Calculation of the 90% CI values from pop PK model estimates

From: "Xiao, Alan" alan_xiao@merck.com Subject: [NMusers] Calculation of the 90% CI values from pop PK model estimates Date: Thu, 15 Sep 2005 18:50:49 -0400 Hello, Could anyone share his/her experience/opinion on the following scenario? Assuming a linear PK model with clearance (CL) as a function of weight (WT), drug-drug interaction 1 (DDI1), etc: CL=theta1*{1+theta2*DDI1+theta3*[(WT/WT0)**theta4-1]}*exp(eta1) with parameter estimates as (Mean+/-SE): theta1=30+/-2; theta2=-0.3+/-0.1; theta3=0.8+/-0.3; theta4=2+/-0.8; and eta1=0.1+/-0.03. WT0 is the median value of the weight distribution of the whole population in the data file for model development. The population size is 1000, of which 10 subjects were on DDI1. The task is to calculate the geometric mean AUC ratio and its 90% CI values for the effect of weight: 140 vs 70 and for the effect of DDI1: DDI1 vs. non-DDI1. ANY comments/questions/suggestions are appreciated. Alan Alan Xiao, Ph.D. Clinical PK, MRL Merck & Co, Inc.

From: "Jakob Ribbing" Jakob.Ribbing@farmbio.uu.se Subject: RE: [NMusers] Calculation of the 90% CI values from pop PK model estimates Date: Fri, 16 Sep 2005 11:51:58 +0200 Alan, Immanuel Looking only at the point estimates and SE:s, the effect of weight on CL seems to be rather uncertain, which is not what one would expect from analysing such a large study population. Could this be due to correlation of estimate between theta3 and theta4? In that case sampling from the covariance-matrix-of estimate (rather than just using SE:s) may be more appropriate (which could be what Immanuel implied with that his simple approach may not be good enough). Including covariance-of estimate would give tighter confidence intervals. If AUC is only dependant on CL (and dose) the geometric-mean AUC can be calculated at CL(eta=0) without the need of simulation. To account for the parameter uncertainties in the weight-effect sampling from the covariance-matrix-of estimate could easily be done in almost any programming language (eg. MATLAB (mvnrnd) or SPlus/R (rmvnorm)). To calculate the effect of DDI1 on CL, the 90-confidence interval for theta2 could simply be applied. Using likelihood profiling may be beneficial for the DDI1-effect but if time and computer power allows a stratified bootstrap could be more reliable for calculating both DDI1 and weight effects. One problem may be that many different concomitant medications were considered as possible DDI:s (which is implied by the name: drug-drug interaction 1). The estimate of the DDI1-effect is then often exaggerated due to selection bias. This is so even if the p-value for selection was corrected for the multiple comparisons of the many DDI:s; one can not know if DDI1 was one of many small-clinically-irrelevant interactions (eg. 15% effect) and that DDI1 randomly seemed more important in these ten individuals (which were on the concomitant medication) OR if the estimated effect (30%) is real. If the highest DDI1-effect within the 90%-confidence interval (CL ~50% lower?) is judged not to be clinically relevant, the selection bias is not a big problem. It will still affect the predictive performance of the model but predicting was not the current task. To fully account for the selection bias is very computer intensive: One way is to apply the whole covariate-selection procedure on a HUGE amount of bootstrap datasets to estimate the selection bias (i.e. the bias one could expect in the subset of datasets where the covariate has been selected). Does anyone know if this has been done in our area? If anyone would actually want to do this: We have previously* investigated the different contributions to selection bias and concluded that competition between (correlated) covariates is not increasing the selection bias much more if statistical significance is already required for covariate selection. Given this I would believe that it is enough to only test for selecting DDI1 on the bootstrap datasets with the effect of weight on CL and any other covariate effects on other parameters already in the model. This would massively reduce the time for the covariate analysis of a bootstrap dataset, since no investigation of all other covariates (which were not selected from the original dataset) is necessary. Taking this approach may also allow a reduction in the number of bootstrap datasets needed for a precise estimate of the selection bias. Any comments to this idea? Regards, Jakob Jakob Ribbing, MSc Division of Pharmacokinetics and Drug Therapy Department of Pharmaceutical Biosciences Uppsala University Box 591 SE-751 24 Uppsala SWEDEN Office : +46 18 471 44 37 Mobile : +46 70 450 33 77 Facsimile: +46 18 471 40 03 Email: jakob.ribbing@farmbio.uu.se *Jakob Ribbing and E. Niclas Jonsson, Power, Selection Bias and Predictive Performance of the Population Pharmacokinetic Covariate Model, JPP 31: 109-134 (2004).

From: "Gastonguay, Marc" marcg@metrumrg.com Subject: Re: [NMusers] Calculation of the 90% CI values from pop PK model estimates Date: Fri, 16 Sep 2005 07:24:39 -0400 Alan, Instead of writing your model as: CL=theta1*{1+theta2*DDI1+theta3*[(WT/WT0)**theta4-1]}*exp(eta1) You might consider re-estimating with a parameterization that is more closely suited to your purpose, such as: CL=(THETA(1) * THETA(2)**DDI1 * (WT/WT0)**THETA(3) ) * EXP(ETA(1)) ;where DDI1 is a 0,1 indicator variable ;THETA(2) is the DDI1 clearance ratio and is constrained with a lower bound of 0, initial estimate could be 1 Also include this code: CRW= (140/WT0)**THETA(3) )/(70/WT0)**THETA(3) ) ;clearance ratio for WT (140:70kg) in absence of DDI1 Run several hundred or more stratified nonparametric bootstrap estimation runs (shouldn't be too bad for a stable 90% CI, compared to the 95% CI we are usually interested in) to obtain empirical 90%CI on all parameters and derived variables of interest (specifically THETA(2) and CRW). You'd have to invert the clearance ratio to get the AUC ratio, but I think you get the idea... Marc --------------------------------- Marc R. Gastonguay, Ph.D. Metrum Research Group LLC www.metrumrg.com _______________________________________________________