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

Hi BE-proff,

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

We get an upper CL of 32.11% for the small study and 29.19% for the large one. Q.E.D.

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.

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