Impact of handling missing PK data on PD estimation – explicit modeling of BLQ data in WinBUGS® reduced bias in the PD predictions - a preclinical example.
Dartois C, Looby M, He H, Steimer J-L, and Pillai G.
Modeling and Simulation, Novartis Pharma AG, Basel, Switzerland
Objectives: Purpose of this project was to compare 2 drugs, a lead compound and its backup on a pharmacodynamic endpoint based on their relative potency in animals.
Methods: Data came from 2 studies in which the 2 drugs were administered in single dose, some in cross-over and at different dose levels (from 0.1 to 10 mg and from 2 to 100 mg for the lead and its backup, respectively). PK and PD samples were taken at the same time, between 0.5 to 48h with non-balanced designs between the 2 studies. Exploratory analysis of the raw data was performed to highlight features of the design which could have an impact on modeling. Then, a non linear mixed effect approach was applied. Models were evaluated through a goodness of fit (GOF) and a visual predictive check.
Results: Exploratory analysis highlighted for the 2 drugs, a high variability in the absorption phase, and for the lead, paucity of data in the expected IC50 region. The lower limit of quantification (LOQ) of this drug was indeed approximately equal to IC50/2.5 and one quarter of data was below the LOQ (BLQ). Basic PKPD models for the 2 drugs, were analyzed using NONMEM, included 2 compartments and an Emax model, linked by common PD baseline. IIV variabilities were defined as log-normal. An inter-occasion effect was added on absorption parameters, an additive residual error model on log-transformed PK data. In the first approach, all BLQ data were discarded. Predictions of the missing data were often above LOQ and so induced an apparent bias in the PD estimation. It explained why a second approach was tested. The same PK models were fitted in Winbugs®, taken into account the different LOQ, with same considerations as in the first approach except for the inter-occasion effect, not included. Individual PK predictions were then introduced in the PD model fitted in NONMEM. For the 2 compounds, PKPD standard GOF of the 2 approaches were not really distinguishable. The second approach allowed to decrease significantly the number of missing data predictions above LOQ for the lead and in this way revealed this method to be more reliable. Other graphics showed the large impact of the second approach on the estimation of the PD parameters.
Conclusions: Handling missing data in PKPD modeling is a concrete question for which currently no perfect method is available [1]. More precisely, the handling of PK missing data may have a great impact on the PD estimations. In this project, the first method which was recommended despite its simplicity [2], used NONMEM® and discarded all PK data below LOQ. The second method used Winbugs®, in which BLQ data are identified and their influence on the likelihood is assessed. This second method which is also very simple to implement, offered largely more reliable PKPD results.
References:
[1] Beal, SL. Conditioning on certain random events associated with statistical variability in PK/PD. JPP,2005(32)2.
[2] Beal, SL. Way to fit a PK Model with some data below the quantification limit. JPP 2001, (28)5.
