An Overview of Adaptive Designs and Some of Their Challenges, Benefits, and Innovative Applications

Adaptive designs are increasingly developed and used to improve all phases of clinical trials and in biomedical studies in various ways to address different statistical issues. We first present an overview of adaptive designs and note their numerous advantages over traditional clinical trials. In particular, we provide a concrete demonstration that shows how recent adaptive design strategies can further improve an adaptive trial implemented 13 years ago. Despite their usefulness, adaptive designs are still not widely implemented in clinical trials. We offer a few possible reasons and propose some ways to use them more broadly in practice, which include greater availability of software tools and interactive websites to generate optimal adaptive trials freely and effectively, including the use of metaheuristics to facilitate the search for an efficient trial design. To this end, we present several web-based tools for finding various adaptive and nonadaptive optimal designs and discuss nature-inspired metaheuristics. Metaheuristics are assumptions-free general purpose optimization algorithms widely used in computer science and engineering to tackle all kinds of challenging optimization problems, and their use in designing clinical trials is just emerging. We describe a few recent such applications and some of their capabilities for designing various complex trials. Particle swarm optimization is an exemplary nature-inspired algorithm, and similar to others, it has a simple definition but many moving parts, making it hard to study its properties analytically. We investigated one of its hitherto unstudied issues on how to bring back out-of-range candidates during the search for the optimum of the search domain and show that different strategies can impact the success and time of the search. We conclude with a few caveats on the use of metaheuristics for a successful search.

Model-robust designs for nonlinear quantile regression

We construct robust designs for nonlinear quantile regression, in the presence of both a possibly misspecified nonlinear quantile function and heteroscedasticity of an unknown form. The asymptotic mean-squared error of the quantile estimate is evaluated and maximized over a neighbourhood of the fitted quantile regression model. This maximum depends on the scale function and on the design. We entertain two methods to find designs that minimize the maximum loss. The first is local - we minimize for given values of the parameters and the scale function, using a sequential approach, whereby each new design point minimizes the subsequent loss, given the current design. The second is adaptive - at each stage, the maximized loss is evaluated at quantile estimates of the parameters, and a kernel estimate of scale, and then the next design point is obtained as in the sequential method. In the context of a Michaelis-Menten response model for an estrogen/hormone study, and a variety of scale functions, we demonstrate that the adaptive approach performs as well, in large study sizes, as if the parameter values and scale function were known beforehand and the sequential method applied. When the sequential method uses an incorrectly specified scale function, the adaptive method yields an, often substantial, improvement. The performance of the adaptive designs for smaller study sizes is assessed and seen to still be very favourable, especially so since the prior information required to design sequentially is rarely available.

Challenging the dose-response-time data approach: Analysis of a complex system

This study presents an extensive dose-response-time (DRT) meta-analysis of the nicotinic acid-induced inhibition of free fatty acids and insulin release. The purpose was to quantify the implications of lacking exposure data when analysing complex pharmacodynamic systems. The DRT model successfully characterised various response behaviours-including time-delays, rebound, feedback mechanisms, and adaptation-on both the individual and the population level. Comparing the fitted DRT model to an exposure-driven reference analysis showed that bias and uncertainty were introduced in the parameter estimates. However, most estimates were within one standard error from the reference. In both approaches, a few parameters suffered from practical identifiability issues, likely due to large differences in half-lives of the different rate processes. Moreover, the optimal dosing strategies predicted by the DRT model differed slightly from those of the exposure-driven analysis, having a lower optimal steady-state reduction of free fatty acids exposure.

Impact of mathematical pharmacology on practice and theory: four case studies

Drug-discovery has become a complex discipline in which the amount of knowledge about human biology, physiology, and biochemistry have increased. In order to harness this complex body of knowledge mathematics can play a critical role, and has actually already been doing so. We demonstrate through four case studies, taken from previously published data and analyses, what we can gain from mathematical/analytical techniques when nonlinear concentration-time courses have to be transformed into their equilibrium concentration-response (target or complex) relationships and new structures of drug potency have to be deciphered; when pattern recognition needs to be carried out for an unconventional response-time dataset; when what-if? predictions beyond the observational concentration-time range need to be made; or when the behaviour of a semi-mechanistic model needs to be elucidated or challenged. These four examples are typical situations when standard approaches known to the general community of pharmacokineticists prove to be inadequate.