Performance of non-linear mixed effects models with and without taking informative dropout into account
Marcus A. Björnsson (1,2), Lena E. Friberg (2), Ulrika S.H. Simonsson (2)
(1) Clinical Pharmacology Science, AstraZeneca R&D, Södertälje, Sweden; (2) Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden
Objectives: The objective of this simulation study was to investigate the performance of non-linear mixed effects models with and without taking informative dropout into account.
Methods: Simulations were performed using an inhibitory Emax drug effect model combined with an exponential placebo effect model. Dropout was simulated using a hazard function in which the hazard was exponentially related to the individual predicted efficacy score, adapted from Björnsson and Simonsson [1]. The base scenario consisted of a placebo group and three active treatment groups, each with 45 subjects, and with a dropout rate between 25 and 55%. The simulated efficacy data were analysed using non-linear mixed effects modelling with or without including the dropout model. The impact of number of dose groups, number of subjects per group, number of observations per subject, dropout rate, and size of the placebo effect were investigated with respect to bias in the parameter estimates. The Laplacian estimation method in NONMEM 7 (ICON, Hanover, MD, USA) [2] and PsN [3] were used for the stochastic simulations and estimations.
Results: In the base scenario, bias was less than 5% in all fixed effects parameters when the same model, including dropout, was used for simulation and estimation. Bias was larger in EC50 when dropout was not included in the estimation model, although the bias was still less than 10% for the base scenario. The bias in EC50 increased with increasing dropout rate, increasing placebo effect and decreasing number of observations per subject. The increase in bias was larger when dropout was ignored. Bias in the rate constant for the onset of placebo effect was approximately 15-20% in most tested scenarios when dropout was not included in the estimation. Also in cases where parameter estimates were relatively accurate, simulation based diagnostics were poor when dropout was not accounted for.
Conclusions: Ignoring informative dropout can lead to biased parameter estimates, although the bias in many cases was found to be relatively low. The bias was dependent on dropout rate, placebo effect and number of observations per patient. Inclusion of a dropout model is essential in simulation based diagnostics when informative dropout is present, even when the parameters are estimated without bias.
References:
[1] Björnsson MA, Simonsson USH. Modelling of pain intensity and informative dropout in a dental pain model after naproxcinod, naproxen and placebo administration. Br J Clin Pharmacol 2011; accepted article, online
[2] Beal SL, Sheiner LB, Boeckmann AJ, eds. NONMEM users guides. Ellicott City, MD: ICON Development Solutions, 1989-2006
[3] Lindbom L, Pihlgren P, Jonsson EN. PsN-Toolkit--a collection of computer intensive statistical methods for non-linear mixed effect modeling using NONMEM. Comput Methods Programs Biomed 2005; 79:241-257
