From: Xiaofeng Wang - xiaofeng.wang@bms.com Subject: [NMusers] simulation Date: 1/27/2004 10:50 AM Colleagues: If I know the PK model, the matrix of Omega, Sigma, also the covariate models, how can I predict the time-concentration of a particular subject with 95% confidence interval using NONMEM? Thank you for your help, xiaofeng _______________________________________________________ From: Xiaofeng Wang - xiaofeng.wang@bms.com Subject: RE: [NMusers] simulation Date: 1/27/2004 11:27 AM Hello again: I would like to calculate the 95% confident interval through variance matrix, C. Since I already know Omega, Sigma, the PK models, and the covariate model, mathematically the variance-covariance matrix of yi, Ci, can be calculated. In this case, I don't have to simulate 1000 times and then calculate the mean and 95% confident interval. xiaofeng _______________________________________________________ From: "Kowalski, Ken" - Ken.Kowalski@pfizer.com Subject: RE: [NMusers] simulation Date: 1/27/2004 1:10 PM Xiaofeng, Essentially what you are asking for are the standard errors (SEs) for the IPREDs. These SEs are not easy to get as they involve a second level of estimation provided by the empirical Bayes predictions of the ETAs. You might be able to trick NONMEM to provide the covariance matrix for the ETA predictions by constructing single subject datasets where the ETAs are the parameters you want to estimate to minimize the OFV and the $COV output from such NONMEM runs would provide the covariance matrix of these ETA predictions. I believe examples of this are provided somewhere in the NONMEM manuals and/or one of the NONMEM workshop course notes. However, I don't know if this approach gives you the same ETA predictions as what NONMEM provides directly from the posthoc and/or conditional estimation methods when fitting the population model. Even so, once you get the covariance matrix of the ETA predictions for a given subject you still need to do some sort of linearization to get the SEs for the IPREDs (incorporating both the uncertainty in the population estimates and the ETA predictions). A few years ago I was interested in looking at whether an improvement could be made on the original GAM procedure by using the covariance matrix of the ETA predictions to properly weight them in the GAM estimation. I came to the conclusion that estimating these covariance matrices for the ETA predictions was more trouble than its worth. I'm interested if anyone else in Nmusers has tried to do this and whether they have a slicker approach to obtain these SEs. Regards, Ken _______________________________________________________ From: Xiaofeng Wang - xiaofeng.wang@bms.com Subject: RE: [NMusers] simulation Date: 1/27/2004 2:14 PM Hi Ken: Thank you for message and elaboration of the question I have. yes, you are right that I was asking for the SEs for the IPREDs. I tried to go in this direction: for example, from FO, the PK model can be linearized as yij=fi(Theta1, ...) +gij etai +hij epij, where gij is the partial derivative of the model at etai=0. then the variance of yij is G'i Omega Gi +diag (Hi'Sigma Hi). If I have the PK model, the covariate model, as well as Omega and Sigma, the variance (or SEs) of yij can be calculated and then the 95% CI of yij. From NONMEN manual, the matrix G and H can be obtained when running estimation (I don't know how to write the code to get these two matrix, if anyone can point it out for me). I dont' know in the simulation mode, if G and H can be also obtained. In fact, H is easy to obtained once the error model was determined. However, G is involved the estimate of all the partial derivative at eta. xiaofeng _______________________________________________________ From: "Hutmacher, Matt" - mhutmach@amgen.com Subject: RE: [NMusers] simulation Date: 1/27/2004 3:46 PM Xiaofeng, As Ken stated, it is a bit of work to try and get the covariance matrix of estimates for the empirical Bayes predictions of the etas. If you are able to use SAS (or know someone that does), it is much simpler to get the standard errors you desire. These quantities are computed by the delta method and can be output using a single line of code. However, if you have a complex model or a nonstandard dosing history, it will require some effort to program the model for fitting. Matt _______________________________________________________