Multilevel nested random effect model implementation
Pascal Girard1,2, Silvy Laporte-Simitsidis3, Sylvie Chabaud1
1) Service Pharmacologie Clinique , Faculté Médecine Laennec, Lyon France; 2) Pharsight, CA Mountain View, USA and 3) Unité Pharmacologie Clinique, Hôpital Bellevue, Saint Etienne France.
Almost 30 years ago, pharmacokineticists introduced the nested random effect models in the field of non linear models in order to simultaneously describe inter-individual variability (IIV) of PK parameters and random residual variability (RESV).1 This leads to the large development of population PK-PD modelling that we know today, and which is mostly based on these 2 nested random effects: RESV nested in IIV. More recently, new levels of randomness have been considered, as inter-occasion variability (IOV) and inter-study variability (ISV) when pooling PK-PD data sets coming from different centers or studies.2,3 In every cases, the introduction of a new random effect means the introduction of a new level of nesting: for example in the case of inter-occasion variability, RESV is nested in IOV that is nested in IIV (noted RESV<IOV<IIV) and in the case of inter-study variability we have RESV<IIV<ISV. The level of complexity can of course be increased by mixing al these levels together which gives RESV<IOV<IIV<ISV. These types of models are characterised as multilevel nested random effect models. Many other situations can lead to multilevel random effects: for example, in toxicokinetics, one may consider inter-litter or inter-batch variability; in cosmetology, the zone where the cosmetic is applied in one individual can also be considered as generating random variations. Usual population PK-PD software only allows the estimation of 2 levels of randomness, the traditional RESV and IIV. The recently released new version of nlme function, that can be found in SplusÒ and R languages, allows the implementation of multilevel nested random effects.4 We have applied nlme to simulated data sets with 3 (RESV<IIV<ISV ) and 4 levels (RESV<IOV<IIV<ISV) of random effects, and to real data for which IOV was previously modelised. In every cases the results are compared to two stage method and when possible with NONMEM. It was found that all methods give consistent results in terms of precision and bias of parameter estimates. The pro and cons of the different modelling approaches will be discussed.
1. Sheiner LB, Rosenberg B, Melmon KL. Modelling of individual pharmacokinetics for computer aided drug dosage. Computer Biomed Res 1972; 5:441-459.
2. Karlsson MO, Sheiner LB. The importance of modeling interoccasion variability in population pharmacokinetic analyses. J Pharmacokinet Biopharm 1993; 21:735-750.
3. Laporte-Simitsidis S, Girard P, Mismetti P, Chabaud S, Decousus H, Boissel JP. Inter-study variability in population pharmacokinetic meta-analysis: when and how to estimate it? J Pharm Sci 2000; 89.
4. Pinheiro JC, Bates DM. Mixed Effects Models in S and S-Plus. Springer Verlag, 2000.