In March 2006 a first-in-man trial took place using healthy volunteers involving the use of monoclonal antibodies. Within hours the subjects had suffered such adverse effects that they were admitted to intensive care at Northwick Park Hospital. In April 2006 the Secretary of State for Health announced the appointment of Professor (now Sir) Gordon Duff, who chairs the UK's Commission on Human Medicines, to chair a scientific expert group on phase 1 clinical trials. The group reported on December 7th, 2006 (Expert Scientific Group on Clinical Trials, 2006a). Clinical trials have a well-established regulatory basis both in the UK and worldwide. Trials have to be approved by the regulatory authority and are subject to a detailed protocol concerning, among other things, the study design and statistical analyses that will form the basis of the evaluation. In fact, a cornerstone of the regulatory framework is the statistical theory and methods that underpin clinical trials. As a result, the Royal Statistical Society established an expert group of its own to look in detail at the statistical issues that might be relevant to first-in-man studies. The group mainly comprised senior Fellows of the Society who had expert knowledge of the theory and application of statistics in clinical trials. However, the group also included an expert immunologist and clinicians to ensure that the interface between statistics and clinical disciplines was not overlooked. In addition, expert representation was sought from Statisticians in the Pharmaceutical Industry (PSI), an organization with which the Royal Statistical Society has very close links. The output from the Society's expert group is contained in this report. It makes a number of recommendations directed towards the statistical aspects of clinical trials. As such it complements the report by Professor Duff's group and will, I trust, contribute to a safer framework for first-in-man trials in the future. Tim Holt ("President, Royal Statistical Society") Copyright 2007 Royal Statistical Society.
The optimum design of experiments for nonlinear models requires parameter sensitivities, that is the derivatives of the response with respect to the parameters. If the differential equations forming the kinetic model do not have an analytical solution, numerical derivatives have to be used. We describe the "direct" method for calculating the sensitivities and apply it to the design of experiments for estimating the order of chemical reactions.
We find closed-form expressions for the D-optimum designs for three- and four-parameter nonlinear models arising in kinetic models for enzyme inhibition. We calculate the efficiency of designs over a range of parameter values and make recommendations for design when the parameter values are not well known. In a three-parameter experimental example, a standard design has an efficiency of 18.2% of the D-optimum design. Experimental results from a standard design with 120 trials and a D-optimum design with 21 trials give parameter estimates that are in close agreement. The estimated standard errors of these parameter estimates confirm our theoretical results on efficiency and thus on the serious savings that can be made by the use of D-optimum designs.
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