Re: BQL values, version 3

Date: Fri, 30 Jul 1999 16:25:32 -0700 From: LSheiner <lewis@c255.ucsf.edu> Subject: Re: BQL values, version 3 "J.G. Wright" wrote: > > There are two things to bear in mind when dealing with BQL observations. > > 1) A BQL observation does not necessarily mean that the "true" value is > below BQL. Sometimes observations above BQL will be recorded as below BQL > because of assay variability etc. Thus the support for a BQL observation > on the likelihood should actually extend above BQL. Exactly how much is > hard to determine. I don't think this is right. The likelihood conditions on the OBSERVED data. What was observed is BQL. It has a certain probability under the model (the model might indeed have its expectation > QL, but that doesn't chagne the observation, only its likelihood), and that is given by the integral I defined. > > 2) Some account of the uncertainty induced by these censored obervations > has to be acknowledged. One approach to this is multiple imputation, > where you create numerous datasets with different random values(generated > from a sensible model) and analyse each dataset separately. Then combine > across datasets to get an average value and confidence intervals which > acknowledge this uncertainty (definitely superior to a single imputation). > This is debatably a discrete analogue of an > EM-type analogue, with the advantage that it can be easily implemented in > NONMEM. > > Of course, the choice of imputation model is crucial. However for > regulatory submission, a conservative method (with large variability) is > probably the best option. > Again, I don't beleive so: the uncertainty in the BQL observation is captured by the probability model for it just as is the uncertainty of a >QL observation. BUT, 1. In my simplified approach, I am indeed, not proerly acknowledging uncertainty since I am imputing the missing observation as QL/2. 2. Multiple imputation may indeed be a way to deal with the BQL problem if you don't want to do the integration: as Jim says, create say 10 data sets filling in the BQL obnservations with reasonable imputed values including (large) uncertainty. Then proceed as appropriate for mult imputation. This amounts to treating the BQL observations as "missing data", which, within the constraint that they are BQL, they are. 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