RE: Standard errors of estimates for strictly positive parameters

From: [email protected] [mailto:[email protected]] On Behalf Of Chaouch Aziz Sent: 11 February 2015 17:22 To: [email protected] Subject: [NMusers] Standard errors of estimates for strictly positive parameters Hi, I'm interested in generating samples from the asymptotic sampling distribution of population parameter estimates from a published PKPOP model fitted with NONMEM. By definition, parameter estimates are asymptotically (multivariate) normally distributed (unconstrained optimization) with mean M and covariance C, where M is the vector of parameter estimates and C is the covariance matrix of estimates (returned by $COV and available in the lst file). Consider the 2 models below: Model 1: TVCL = THETA(1) CL = TVCL*EXP(ETA(1)) Model 2: TVCL = EXP(THETA(1)) CL = TVCL*EXP(ETA(1)) It is clear that model 1 and model 2 will provide exactly the same fit. However, although in both cases the standard error of estimates (SE) will refer to THETA(1), the asymptotic sampling distribution of TVCL will be normal in model 1 while it will be lognormal in model 2. Therefore if one is interested in generating random samples from the asymptotic distribution of TVCL, some of these samples might be negative in model 1 while they'll remain nicely positive in model 2. The same would happen with bounds of (asymptotic) confidence intervals: in model 1 the lower bound of a 95% confidence interval for TVCL might be negative (unrealistic) while it would remain positive in model 2. This has obviously no impact for point estimates or even confidence intervals constructed via non-parametric bootstrap since boundary constraints can be placed on parameters in NONMEM. But what if one is interested in the asymptotic covariance matrix of estimates returned by $COV? The asymptotic sampling distribution of parameter estimates is (multivariate) normal only if the optimization is unconstrained! Doesn't this then speak in favour of model 2 over model 1? Or does NONMEM take care of it and returns the asymptotic SE of THETA(1) in model 1 on the log-scale (when boundary constraints are placed on the parameter)? Thanks, Aziz Chaouch This message and any attachment are confidential and may be privileged or otherwise protected from disclosure. If you are not the intended recipient, you must not copy this message or attachment or disclose the contents to any other person. If you have received this transmission in error, please notify the sender immediately and delete the message and any attachment from your system. Merck KGaA, Darmstadt, Germany and any of its subsidiaries do not accept liability for any omissions or errors in this message which may arise as a result of E-Mail-transmission or for damages resulting from any unauthorized changes of the content of this message and any attachment thereto. Merck KGaA, Darmstadt, Germany and any of its subsidiaries do not guarantee that this message is free of viruses and does not accept liability for any damages caused by any virus transmitted therewith. Click http://www.merckgroup.com/disclaimer to access the German, French, Spanish and Portuguese versions of this disclaimer.