Simultaneous modeling of the three ACR improvement thresholds – 20, 50 and 70% - in rheumatoid arthritis patients treated with certolizumab pegol
Brigitte D. Lacroix(1,2), Maria Laura Sargentini-Maier(2), Mats O. Karlsson(1) and Lena E. Friberg(1)
(1)Department of Pharmaceutical Biosciences, Uppsala University, Sweden;(2)Pharmacometrics, Global Exploratory Development, UCB Pharma SA, Belgium
Background: Various approaches have been proposed to model the ACR (American College of Rheumatology) 20% and 50% improvement criteria in rheumatoid arthritis (RA) [1,2,3,4]. However, dichotomizing the composite ACR assessment into such binary variables is throwing away much information.
Objectives: To develop a new approach integrating the information from the 3 commonly used improvement thresholds of 20, 50 and 70% in order to be more informative in evaluating the drug effects.
Methods: Data from 1747 patients on certolizumab pegol (CZP) and 633 patients on placebo treatment were used for non‑linear mixed effects modeling. Placebo or CZP at doses ranging from 50 to 800 mg was administered subcutaneously every 2 or 4 weeks for 8 to 48 weeks. At each visit, the subjects' response statuses with respect to the 3 ACR thresholds was assessed and converted in 4 categorical increasing response scores, 1) ACR20 non-responder, 2) ACR20 but not ACR50 responder, 3) ACR50 but not ACR70 responder and 4) ACR70 responder.
The model was constructed as a compartmental model with 4 compartments predicting the probabilities of the 4 ACR responses over time. Compared to the Markov model[3,4], this approach allows to describe all possible transitions between the 4 scores with fewer parameters, and to account for the score at the preceding visit within a model that is continuous in time (i.e. may predict intermediate states at intermediate times).
Dropout was modeled separately using a logistic regression model and the influence of the previous ACR response level on dropout probability was investigated.
Results: The model predicted the number of transitions and proportion of patients of each ACR response level well. The probability of attaining a higher ACR response increased non-linearly with time, with a fast onset of response, slightly delayed for increasing stringent criteria (90% of maximal effect at W12, W16 and W18 for ACR20, 50 and 70, respectively). The probability of attaining a higher ACR response increased with CZP exposure, affecting both transfer constant to higher and lower scores. The dropout probability increased with time and decreased with increasing ACR response at the preceding assessment.
Conclusions: This new modeling approach, integrating the outcomes from the 3 ACR improvement thresholds, enables greater information to be obtained from conventional ACR assessments. It allows simulation of coherent ACR20, ACR50 and ACR70 outcomes at a given visit for a given subject.
References:
[1] Lee, H., Kimko, H.C., Rogge, M., Wang, D., Nesterov, I., Peck, C.C. Population pharmacokinetic and pharmacodynamic modeling of etanercept using logistic regression analysis. Clin. Pharmacol. Ther. 73, 348-365 (2003).
[2] Hutmacher, M.M., Krishnashnaswami, S. & Kowalski, K.G. Exposure-response modeling using latent variables for the efficacy of a JAK3 inhibitor administered to rheumatoid arthritis patients. J. Pharmacokinet. Pharmacodyn. 35, 139-157 (2008).
[3] Lacroix, B.D., Lovern, M.R., Stockis A., Sargentini-Maier M.L., Karlsson M.O. & Friberg L.E. A pharmacodynamic markov mixed-effects model for determining the effect of exposure to certolizumab pegol on the ACR20 score in patients with rheumatoid arthritis. Clin Pharm Ther. 86, 387-395 (2009).
[4] Lacroix. Exposure-Response Modeling of the ACR50 Score in Rheumatoid Arthritis Patients Treated with Certolizumab Pegol. PAGE 18 (2009) Abstr 1585 [www.page meeting.org/?abstract=1585].