RE: treatment of BQL

From: "Gibiansky, Leonid" <GibiansL@globomax.com> Subject: RE: treatment of BQL Date: Tue, 5 Oct 1999 09:13:57 -0400 Dear James, My idea is to fix DV to, say, BQL/2, if DV < BQL. Then fix IPRED=F, if F > BQL, and fix IPRED=DV (=BQL/2) if F < BQL and DV < BQL. This way, the minimization procedure will "push" the model to the BQL/2 value, but will not penalize for the difference as soon as F reaches BQL. Yes, I will create discontinuous objective function surface. But fixing DV=BQL (for DV < BQL) is not too good either. My experiments show that in this case (DV=BQL for DV < BQL) there is no "force" to push F below BQL, and it takes a lot of iterations to overcome the IPRED=BQL level. I was using this trick in the minimization algorithm based on the least square and iterative weighted (1/y) least square objective functions, and I have a pretty good feeling of what was going on there. Now I'd like to use similar trick in NONMEM. I do not think that it is worth the trouble trying to create smooth objective function via the smooth penalization, at least before I face any serious convergence problems (oscillations near the jump in objective function). I have some problems with the idea >impute values from some flattened distribution anyway, acknowledging that >with time the values are likely to be at the bottom end of BQL whereas >early BQLs may correspond to true values above QL. since in this method you will need to impose your prior knowledge on the long-term behavior of the system. I tried it and ended up with the additional compartment that served only to fit those imputed values. The idea of fixing DV=BQL/2 and then fixing high variance of the error term associated with the BQL observations worked fine, but I'd like to create something that directly corresponds to our knowledge: observation is somewhere in the interval [0,BQL]. It is like using the inequality DV < BQL (*) instead of equality DV=?? in the minimization procedure. Lagrange multiplier corresponding to the inequality is equal to zero (no penalization) if IPRED < BQL. I do not know how to do it in NONMEM (in my procedure, I just excluded penalty for the difference multiplying it by zero if DV<BQL and F < BQL). So I am trying to modify prediction and observation to achieve the same result. I agree that we need simulations to solve this problem. My question was whether there are any obvious deficiencies in such use of NONMEM, or whether there are any other NONMEM ways to implement this idea. Thanks for the comments! Leonid