Bayesian design and conduct of phase II single-arm clinical trials with binary outcomes: a tutorial

The aim of phase II single-arm clinical trials of a new drug is to determine whether it has sufficient promising activity to warrant its further development. For the last several years Bayesian statistical methods have been proposed and used. Bayesian approaches are ideal for earlier phase trials as they take into account information that accrues during a trial. Predictive probabilities are then updated and so become more accurate as the trial progresses. Suitable priors can act as pseudo samples, which make small sample clinical trials more informative. Thus patients have better chances to receive better treatments. The goal of this paper is to provide a tutorial for statisticians who use Bayesian methods for the first time or investigators who have some statistical background. In addition, real data from three clinical trials are presented as examples to illustrate how to conduct a Bayesian approach for phase II single-arm clinical trials with binary outcomes.

Implementation of a Bayesian design in a dose-escalation study of an experimental agent in healthy volunteers

Bayesian decision procedures have recently been developed for dose escalation in phase I clinical trials concerning pharmacokinetic responses observed in healthy volunteers. This article describes how that general methodology was extended and evaluated for implementation in a specific phase I trial of a novel compound. At the time of writing, the study is ongoing, and it will be some time before the sponsor will wish to put the results into the public domain. This article is an account of how the study was designed in a way that should prove to be safe, accurate, and efficient whatever the true nature of the compound. The study involves the observation of two pharmacokinetic endpoints relating to the plasma concentration of the compound itself and of a metabolite as well as a safety endpoint relating to the occurrence of adverse events. Construction of the design and its evaluation via simulation are presented.

A Bayesian design criterion for locating the optimum point on a response surface

Most factorial experiments in industrial research form one stage in a sequence of experiments and so considerable prior knowledge is often available from earlier stages. A Bayesian A-optimality criterion is proposed for choosing designs, when each stage in experimentation consists of a small number of runs and the objective is to optimise a response. Simple formulae for the weights are developed, some examples of the use of the design criterion are given and general recommendations are made. (C) 2003 Elsevier B.V. All rights reserved.

Bayesian Geostatistical Design

This paper describes the use of model-based geostatistics for choosing the optimal set of sampling locations, collectively called the design, for a geostatistical analysis. Two types of design situations are considered. These are retrospective design, which concerns the addition of sampling locations to, or deletion of locations from, an existing design, and prospective design, which consists of choosing optimal positions for a new set of sampling locations. We propose a Bayesian design criterion which focuses on the goal of efficient spatial prediction whilst allowing for the fact that model parameter values are unknown. The results show that in this situation a wide range of inter-point distances should be included in the design, and the widely used regular design is therefore not the optimal choice.

Delineamentos experimentais eficientes para estudos de cinética química

In this paper we show how to obtain efficient designs of experiments for fitting Michaelis-Menten and Hill equations useful in chemical studies. The search of exact D-optimal designs by using local and pseudo-Bayesian approaches is considered. Optimal designs were compared to those commonly used in practice using an efficiency measure and theoretical standard errors of the kinetic parameter estimates. In conclusion, the D-optimal designs based on the Hill equation proved efficient for estimating the parameters of both models. Furthermore, these are promising with respect to practical issues, allowing efficient estimation as well as goodness-of-fit tests and comparisons between some kinetic models.

Delineamentos D-ótimos para os modelos de Michaelis-Menten e de Hill

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Delineamentos experimentais eficientes para estudos de cinética química

In this paper we show how to obtain efficient designs of experiments for fitting Michaelis-Menten and Hill equations useful in chemical studies. The search of exact D-optimal designs by using local and pseudo-Bayesian approaches is considered. Optimal designs were compared to those commonly used in practice using an efficiency measure and theoretical standard errors of the kinetic parameter estimates. In conclusion, the D-optimal designs based on the Hill equation proved efficient for estimating the parameters of both models. Furthermore, these are promising with respect to practical issues, allowing efficient estimation as well as goodness-of-fit tests and comparisons between some kinetic models.

