Dose escalation studies: a comparison among Bayesian models
A. Russu (1), G. De Nicolao (1), I. Poggesi (2), R. Gomeni (2)
(1) Department of Computer Engineering and Systems Science, University of Pavia, Pavia, Italy; (2) GlaxoSmithKline, Clinical Pharmacology/Modelling & Simulation, Verona, Italy
Objectives: To apply alternative Bayesian models for the population analysis of the dose-exposure relationship in dose escalation Phase I studies. In these studies, subjects receive increasing dose levels and, at each dose escalation, a decision is made on the next dose level to be administered, based on safety/tolerability constraints. In recent years there has been a growing interest in Bayesian methods applied to such experiments [1,2,3]. In the present work, the performance of four alternative Bayesian models was evaluated on real and simulated datasets and a model comparison procedure was developed for the identification of the most appropriate model.
Methods: The dose-exposure relationship was explored using a log-linear model (i.e. a linear model in log-log scale), a power model, an Emax model, and a nonparametric model based on population smoothing splines [4]. In all cases, a Bayesian population approach was adopted. The parametric models were estimated using WinBUGS 1.4.3. Sum of squared residuals, predictive root mean square error, AIC and BIC were used as model comparison criteria.
Results: Ten phase I dose escalation studies and 60 simulated datasets (generated with the three parametric models) were analyzed. In the experimental datasets, the power and log-linear models provided comparable results in terms of point estimates and credibility intervals, whereas the Emax model proved inadequate when data showed upward curvature. The population spline approach provided good results for both experimental and simulated datasets. In the former case, the goodness of fit was comparable to parametric models. In the simulated benchmark, population splines performed comparably to the true models used to generate the data. The proposed comparison approach correctly identified the true parametric model in most cases.
Conclusions: A thorough model comparison procedure was developed, based on model complexity criteria and crossvalidatory techniques. Applying several criteria represents a useful cross-check when one is faced with the problem of finding the most adequate model. It has been shown that the parallel estimation of four models (three parametric, one nonparametric), complemented with model comparison criteria, can robustly handle a variety of dose-exposure relationships overcoming possible misspecification problems. Moreover, population splines may represent an appealing first-try, especially in early escalation stages, when there is not enough information to support a specific parametric model.
References:
[1] J. Whitehead, Y. Zhou, S. Patterson, D. Webber, S. Francis. Easy-to-implement Bayesian methods for dose escalation studies in healthy volunteers. Biostatistics 2, 47-61.
[2] D.A. Berry, P. Müller, A.P. Grieve, M. Smith, T. Parke, R. Blazek, N. Mitchard, M. Krams. Adaptive Bayesian designs for dose-ranging drug trials. in C. Gatsonis, R.E. Kass, B. Carlin, A. Carriquiry, A. Gelman, I. Verdinelli, M. West (eds.), Case Studies in Bayesian Statistics V. New York: Springer-Verlag; 2001: 99-181.
[3] A. Russu, G. De Nicolao, I. Poggesi, M. Neve, L. Iavarone, R. Gomeni. Dose escalation studies: a comparison between NONMEM and a novel Bayesian tool. Population Approach Group in Europe (PAGE) 2008 Meeting, Marseille, France, June 2008.
[4] G. Pillonetto, G. De Nicolao, M. Chierici, C. Cobelli. Fast algorithms for nonparametric population modeling of large data sets, Automatica, 2009.
