Re: treatment of BQL

Date: Tue, 05 Oct 1999 08:15:17 -0700 From: LSheiner <lewis@c255.ucsf.edu> Subject: Re: treatment of BQL All - The BQL thing just doesn't go away ... I have a feeling we've been through this before. The BQL observations are left censored. They could be any value between 0 and QL. The likelihood contribution for such an observation is therefore the integral of the distribution of observations centered at the prediction, from 0 to QL. This distribution, unfortunately, cannot be normal since such a distribution implies that the "observation" BQL might be negative, so on might use log(y) vs log(f), or approximate the distribution of epsilon near 0 by a half-normal, or such. Unfortunately, this "fix" involves modifying the objective function so that it can include integrals like the ones I described above. That is not easy, and it is why I suggested as a simple expedient, 1. Delete all but the first in each continuous series of BQL observations 2. Set the remaining (first) one DV = QL/2 3. Use an additive plus proportional error model with the SD of the additive part >= QL/2. This should preserve whatever "information" the BQL possesses, and does not require modifying the likelihood. I admit I haven't studied this, but before resporting to elaborate schemes, I would like to see some evidence that this simple one has problems. I agree with Jim's issue with Leonid's solution; introducing discontinuities in the objective function is, it seems to me, more dangerous than approximating an integral with a point on the integrant, as I have suggested. 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