RE: FW: OMEGA HAS A NONZERO BLOCK

From:"Kowalski, Ken" Subject:RE: FW: [NMusers] OMEGA HAS A NONZERO BLOCK Date:Fri, 4 Oct 2002 10:43:55 -0400 Nick, With regards to your Item 1, I think we are going to have to agree to disagree. Throwing away the objective function is not appealing to me...the choice of values for fixing parameters (e.g., elements of Omega) that you consider unrealistic is completely arbitrary. I suspect the reason NONMEM never estimates a covariance to be zero is that covariances can be positive or negative so zero is not on the boundary. But what about my analogy regarding a variance component (diagonal element of Omega) going to zero which is on the boundary? Surely you've seen NONMEM estimate a zero variance component. Isn't a zero variance component estimated for say ka or V unrealistic? Again, this can happen because of lack of information in the design/data to estimate this variance component. Isn't it common practice to then fix this variance component to zero rather than some arbitrary non-zero value? Going back to Steve Duffull's problem, what if by chance the Omega reported in the NONMEM output rounded to 3 significant digits didn't have problems (i.e., just squeaked by and was positive semi-definite) and let's say for this to happen the correlation was estimated to be 0.99. Doesn't an estimate of 0.99 for the correlation concern you? If so, how low does the correlation have to be for you to consider it realistic? Call it a trick if you like, but my proposed solution is supported by the data and is simply a more parsimonious form for Omega that will result in the identical fit that Steve obtained. Regarding Item 2, fixing the correlation to something less than 1 (say 0.5) is going to result in a poorer fit since NONMEM is wanting to estimate the correlation to be 1. As we discussed a year ago, I contend that my model constraining the correlation to 1 will result in a more realistic simulation of the data (i.e., a posterior predictive check) than fixing the correlation to something considerably lower that is not supported by the current data. Regarding Item 3, I think we are in agreement provided one has a strong enough prior presumably supported by other data. This I think is a reasonable alternative to my solution to the ill-conditioned Omega problem. I make the distinction between a strong prior supported by an independent set of data (perhaps data-rich healthy volunteer data) and fixing the correlation arbitrarily. Ken