Jérémy Seurat (1), France Mentré(1) and Thu Thuy Nguyen (1)
(1) IAME, INSERM, UMR 1137, University Paris Diderot, Paris, France
Objectives:
Nonlinear mixed effect models (NLMEMs) are widely used for the analysis of longitudinal data obtained during clinical trials. An appropriate choice of design is crucial to get precise estimation of parameters and/or good power of tests, especially in the case of sparse sampling. For this purpose, optimal design based on the expected Fisher Information Matrix (FIM) can be used instead of clinical trial simulations (CTS). A method evaluating the FIM, without any linearization, based on Monte-Carlo and Hamiltonian Monte-Carlo (MC/HMC), was proposed [1] and implemented in the R package MIXFIM, which performs well with both continuous and discrete data. Nevertheless, this approach requires a priori knowledge of the model, which may lead to non-informative designs if the guessed model was inaccurate. We aimed to propose a new robust design approach based on MC/HMC to account for model uncertainty and to ensure a compromise between the overall precision of estimation and the power of the Wald test to detect a covariate effect. We illustrated and evaluated by CTS the proposed approach through an example of designing a longitudinal trial with binary outcomes.
Methods:
First, to find informative designs given one predefined model, different optimality criteria based on the FIM evaluated by MC/HMC were computed, according to different purposes: the D-optimality (i.e. maximizing the determinant of the FIM) to optimize the precision of the whole set of parameters, the DS-optimality to accommodate situations in which only a subset of the parameters is of interest (e.g. covariate effects), and the DDS-optimality to find a compromise between the D- and DS-optimality [2]. Then, to account for model uncertainty in design optimization, we assumed a set of predefined candidate models with their respective weights and we computed robust designs across these models using compound CD-, CDS– and CDDS-optimality [3,4].
These methods were applied to design a study with two treatment groups, using a logistic model for repeated binary responses which correspond, for example, to a decrease of 11.1 points of the UDysRS Part III Impairment scale in Parkinson disease [5]. Four candidate models describing the evolution of the logit-probability of the response over time, from 0 to 12 months, were defined: M1 linear, M2 log-linear, M3 quadratic and M4 exponential models. Assuming the first and the last time fixed to 0 and 12 respectively, we performed combinatorial optimization of 2 among 11 times, between 1 to 11, to obtain different four-samplings protocols which were optimal for each model separately or optimal over the four models. Using the expected FIM, we also predicted the average power to detect a significant treatment effect over the four models, with different optimized protocols, vs. a non-optimized equi-spaced protocol ξES = (0,4,8,12).
CTS were then used to evaluate the performances of the CDDS –optimal design (ξCDDS) vs. the DDS-optimal design for a given model Mk (ξDDSk) vs. the equi-spaced design (ξES) in terms of bias and imprecision of estimates. For that we simulated 500 datasets under each model and analyzed them using SAEM algorithm in MONOLIX 2016R1 [6]. The relative standard errors and power of test observed from CTS were also compared to those predicted using the expected FIM.
Results:
The robust optimal design was different than the one optimized for each model, e.g ξCDDS = (0,4,11,12) across four models vs. ξDDS1 = (0,2,11,12) for M1. Misspecification of models led to designs with D-efficiencies as low as 64.6%. The compound criteria provide robust CD-, CDS– and CDDS-optimal designs which are efficient across the four candidate models, with D-efficiencies always above 80%. With the designs ξES, ξDDS1, and ξCDDS, we predicted respectively 358, 320 and 274 subjects needed to achieve an average power of 90% to detect the treatment effect over the four models. The simulation study confirmed that, for the same number of subjects, the robust design ξCDDS is more informative and performed better than ξDDS1 and ξES. This design gave acceptable estimation errors and good power, closed to those predicted using the expected FIM.
Conclusions:
The proposed design strategy based on MC/HMC and compound optimality theory, is a relevant approach which can be used to efficiently design longitudinal studies. This approach accounts for model uncertainty and ensures a balance between the overall precision of estimation and the power of the Wald test to detect a covariate effect.
References:
[1] Riviere M-K, Ueckert S, Mentré F. An MCMC method for the evaluation of the Fisher information matrix for non-linear mixed effect models. Biostat Oxf Engl. 2016;17:737–50.
[2] Atkinson AC, Bogacka B. Compound D- and Ds-Optimum Designs for Determining the Order of a Chemical Reaction. Technometrics. 1997;39:347–56.
[3] Atkinson AC. DT-optimum designs for model discrimination and parameter estimation. J Stat Plan Inference. 2008;138:56–64.
[4] Nguyen TT, Bénech H, Delaforge M, Lenuzza N. Design optimisation for pharmacokinetic modeling of a cocktail of phenotyping drugs. Pharm Stat. 2016;15:165–77.
[5] Mestre TA, Beaulieu-Boire I, Aquino CC, Phielipp N, Poon YY, Lui JP, et al. What is a clinically important change in the Unified Dyskinesia Rating Scale in Parkinson’s disease? Parkinsonism Relat Disord. 2015;21:1349–54.
[6] Kuhn E, Lavielle M. Maximum Likelihood Estimation in Nonlinear Mixed Effects Models. Comput Stat Data Anal. 2005;49:1020–1038.
Reference: PAGE 27 (2018) Abstr 8481 [www.page-meeting.org/?abstract=8481]
Poster: Methodology - Study Design