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

posted by Helmut Homepage – Vienna, Austria, 2018-02-11 18:31 (1870 d 06:29 ago) – Posting: # 18396
Views: 14,511

Dear Detlew

❝ That's not the whole truth about the state of affairs :no:.

❝ 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.

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