I strongly doubt that since the between- and within-variance components are mutually independent.

I would assume that volunteers with very constant everyday habits, including sleeping, diet (!), GI-transit time etc. etc. have reduced intraindivdual variability. Maybe do a BE-study in a monastery as proof-of-concept?

For your in vitro dissolution testing you don't mix within one experiment (!) basket and paddle employing various rotation speeds, use flasks of different volumes, different buffers, temperatures etc. pp. to reduce variability, or? So why shouldn't high standardization work with your in vivo dissolution system, too?

Kindest regards, nobody
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