M. Vigan (1), J. Stirnemann (2,3), F. Mentré (1)
(1) INSERM, UMR 738, Univ Paris Diderot, Sorbonne Paris Cité, Paris, France; (2) Referral Center for Lysosomal Diseases, Paris, France; (3) Hospital Jean-Verdier, Univ Paris XIII, Bondy, France.
Objectives: The analysis of repeated time to event (RTTE) data requires frailty models [1] and specific estimation algorithms. Karlsson et al. [2] compared SAEM and Laplace estimation in NONMEM but neither SAEM in MONOLIX nor Adaptative Gaussian Quadrature (AGQ) in SAS. The first aim of this simulation study is to assess the performance of the SAEM [3] algorithm in MONOLIX and the AGQ procedure in PROC NLMIXED of SAS. Gaucher Disease (GD) [4] is a rare autosomal–recessive disorder, due to the deficiency of a lysosomal enzyme, glucocerebrosidase. The second aim of this study is to evaluate the frequency of occurrence of bones events (BE) in GD patients treated by imiglucerase.
Methods: This simulation study mimicked GD data. We simulated occurrence of BE by an exponential model with random effects additive on log lambda. We simulated 100 datasets with 200 subjects. We defined the fixed effects lambda=0.002 month-1, its variance omega2=1 and a maximum follow-up of 144 months. We simulated 3 types of censorship: max follow-up, low or high censure. Number of subjects, lambda and omega were varied to evaluate the estimation capacities of the algorithms. They were evaluated through the relative bias and the relative root mean square error (RMSE). For the application, we analyzed occurrence of BE in the 185 patients of the French GD registry treated by imiglucerase. Data were censored until the closing date or treatment discontinuation. Estimations were performed with SAS v.9.3 [5] (with 5 quadrature points) and MONOLIX v.4.0 [6] (with 3 Markov chains).
Results: The two algorithms showed equal performances. Biases on lambda are low (-2% to 2%), and biases on omega are slightly negative (-9% to -2%). RMSE are reasonable and decrease as the number of subject increases (<30% with 200 patients and <22% with 400). When lambda increases, both RMSE decrease and when omega increases, its RMSE decreases. Among the 185 treated GD patients, 26 had BE with a total number of 36 BE. The probability of first BE occurring by 10 years during treatment is estimated at 19%. BE modeling by an exponential model adequately fits GD data.
Conclusions: Despite the small number of repeated events, both algorithms provide a good estimate of the parameters. We need to extend this simulation study to other conditions, and study the covariate impact. To our knowledge, it was the first study of RTTE simulation analyzed with MONOLIX.
References:
[1] Hougaard, P. (1995), Frailty model for survival data, Lifetime Data Analysis, 1(3):255-273.
[2] Karlsson, K.E., Plan, E.L., Karlsson, M.O. (2011), Performance of three estimation methods in repeated time-to-event modeling, The American Association of Pharmaceutical Scientists Journal, 13(1):83-91.
[3] Kuhn, E., Lavielle, M. (2005), Maximum likelihood estimation in nonlinear mixed effects models, Computational Statistics and Data Analysis, 49(4):1020-1038.
[4] Stirnemann, J., Belmatoug, N., Vincent, C., Fain, O., Fantin, B., Mentré, F. (2010), Bone events and evolution of biologic markers in Gaucher disease before and during treatment, Arthritis Research and Therapy, 12(4):R156.
[5] Littell, R.C., Milliken, G.A., Stroup, W.W., Wolfinger, R.D., Schabernberger, O. (2006), SAS for Mixed Model (2nde ed), SAS Institute Inc.: Cary, NC.
[6] http://www.lixoft.net.
Reference: PAGE 21 (2012) Abstr 2453 [www.page-meeting.org/?abstract=2453]
Poster: Estimation methods