Dose-finding Experiments with Mixed Continuous and Discrete Responses
Valerii Fedorov, Yuehui Wu and Rongmei Zhang
Published as GSK DDS Technical Report 2010-02
Abstract: In dose-finding clinical studies, it is common that multiple endpoints are of interest. For instance, in phase I/II studies efficacy and toxicity are often the primary endpoints which are observed simultaneously and need to be evaluated together. Motivated by this, we confine ourselves to bivariate responses and focus on the most analytically difficult case: a mixture of continuous and categorical responses. We adopt the bivariate probit dose-response model and quantify our goal by a utility function. Locally optimal designs, two-stage optimal designs, and fully adaptive designs are studied under different ethical and cost constraints in the experiments. We assess the performance of two-stage designs and fully adaptive designs
via simulations. Our simulations suggest that the two-stage designs are as efficient as and may be more efficient than the fully adaptive designs if there is a moderate sample size in the initial stage. In addition, two-stage designs are easier to construct and implement, and thus can be a useful approach in practice.
Drug Supply Modeling Software: User Manual
Vladimir Anisimov, Valerii Fedorov, Richard Heiberger, Sourish Saha and Mark Kothapalli
Published as GSK DDS Technical Report 2010-01
Abstract: The design of multicentre clinical studies consists of several interconnected stages including patient recruitment prediction, choosing a randomization scheme and a statistical model for analyzing patient responses, and drug supply planning. The Research Statistics Unit (RSU) at GlaxoSmithKline (GSK) has developed a risk-based supply modeling tool using statistical principles. The tool predicts drug supply needed to cover patient’s demand in a single study with a given risk of running out of stock for a patient. In order to support Clinical Trials Supply and Global Supplies Operations teams at GSK, the RSU created a user-friendly RExcel interface embedding the risk-based supply modeling tool into the Excel environment. This manual discusses screenshots to guide the user through using the interface.
Comparisons of minimisation and Atkinson’s algorithm
Stephen Senn, Vladimir Anisimov and Valerii Fedorov
Published in Statistics in Medicine, 2010, V. 29, 7/8, pp. 721-730
Abstract: Some general points regarding efficiency in clinical trials are made. Reasons as to why fitting many covariates to adjust the estimate of the treatment effect may be less problematic than commonly supposed are given. Two methods of dynamic allocation of patients based on covariates, minimization and Atkinson’s approach, are compared and contrasted for the particular case where all covariates are binary. The results of Monte Carlo simulations are also presented. It is concluded that in the cases considered, Atkinson’s approach is slightly more efficient than minimization although the difference is unlikely to be very important in practice. Both are more efficient than simple randomization, although it is concluded that fitting covariates may make a more valuable and instructive contribution to inferences about treatment effects than only balancing them.
Statistics in Pharmaceutical Development and Manufacturing
John J. Peterson, Ronald D. Snee, Paul R. McAllister, Timothy L. Schofield, and Anthony Carella
Abstract: The pharmaceutical industry is undergoing rapid change and facing numerous challenges, including the demands of global competition, the need to speed up the drug development process, and the Food and Drug Administration’s (FDA’s) expectations for the incorporation of the principles of quality by design (QbD) and process analytical technology (PAT) in process and analytical development. Statistical thinking and methods play a significant role in addressing these issues. This article provides an overview of the use of statistical thinking and methods in the R&D and manufacturing functions of the pharmaceutical industry. The exposition includes the history of pharmaceutical quality and regulation, phases of pharmaceutical development and manufacturing and the basic quality and statistical tools employed in each, emerging statistical methods, the impact of statistical software and information technology, and the role of statisticians in pharmaceutical development and manufacturing. Four case studies are included to illustrate how these issues play out in actuality. A summary provides a succinct synopsis of those issues and concludes that the complex, technical nature of pharmaceutical development and manufacturing offers many opportunities for the effective use of statistical thinking and methods and that those who use these methods can become catalysts for both process development understanding and product quality improvement.
Using Experimental Design and Randomisation to Construct a Mixed Model
Simon Bate and Marion Chatfield
In many areas of scientific research scientists routinely use complex experimental designs when conducting their experiments. With the advent of the modern statistical package, and a lack of trained statisticians, the scientist often carries out the analysis of data generated from such experiments. This can lead to incorrect and misleading results, especially if the scientist fails to correctly identify the experimental design they are using and the influence the design has on the statistical analysis.
