Placebo-corrected PD models

From:"Austin, Daren J" Subject:[NMusers] Placebo-corrected PD models Date:Fri, 17 May 2002 10:45:34 +0100 Dear group, I am fitting data from an ex-vivo assay that is subject to both a significant placebo response and considerable between-subject variation. I would like to fit some form of concentration response function and have used two response functions: R1 = Log(Response(t)/Placebo(t)) and R2 = Log(Response(t)/Response(0)) - Log(Placebo(t)/Placebo(0)) The first corrects piece-wise for placebo, whereas the second additionaly corrects for baseline effects (inter-occasion variability). The second is equal to the first with the addition of Log(Placebo(0)/Response(t)) for each subject/dose. Log-transformation is essential to stabilise variance. I would ultimately like to measure percentage inhibition of placebo response, which is obtained by back-transforming the model/data to get INHIB=100*(1-EXP(R1 or R2)). Note that with this transformation the natural range of inhibition is bounded [-INFTY, 100] meaning that you can never inhibit more that the placebo response (but can be infinitely worse). I fit this to an approximation of a sigmoid Emax curve in which R(CONC) = -Emax (CONC/EC50)**n/(1+(CONC/EC50)**n) ~ -Emax (CONC/EC50)**n for CONC<<EC50 R(CONC) = - (CONC/Cs)**n because there is no evidence that the data turns over to give Emax at observed concentrations. Cs is a "scale" concentration and is related to EC50 and Emax by Cs = EC50/(Emax**1/n) and the IC50, which is what I am ultimately interested in estimating, can be calculated using IC50 = Cs.(ln(2))**1/n. My question is which response to use: placebo-corrected (R1) or double baseline placebo corrected (R2)? I fit the same model but the objective function drops by about 30 (-30 to -60) when R2 is used instead of R1. This represents a higher log-likelihood so does that mean I should accept the response with the highest log-likelihood? I have additional data (at TIME=0) if I retain R1, but have chosen to discard it to compare the two models. This data provides information on the residual epsilon. I am familiar with the theory behind model selection via objective function changes, but have not seen much about data selection. I suppose I could rely on AIC and the one with the highest LL wins (models have same df), but is there any other criteria? The analysis I have done is equivalent to including two covariates (baselines) but they are in the data rather than the model! The final models are pretty much the same but parameters may be better estimated (lower CVs) for one rather than the other and I would like generic guidance for other data sets where inhibition is being studied. So that direct comparisons can be made between studies. I also wonder if anyone else has used the above method to analyse highly variable inhibition data. Kind regards, Daren Dr. Daren J. Austin Pharmacometrician Clinical Pharmacology Discovery Medicine GlaxoSmithKline daren.austin@gsk.com Tel: 7-711 2073 or +44 (0) 20 8966 2073 Fax: 7-711 2123 or +44 (0) 20 8966 2603