Missing data

A common challenge for pharmacokinetic modellers is what to do with measurements that are known to be less than the lower limit of quantification (LLOQ). These measurements are, unfortunately, often recorded as BLQ (Below Limit of Quantification), even though the chemical analyst was able to quantify the measurement below this limit. The limit is defined for the purposes of qualifying bioanalytical procedures (1). The FDA Guidance uses the LLOQ to identify the lowest standard on a calibration curve which should have a precision of 20% and accuracy between 80-120%. Note that this is a not a guidance for how measurements should be used for pharmacokinetic modelling.

A variety of methods have been proposed (2) and evaluated for using these BLQ values in a mixed effects model (2-7). The performance of the methods have been evaluated mainly using simulation procedures. NONMEM VI 1.2 and later offers 3 specific methods. Monolix offers a single method.

This workshop will describe the properties of the methods and demonstrate how to use them using NONMEM and Monolix. A practical session will give participants the chance to try out the methods using NONMEM and to gain some experience of simulation based methods for evaluating the procedures.

  1. FDA. Bioanalytical Method Validation http://www.fda.gov/cder/guidance/4252fnl.htm. 2001.
  2. Beal SL. Ways to fit a PK model with some data below the quantification limit. Journal of Pharmacokinetics & Pharmacodynamics. 2001;28(5):481-504.
  3. Byon W, Fletcher CV, Brundage RC. Impact of censoring data below an arbitrary quantification limit on structural model misspecification. J Pharmacokinet Pharmacodyn. 2008;35(1):101-16.
  4. Ahn JE, Karlsson MO, Dunne A, Ludden TM. Likelihood based approaches to handling data below the quantification limit using NONMEM VI. J Pharmacokinet Pharmacodyn. 2008;35(4):401-21.
  5. Hennig S, Waterhouse TH, Bell SC, France M, Wainwright CE, Miller H, et al. A d-optimal designed population pharmacokinetic study of oral itraconazole in adult cystic fibrosis patients. Br J Clin Pharmacol. 2007;63(4):438-50.
  6. Samson A, Lavielle M, Mentre F. Extension of the SAEM algorithm to left-censored data in nonlinear mixed-effects model: Application to HIV dynamics model. Computational Statistics & Data Analysis. 2006;51(3):1562-74.
  7. Duval V, Karlsson MO. Impact of omission or replacement of data below the limit of quantification on parameter estimates in a two-compartment model. Pharm Res. 2002;19(12):1835-40.

Nick Holford