In this paper we describe a procedure that would allow non-statisticians to identify the structure of the experimental design without an in-depth knowledge of design theory. Once this has been achieved it should then be possible for them to produce an appropriate model for the statistical analysis. By placing experimental design at the centre of the statistical process we are able to simplify the statistical model selection. This procedure should also make the benefits of good experimental design more accessible to both statisticians and non-statisticians alike.
An Adaptive Optimal Design for the EMAX Model and its Application in Alzheimer’s Disease
Sergei Leonov and Sam Miller
Abstract: A project team working on a compound to treat Alzheimer’s disease is carrying out a first-time-in-human dose-escalation study in patients. The team wished to maximize the efficiency of the study by using doses targeted at maximizing information about the dose-response relationship within certain safety constraints. We have developed a GUI-based adaptive optimal design tool to recommend doses when the response follows an Emax model, with functionality for pre-trial simulation and in-stream analysis.
Consequences of Dichotomization
Valerii Fedorov, Frank Mannino and Rongmei Zhang
ABSTRACT Dichotomization is the transformation of a continuous outcome (response) to a binary outcome. This approach, while somewhat common, is not harmless from the viewpoint of statistical estimation and hypothesis testing. We show that this leads to a loss of information, which can be large. For normally distributed data, this loss in terms of Fisher’s information is at least 1 − 2/pi (or 36%). In other words, 100 continuous observations are statistically equivalent to 158 dichotomized observations. The amount of information lost depends greatly on the prior choice of cut points, with the optimal cut point depending upon the unknown parameters. The loss of information leads to a loss of power or conversely a sample size increase to maintain power. Only in certain cases, for instance in estimating a value of the cumulative distribution function and when the analysis model is very different from the true model, can the use of dichotomized outcomes be considered a reasonable approach.
Testing for Excess Over Highest Single Agent with an Application to High-throughput Screening of Pairs of Compounds
John J. Peterson
Abstract: Combination drug therapy offers much promise for discovering pharmaceutical treatments that are efficacious and safe. A key efficacy criterion for a combination of two compounds is that the combination is superior to both of its component compounds used alone. This article proposes a simultaneous testing procedure, based upon step-down trend tests, that identifies dose combinations for pairs of compounds that produce efficacy results with excess over highest single agent (i.e. the combination is superior to both of the component compounds). This testing procedure is applied to data from experiments for a pilot high-throughput screening study for pairs of compounds evaluated at nine dose levels using 9×9 factorial experiments. This procedure is easily automated and can be computed using the SAS® MULTTEST procedure.
O’Brien’s OLS and GLS Statistics in Clinical Trials: Multivariate Approach
Nigel Dallow, Sergei Leonov and James Roger
Abstract: Multivariate techniques of O’Brien’s OLS and GLS statistics are discussed in the context of their application in clinical trials. We introduce the concept of an operational effect size and illustrate its use to evaluate power. An extension describing how to handle covariates and missing data is developed in the context of Mixed models. This extension allowing adjustment for covariates is easily programmed in any statistical package including SAS. Monte Carlo simulation is used for a number of different sample sizes to compare the actual size and power of the tests based on O’Brien’s OLS and GLS statistics.
Estimation of Population PK Measures: Selection of Sampling Grids
Valerii Fedorov and Sergei Leonov
Abstract: In clinical pharmacokinetic (PK) studies multiple blood samples are taken for each enrolled patient, and various population PK measures, such as area under the curve (AUC), maximal concentration (Cmax) and time to maximal concentration (Tmax) are estimated. In this paper we compare a model-based approach, where parameters of a compartmental model are estimated and the explicit formulae for PK measures are used, and an empirical, or model-independent, approach, where numerical integration algorithms are used for AUC and sample estimates for Cmax and Tmax. Since regulatory agencies usually require the model-independent estimation of PK measures, we focus on the empirical approach while using the model-based approach as a benchmark. We show how to “split” a single sampling grid into two or more subsets, which substantially reduces the number of samples taken for each patient, but often has little effect on the precision of estimation of PK measures in terms of mean squared error (MSE). For a number of special cases we derive explicit formulae for the MSE of the empirical estimator of AUC. When costs of patient’s enrolment and costs of analyzing samples are introduced, these formulae allow the optimal selection of the number of patients and samples per patient.
