Re: Concentration values below assay limits

From laarons@fs1.pa.man.ac.uk Thu May 22 05:33:07 1997 Subject: Re: Concentration values below assay limits I don't think this is going to be much use to you but we have handled levels below the limit of quantification in the following way (the method was developed by David Lunn <d.lunn@ic.ac.uk>) We incorporated integral contributions to the likelihood, i.e. INTEGRAL{from y = 0 to QL} Likelihood dy But this is difficult, obviously, because you need to integrate numerically and the support of the likelihood over this region is unknown because it depends on theta, etc. From an MCMC perspective this is alleviated somewhat because you can integrate at each iteration, but the shape of the likelihood is still unknown - i.e. you have to make sure that your integration routine is very robust. Most existing software (except BUGS ) will not let this be done. The logic behind the method is that samples near to the LOQ, as determined by the model and associated parameter estimates, carry more information than those samples later in time which, according to the model, should be approaching zero. Clearly there is the possibility for model misspecification here, but arguing about model adequacy based on data below the LOQ is probably not a wise thing to do. __________________________________________________ Leon Aarons School of Pharmacy and Pharmaceutical Sciences University of Manchester Manchester, M13 9PL, U.K. tel +44-161-275-2357 fax +44-161-275-2396 email l.aarons@man.ac.uk ****