Confidence intervals for Emax model

From:"Austin, Daren J" Subject:[NMusers] Confidence intervals for Emax model Date:Thu, February 28, 2002 4:13 am I have fitted an Emax model to some population data with both NONMEM and PROC NLMIX in SAS, and was pleased to find that they agree exactly (use METHOD=1 for NONMEM or method=firo for SAS). I have only one eta parameter on Emax, which is well estimated and an additive error structure. I would now to construct 95% confidence intervals. I pressume that because both the variability on Emax and the residual enter linearly that I can just add together so that U95% = theta1*EXP(1.96*SQRT(eta1))*conc/(theta2+conc)+1.96*SQRT(eps1) L95% = theta1*EXP(-1.96*SQRT(eta1))*conc/(theta2+conc)-1.96*SQRT(eps1) This assumes that the intra and inter-subject variabilities are uncorrelated which seems reasonable in this instance (no comedications for example). Of course had I put variability on the EC50 the approximation would definitel;y not be valid. I realise that I could just simulate away and pull out the 2.75thand 97.5th centiles, but is there a better way? For those that are interested the SAS code is as follows (I have deliberately written the code as NONMEM-esque), data is for heart rate, hence a residual of sqrt(eps) ~ 7bpm proc nlmixed data=test method=firo; /* method=0 */ parms theta1=20 theta2=60 eta1=0.1 eps=50; /* initial conditions */ Emax=theta1*exp(e1); EC50=theta2; pred=Emax*CONC/(EC50+CONC); model F ~ normal(pred,eps); /* error structure */ random e1 ~ normal(0,eta1) subject=subject; predict pred out=pred; run; At present only additive error is possible in SAS. Kind regards, Daren Dr. Daren J. Austin Pharmacometrician GlaxoSmithKline Research & Development Greenford Road, Greenford, Middlesex UB6 0HE dja17709@gsk.com Tel: 7-711 2073 or +44 (0) 20 8966 2073 Fax: 7-711 2123 or +44 (0) 20 8966 2603