BQL values, version 3
Date: Fri, 30 Jul 1999 15:55:10 -0500
From: S Thomas Forgue <FORGUE_S_THOMAS@Lilly.com>
Subject: BQL values, version 3
NONMEM Users:
Reference is made to NONMEM UsersNet Archive; Subject 116: "Concentration values below assay limits" [May 1997].
We are modeling (ADVAN2) plasma concentrations of a polypeptide drug (1461 observations from 358 patients in a Phase 3 clinical study). Fully 33% of the observations are BQL (< 50 pg/mL). Peak concentrations are typically 200 - 300 pg/mL. The proportion of BLQ values increases greatly with increasing time from last dose. How we treat these BQL values has a *marked* effect on estimates of drug exposure -- with clinically important consequences concerning safety assessment.
We are aware of some approaches to estimate BQL values directly from detector response data; however current reality is that we accept databases from our analytical laboratories with assigned "BQL" values. Please, let's table that issue for now.
The trivial solution of just omitting BQL values has little support within our group, unless these data represent a "negligible" fraction. Dr. Sheiner's suggestion was (in part) to use an additive and proportional residual error structure, fix variance of the additive epsilon to (QL/2)**2 [one possibility] and enter the BQL observations as QL/2. [Please see the archive reference for his actual comments]. This is easily implemented and works "well" in our polypeptide problem. We do not have consensus among our PK'ists and statisticians that this is necessarily the best solution for the polypeptide study. What are the alternatives? Dr. Aarons alluded to an iterative numerical intergration routine based on likelihood theory. We are thinking about an iterative Monte Carlo strategy of imputing BQL values randomly drawn from the left tail of a log-normal distribution of plasma concentrations.
***THE REQUEST*** We will appreciate knowing of any *statistically sound and pragmatic* approach to the BQL issue that we can implement within the next month and submit with confidence to worldwide regulatory agencies. Our thanks in advance for your time and expertise.
Ben Cerimele, Tom Forgue, Mike Heathman and Julie Satterwhite