From: Paul Hutson <prhutson@pharmacy.wisc.edu>
Subject: Correlations for power analysis
Date: Fri, 08 Dec 2000 09:08:21 -0600
Greetings, everyone.
I am trying to power a validation study using limited sampling to estimate the AUC (or clearance). We are collecting a full PK set as the gold standard, but are utilizing samples drawn at two pre-determined time points in the Bayesian analysis. What level of correlation or predictive performance would be considered acceptable by this group?
I was planning to use the correlation instead of the predictive performance (mpe rmse) in the power / sample size analysis since I am unfamiliar with how to utilize the predictive performance parameters. Does this seem reasonable?
Thank you.
Paul Hutson, Pharm.D.
Associate Professor (CHS)
UW School of Pharmacy
425 N. Charter St
Madison, WI 53706-1515
Tel: (608) 263-2496
FAX: (608) 265-5421
Pager: (608) 265-7000, #7856
Correlations for power analysis
From: "Jogarao Gobburu 301-594-5354 FAX 301-480-3212" <GOBBURUJ@cder.fda.gov>
Subject: Re: Correlations for power analysis
Date: Fri, 08 Dec 2000 11:11:00 -0500 (EST)
Dear Paul,
I am sure you have a reason for being interested ONLY in AUC. The AUC as such will not give you any information unless you have a PK - PD relationship. It is a good idea (after Dr. Sheiner's suggestion at the FDA's CardioRenal Advisory committee meeting held on 20 Oct 2000) to ask the following questions to the domain-experts (clinicians,regulators..):
1. What do you want to know?
Domian-experts (DEs) probably want to know THE 2 sampling points that are 'qualified' to predict the AUC (gold standard).
2. What are you willing to assume?
DEs probably are willing to assume that the drug's PK/PD can be described by a particular model, that you might have. And that the clinically relevant change is 'so much' (say 20% from baseline) (based on prior experience, time honored ranges, gut feelings, etc). You then translate that to your AUCs.
3. How certain do you want to be?
DEs, further, want to know the limited sampling points that render the prediction with a power of 90% (equivalence of limited sampling and gold standard AUCs).
So, you take these 'answers' and determine the power of the limited sampling approach to predict AUCs to be within 20% (could be asymmetric) of the gold standard 90% of the times. I would perform Monte Carlo simulations to design the trial. A statistician could derive an analytical solution to this problem, probably.
Regards,
Joga Gobburu
Pharmacometrics,
CDER, FDA.
From: "Paul Williams" <pwilliams@uop.edu>
Subject: Re: Correlations for power analysis
Date: Fri, 08 Dec 2000 08:41:38 -0800
Paul,
I am assuming from your note that you are going to plot prediction [x axis] vs observed [y axis]. If this is your approach you should be interested in more than the correlation because there can still be some systematic error in the model even when there is a high degree or correlation between the predicted and observed. If this is your approach then you should also be interested in the slope [slope should not be different from 1] and intercept [intercept should not be different from 0] of this regression in addition to the correlation between the predicted and observed. Of course the whole problem with regression is the strong influence of outliers. There are ways to deal with these ourliers also. If it appears that outliers are a problem you could take a look at a text "Introduction to Robust Estimation and Hypothesis Testing" by Rand R. Wilcox.
What is a good correlation would depend on the intended use of the model and what are the consequences of having a poor correlation.
If you decide to go ahead with the predictive performance parameter method, see a paper in Pharmacotherapy entitled "Direct Comparison of Three Methods for Predicting Digoxin Concentrations, November 1996. In this paper we outlined and applied a validation method that accounts for several nonindependent and unbalanced observations within the same subject.
Cheers!
Paul Williams