The mysterious ρ -between or within studies [General Sta­tis­tics]

Dear Detlew

❝ That's not the whole truth about the state of affairs .

❝ The question is: Correlation of treatment differences between studies or within studies.

❝ For the latter I recall you two references:

Phillips KF.

Power for Testing Multiple Instances of the Two One-Sided Tests Procedure

❝ Int J Biostat. 2009;5(1):Article 15. doi:10.2202/1557-4679.1169

❝ Quote from Kem Phillips:

❝ "The correlation will usually be difficult to estimate, unless a similar experiment has been conducted...".

❝ That smells for me like within a study.

Yep, then I expect a high correlation (based on my limited knowledge of PK). For my data sets I get with
pearson <- cor.test(log(study$AUC), log(study$Cmax)) rho[set, "estimate"] <- pearson$estimate rho[set, "lower"] <- as.numeric(pearson$conf.int)[[1]] rho[set, "upper"]    <- as.numeric(pearson\$conf.int)[[2]] summary(rho, digits=5)     estimate           lower               upper       Min.   :0.20123   Min.   :-0.094923   Min.   :0.40858  1st Qu.:0.70335   1st Qu.: 0.516584   1st Qu.:0.82721  Median :0.81713   Median : 0.677607   Median :0.89959  Mean   :0.77413   Mean   : 0.633948   Mean   :0.86544  3rd Qu.:0.90122   3rd Qu.: 0.827646   3rd Qu.:0.94461  Max.   :0.98928   Max.   : 0.977336   Max.   :0.99494

IIRC, Chow & Liu state somewhere that the mean of within-subject ratios is a biased estimate…

Another question: What is a “similar experiment”? Given the dispersion in the summary above I would rather say that trying to get an estimate across different drugs (or even for the same drug but IR/IR and MR/MR) is futile. Will try again with the analyte as a factor.

Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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