Bayesian population modeling of phase I dose escalation studies: Gaussian process versus parametric approaches

Bayesian optimization for estimating the maximum tolerated dose in Phase I clinical trials

We introduce a Bayesian optimization method for estimating the maximum tolerated dose in this article. A number of parametric model-based methods have been proposed to estimate the maximum tolerated dose; however, parametric model-based methods need an assumption that dose-toxicity relationships follow specific theoretical models. This assumption potentially leads to suboptimal dose selections if the dose-toxicity curve is misspecified. Our proposed method is based on a Bayesian optimization framework for finding a global optimizer of unknown functions that are expensive to evaluate while using very few function evaluations. It models dose-toxicity relationships with a nonparametric model; therefore, a more flexible estimation can be realized compared with existing parametric model-based methods. Also, most existing methods rely on point estimates of dose-toxicity curves in their dose selections. In contrast, our proposed method exploits a probabilistic model for an unknown function to determine the next dose candidate without ignoring the uncertainty of posterior while imposing some dose-escalation limitations. We investigate the operating characteristics of our proposed method by comparing them with those of the Bayesian-based continual reassessment method and two different nonparametric methods. Simulation results suggest that our proposed method works successfully in terms of selections of the maximum tolerated dose correctly and safe dose allocations.

Population modelling of patient responses in antidepressant studies: a stochastic approach

This paper addresses the problem of modelling longitudinal data describing patients' responses in clinical trials. In particular, a systematic approach relying on a system theoretic paradigm is proposed to deal with contexts where limited physiopathological knowledge is available on disease, drug response, and patients' characteristics. The model relies on the notion of patient's health state which summarizes the patient's condition. In order to cope with the limited number of clinical data usually available, the paper considers a very parsimonious realization where the two state variables are the clinical endpoint and its derivative. Within a population framework, the individual response is modelled as the sum of an individual shift and the average response of subjects belonging to the same study, both described as Markovian processes and identified by empirical Bayes techniques. The proposed approach is validated with experimental data from a Phase II, flexible-dose, depression trial. The dose changes due to the flexible-dose scheme are handled as perturbations on the state. The connection between inter-individual variability and model stability is evaluated showing that the introduction of stable poles helps to describe populations whose range of individual responses does not diverge with time. In this way, good individual fittings and visual predictive checks were obtained for the clinical data. The proposed analysis provides a systematic approach to semi-mechanistic modelling when a precise knowledge of the physiological mechanisms of the disease is incomplete or missing.

Continuous-time Markov modelling of flexible-dose depression trials

The aim of this paper is to provide a systematic methodology for modelling longitudinal data to be used in contexts of limited or even absent knowledge of the physiological mechanism underlying the disease time course. Adopting a system-theoretic paradigm, a population response model is developed where the clinical endpoint is described as a function of the patient's health state. In particular, a continuous-time stochastic approach is proposed where the clinical score and its time-derivative summarize the patient's health state affected by a random term accounting for exogenous unpredictable factors. The proposed approach is validated on experimental data from the placebo and drug arms of a Phase II depression trial. Since some subjects in the trial may undergo changes in their treatment dose due to the flexible dosing scheme, dose escalations are modelled as instantaneous perturbations on the state. In its simplest form--an integrated Wiener process--was able to correctly capture the individual responses in both treatment arms. However, a better description of inter-individual variability was obtained by means of a stable Markovian model. Parameter estimation has been carried out according to the empirical Bayes method.

A PCA approach to population analysis: with application to a Phase II depression trial

For psychiatric diseases, established mechanistic models are lacking and alternative empirical mathematical structures are usually explored by a trial-and-error procedure. To address this problem, one of the most promising approaches is an automated model-free technique that extracts the model structure directly from the statistical properties of the data. In this paper, a linear-in-parameter modelling approach is developed based on principal component analysis (PCA). The model complexity, i.e. the number of components entering the PCA-based model, is selected by either cross-validation or Mallows' Cp criterion. This new approach has been validated on both simulated and clinical data taken from a Phase II depression trial. Simulated datasets are generated through three parametric models: Weibull, Inverse Bateman and Weibull-and-Linear. In particular, concerning simulated datasets, it is found that the PCA approach compares very favourably with some of the popular parametric models used for analyzing data collected during psychiatric trials. Furthermore, the proposed method performs well on the experimental data. This approach can be useful whenever a mechanistic modelling procedure cannot be pursued. Moreover, it could support subsequent semi-mechanistic model building.