Re: BQL values, version 3

Date: Fri, 30 Jul 1999 15:14:13 -0700 From: LSheiner <lewis@c255.ucsf.edu> Subject: Re: BQL values, version 3 Let me amend and amplify my (simple fix) suggestion. I did suggest substituting QL/2 for BQL as a simple strategy that tries to extract some info from the BQL but not work to hard doing so. It turns out (can't recall who pointed this out to me), that if the concs are all BQL after say 6 hours, and there are therefore BQLs at 6, 10, 12, 24, and 48 hours, then it's a bad idea to put them all in at QL/2 because, even with a relatively large additive error variance, such data imply a long flat tail to the C vs t curve (potentially wreaking havoc with AUC extrapolation for example). So, my modified suggestion for a simple fix is to put ONLY the first BQL in (=QL/2) and delete all subsequent ones in each time series (occasion) from an individual. Now, on to the theory. The "right" thing to do is indeed to set the likelihood contribution of a QL equal to the integral over the support of the observation below QL, conditional upon the current values of the pop params. This is tedious and involves some fancy programming. We (JM Gries, Davide Verotta and I) did this in a problem where we couldn't avoid it, and JM (Jean-Michel.Gries@hmrag.com) may be able to supply you with some useful code fragments (but then again, our problem was different, and it may not be easy for him to extract the relevant code). The imputation idea is a good one, but tell us more just what you have in mind. I would imagine you would be imputing essentially a single likelihood contribution for each QL at each function evaluation? If so, the problem is that then the "likelihood" conditional on a fixed set of parameters would be stochastic. Would this "jitter" mess up convergence? Of course, if you imputed say 100 BQL values from the current model for each "observed" BQL, instead of just one, as I assume you intend, and used the average likelihood contribution of these 100, then this would constitute a particular (Monte Carlo) implementation of the "right" method; i.e., integration over the support for the observation below QL. LBS. -- Lewis B Sheiner, MD Professor: Lab. Med., Biopharm. Sci., Med. Box 0626 voice: 415 476 1965 UCSF, SF, CA fax: 415 476 2796 94143-0626 email: lewis@c255.ucsf.edu