Dear all! I want to start a little discussion on BE in WinNonlin. All problems are not only applicable to Phoenix, but to previous versions of WNL as well. Sure you have noticed that a new Guideline on BE was published by the EMA in January and will come into operation 01 August 2010. Two points are important, which are rather tricky to address with PHX/WNL: [ul][li]Two-Stage Sequential Designs[/li][li]Highy Variable Drugs / Drug Products[/li][/ul] I will start with the first point here, and continue with the second one in another post (time allowing). If the intra-subject CV in a pivotal study is uncertain, the new GL allows for a Two-Stage Design: The first stage (part) of the study is performed, the actual CV[sub]intra[/sub] is calculated and following conditions given in the protocol, a second stage may be initiated. A pooled analysis will be performed at an adjusted alpha (e.g., Pocock’s alpha 0.0294). To my knowledge the only method validated for 2×2 BE studies is: Potvin D, Diliberti CE, Hauck WW, Parr AF, Schuirmann DJ, Smith RA Sequential design approaches for bioequivalence studies with crossover designs Pharmaceut. Statist. (2007), DOI: 10.1002/pst.294 The flow-chart is given below:
Now for PHX/WNL. Generally a posteriori power in confirmatory statistics is nonsense; but for Potvin’s method we need a value for the decision tree. Let’s have a look at the infamous Data 2x2.CSV (PHX) or Data22.PWO (WNL), Capsule=reference. We get ‘Power at 20% = 0.898818’. Throughout the last years I have tried a couple of times to reproduce WNL’s power calculation according to the documentation, but failed all the time. Since I didn’t use it anyhow, it didn’t bother me too much. Maybe it’s based on the t-distribution, rather the noncentral t-distribution? It’s wrong, anyhow. Try this simple R/S-Plus-code:
alpha <- 0.05 # significance level CV <- 0.233927817734416 # CVintra (from log data) sigmaW <- sqrt((log(1+CV^2))) # Variance s <- sqrt(2)*sigmaW # Within-subjects standard deviation n <- 40 # total number of subjects # (balanced case: n/2 per sequence) ratio <- 1.04658784494175 # ratio = mu_T/mu_R if(ratio == 1) # simple case of ratio equalling unity # (SA Julious 2004, p1962) { power <- 2*pt(-qt(1-alpha,n-2), n-2, sqrt(n)*log(0.8)/sqrt(2*sigmaW^2))-1 } else # ratio <> 1 power <- pt(-qt(1-alpha,n-2), n-2, sqrt(n)*(log(ratio)-log(1.25))/s) - pt(qt(1-alpha,n-2), n-2, sqrt(n)*(log(ratio)-log(0.80))/s) cat("power:",power,"\n")You can easily adapt this example to SAS ; use probt(x,x,z) instead of pt(x,y,z) and tinv(x,y) instead of qt(x,y). So far, so good. But I get a power of [color=#0000FF]0.958284[/color], nQuery Advisor 7.0 gives [color=#0000FF]0.9582[/color]. Forget PHX’s/WNL’s result of [color=#FF0000]0.8988[/color]! OK; we know that and perform the calculation somewhere else (hey, we can fire up a script from PHX - but that’s nothing for noobs). Now we want to calculate the 1-2×alpha CI (here it’s 94.12%). The core in PHX is the same as in WNL5.x (6.1.0.173, Core Version 17 Oct 2006), so we get in the ASCII-output: Bioequivalence Statistics User-Specified Confidence Level for CI's and Power = 94.1200 Percent of Reference to Detect for 2-1 Tests and Power = 20.0%and an additional line in the CI-table. It’s time to change this stuff. What the hack should ‘Power = 94.1200’ mean? Forget it. Alpha = 2.94, if you want. Also high times to remove the bloody Westlake-part of the table. Often requested, never corrected: Differences between means gives results in lexical order (Capsule - Tablet) - but we are not interested in that; we have defined Capsule as the reference. BTW, great that a similar flaw was correct in the Crossover-Tool (PHX6.0->6.1).
