Re: Estimation method for ETAs with POSTHOC

From: Rong Chen <[email protected]> Reply-To: Rong Chen <[email protected]> Date: Sunday, 7 May 2017 at 12:55 To: "Guo, Tingjie" <[email protected]>, nmusers <[email protected]> Subject: Re: [NMusers] Estimation method for ETAs with POSTHOC Hi Tingjie, I think this article could answer your question by indicating the objective function used to estimate post hoc eta and how to reproduce the estimate process in R. There were R codes example of a one-compartment PK model with 3 etas to be estimated. Title: R-based reproduction of the estimation process hidden behind NONMEM® Part 1: first-order approximation. URL: http://dx.doi.org/10.12793/tcp.2015.23.1.1 Best wishes, Rong ________________________________ From: "Guo, Tingjie" <[email protected]> To: nmusers <[email protected]> Sent: Friday, 5 May 2017, 20:17 Subject: [NMusers] Estimation method for ETAs with POSTHOC Dear NMusers, I have two questions about the mathematical details on POSTHOC estimation in NONMEM. How does NONMEM actually do when doing POSTHOC ($EST METHOD=0 MAXEVEL=0) to get ETAs? I assume but not for sure there is an objective function to be minimized, somewhat like: Objective function = SUM(Yobs-Ypred)^2/sigma^2 + SUM(Para_i-Para_pop)^2/omega^2 Is there an objective function used in NONMEM when doing POSTHOC? If so, what is that function? Secondly, if the answer to above is yes, let’s assume the real objective function is the same as what I mentioned above. I wonder how (NONMEM does) to minimize this function? I am currently trying to do similar things in R/Python language. I tried Metropolis-Hasting algorithm and Simulated Annealing algorithm, but with some technical problems. And the result was not comparable with NONMEM as well. Can someone give me a direction for this? The more mathematically detailed the better. Thanks! Warm regards, Tingjie