## Maximum CV might be misleading [Power / Sample Size]

❝ […] pooled CV in BE-studies […] should be calculated when there are several studies with different CVs and we need "adequate" CV (correct? ).

Correct.

❝ But what prevents us from using the highest CV for sample size calculation?

Nothing.

❝ Any ambushes there?

No obvious ones. The maximum CV might be pure chance and/or the result of a small sample size. The lower the sample size, the higher its uncertainty is. The CV is an estimate, not carved in stone. Hence, it makes sense to take this uncertainty into account and have a look at its upper confidence limit (I generally use an α of 20%).

Let’s consider 2×2 studies with CVs of 25%. Sample size were 12 (pilot study) and 24 (from the literature or a failed pivotal).

`library(PowerTOST)`

round(100*CVCL(CV=0.25, df=12-2, side="upper", alpha=0.2)[[2]], 2)

round(100*CVCL(CV=0.25, df=24-2, side="upper", alpha=0.2)[[2]], 2)

One step further: We get CVs of 25 and 15%. Sample sizes were 12 and 24 in one case and the other way ’round in the other.

`CV <- c(0.25, 0.15)`

n <- c(12, 24)

source <- c("study 1", "study 2")

CVdata1 <- data.frame(CV, n, rep("2x2", 2), source)

CVdata2 <- data.frame(rev(CV), n, rep("2x2", 2), source)

names(CVdata2) <- names(CVdata1) <- c("CV", "n", "design", "source")

print(CVdata1, row.names=FALSE); print(CVdata2, row.names=FALSE)

CV n design source

0.25 12 2x2 study 1

0.15 24 2x2 study 2

CV n design source

0.15 12 2x2 study 1

0.25 24 2x2 study 2

Let’s get the pooled CVs and calculate their upper CLs:

`print(CVpooled(CVdata1, alpha=0.2), verbose=TRUE)`

print(CVpooled(CVdata2, alpha=0.2), verbose=TRUE)

Pooled CV = 0.1866 with 32 degrees of freedom

Upper 80% confidence limit of CV = 0.211

Pooled CV = 0.2232 with 32 degrees of freedom

Upper 80% confidence limit of CV = 0.2527

In the first case the pooled CV with 18.66% is closer to the 15% (from n=24), since the study is more influential than the 25% (from n=12). In the second case the order is reversed (22.32% is closer to 25% than to 15%).

Now back to your question whether it would make sense to use the highest CV. I would always use the upper CL. As shown above for CV 25% and n=24 this is 29.19%. If we have additional information from other studies (

*i.e.*, work with a pooled CV) we have more degrees of freedom which narrows the CI. In the second case the upper CL is 25.17% which is substantially lower than the 29.19% from the single study.

Hope that helps.

*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

### Complete thread:

- Why do we need pooled CV? BE-proff 2016-08-24 08:48 [Power / Sample Size]
- Maximum CV might be misleadingHelmut 2016-08-24 12:07
- Maximum CV might be misleading BE-proff 2016-08-26 10:41
- Pooling – example Helmut 2016-08-26 11:34
- Pooling – example BE-proff 2016-12-28 14:37
- in my protocols… Helmut 2016-12-29 12:27

- Pooling – example BE-proff 2016-12-28 14:37

- Pooling – example Helmut 2016-08-26 11:34

- Maximum CV might be misleading BE-proff 2016-08-26 10:41
- Why do we need pooled CV? ElMaestro 2016-08-24 13:03
- Yessir! Common sense! Helmut 2016-08-24 13:53
- Common sense weighting before pooling mittyri 2016-08-24 15:13

- Gut feeling is the answer! DavidManteigas 2016-08-25 11:09
- The reasons not to pool Astea 2016-08-26 20:40
- The reasons not to pool mittyri 2016-08-28 22:05
- Know your drug/formulation! Helmut 2016-08-29 11:56

- The reasons not to pool Astea 2016-08-26 20:40

- Yessir! Common sense! Helmut 2016-08-24 13:53

- Maximum CV might be misleadingHelmut 2016-08-24 12:07