Concentration values below assay limits

From S=Maier%C=US%G=Gary%I=A%O=ELFSANOFI%OU1=PA01%ELF21@mcimail.com Tue May 20 12:33:16 1997 Subject: Concentration values below assay limits Hello, I was wondering what type of approaches you may use in including or deleting sample concentrations that are below assay quantitation limits. In my particular case approximately 20-25% of the total number of concentration time points in my data set are below assay limits. The details of the study are: 1. 5 dose levels and 8 subjects per dose. 2. Each dose is administered orally over a 5 day period with 4 samples collected on each day (trough, 8,12,16) and a washout to 72 hours on the last study day 3. retrospective analysis I look forward towards reading individual comments Gary Maier Sanofi Pharmaceuticals

From lewis@c255.ucsf.edu Tue May 20 16:32:53 1997 Subject: Re: Concentration values below assay limits I have the feeling this has been discussed before... Briefly, BQL values can convey information, especially if they occur rather isolated in time (that is, there are no above QL levels "nearby"), and should then be included in the data analysis. While the very best way to do so is not yet known, here is a way that works pretty well: 1. Use an error model that has an additive and proportional component; e.g., Y = F + F*EPS(1) + EPS(2) 2. Fix var(eps(2)) to .25*QL**2. Say QL is .5 mcg/ml, then use, e.g., $SIGMA .04 .0625 FIX 3. Record BQL values as QL/2; i.e., for the above example as .25.

From n.holford@auckland.ac.nz Tue May 20 16:57:19 1997 Subject: Re: Concentration values below assay limits Thanks for the recipe. But how about the rationale? In general are you advocating var(eps(2) of f*QL*QL**2 and record BQL values as f*QL (in your example f would be 1/2)? -- Nick Holford, Dept Pharmacology & Clinical Pharmacology University of Auckland, Private Bag 92019, Auckland, New Zealand email:n.holford@auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556 http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.html

From lewis@c255.ucsf.edu Tue May 20 17:11:08 1997 Subject: Re: Concentration values below assay limits Basically, yes, although the formulas are actually: 1. var(eps(2)) = (f*QL)**2, where f can be taklen to be .5, but see below. 2. Record BQL values as QL/2 The rationale is 1. the CV at QL is about f*100% (many define QL to be at f=.2; f=.5 gives BQL observations even less weight and is conservative in that sense). 2. If all we know is that an observation is BQL, a reasonable ignorance assumption is that the true value is drawn from a uniform distribution with support on 0 - QL; a reasonable imputed value is then the mean of this distribution, viz., QL/2. -LBS.

From ef16065@ggr.co.uk Tue May 20 23:08:03 1997 Subject: Re: Concentration values below assay limits Lew, Nick, Have you ever tried to use the actual concentration value determined by the assay although it was BQL ? I tried, had same estimates as with Lew's suggestion, but faster convergence. Any comment on the bioanalytical side? Eliane

From n.holford@auckland.ac.nz Wed May 21 12:36:19 1997 Subject: Re: Concentration values below assay limits Eliane, Yes. But I have little experience. The real issue is why is there a BQL value at all? If you have a suitable error model you can take any "measured" value at low concs and use it in your PK analyses without having to define a BQL. But if the conc analyst will not tell you the conc but will only tell you BQL then you must resort to 'imputation' (ie. faking the data). Try telling your conc analyst that is what you are going to do :-) -- Nick Holford, Dept Pharmacology & Clinical Pharmacology University of Auckland, Private Bag 92019, Auckland, New Zealand email:n.holford@auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556 http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.html

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 ****