Evaluation of an esophageal Doppler probe for the identification of experimental pseudo-electromechanical dissociation: a preliminary study

STUDY OBJECTIVE To determine the effectiveness of an esophageal doppler device to non-invasively detect experimental pseudo-electromechanical dissociation (pseudo-EMD). DESIGN Prospective, controlled, laboratory investigation using an asphyxial canine cardiac arrest model and a newly-developed esophageal flat-flow probe doppler unit. INTERVENTIONS Mongrel dogs (20) were instrumented for hemodynamic monitoring. The esophageal doppler probe was placed in the distal esophagus of each animal. Electromechanical dissociation (EMD) was induced by clamping the endotracheal tube. MEASUREMENTS AND MAIN RESULTS A period of pseudo-EMD was defined as the time where cardiac contractility was present, measured by a micromanometer tipped thoracic aortic catheter, without concurrent femoral pulses by palpation. The pseudo-EMD period could be produced consistently in all 20 animals. The characteristic doppler flow sounds were easily heard using the esophageal device in all animals. The time from endotracheal tube clamping until loss of femoral pulses was 622 +/- 96 s; until loss of radial artery doppler signals was 616 +/- 92 s; until loss of esophageal doppler signals was 728 +/- 88 s; and until loss of aortic fluctuations by thoracic aortic catheter was 728 +/- 82 s. The times to loss of esophageal doppler sounds and loss of aortic fluctuations were not significantly different. However, they were significantly longer than the time to loss of femoral pulses (P < 0.02). CONCLUSIONS The canine asphyxial EMD model can be used for short experimental studies of pseudo-EMD. Pseudo-EMD can be consistently and non-invasively detected with this esophageal doppler device. The device is as reliable as a micromanometer tipped aortic arch catheter in detecting pseudo-EMD. The doppler device could potentially be useful in improving recognition of near cardiac arrest in pre-hospital and emergency department settings. Further research on the utility of this device in other models of low-flow states should be performed.

Performance evaluation in Bayesian adaptive randomization

Bayesian adaptive randomization (BAR) is an attractive approach to allocate more patients to the putatively superior arm based on the interim data while maintains good statistical properties attributed to randomization. Under this approach, patients are adaptively assigned to a treatment group based on the probability that the treatment is better. The basic randomization scheme can be modified by introducing a tuning parameter, replacing the posterior estimated response probability, setting a boundary to randomization probabilities. Under randomization settings comprised of the above modifications, operating characteristics, including type I error, power, sample size, imbalance of sample size, interim success rate, and overall success rate, were evaluated through simulation. All randomization settings have low and comparable type I errors. Increasing tuning parameter decreases power, but increases imbalance of sample size and interim success rate. Compared with settings using the posterior probability, settings using the estimated response rates have higher power and overall success rate, but less imbalance of sample size and lower interim success rate. Bounded settings have higher power but less imbalance of sample size than unbounded settings. All settings have better performance in the Bayesian design than in the frequentist design. This simulation study provided practical guidance on the choice of how to implement the adaptive design. ^

Risk homeostasis theory in simulated environments

This thesis has two aims. First, it sets out to develop an alternative methodology for the investigation of risk homeostasis theory (RHT). It is argued that the current methodologies of the pseudo-experimental design and post hoc analysis of road-traffic accident data both have their limitations, and that the newer 'game' type simulation exercises are also, but for different reasons, incapable of testing RHT predictions. The alternative methodology described here is based on the simulation of physical risk with intrinsic reward rather than a 'points pay-off'. The second aim of the thesis is to examine a number of predictions made by RHT through the use of this alternative methodology. Since the pseudo-experimental design and post hoc analysis of road-traffic data are both ill-suited to the investigation of that part of RHT which deals with the role of utility in determining risk-taking behaviour in response to a change in environmental risk, and since the concept of utility is critical to RHT, the methodology reported here is applied to the specific investigation of utility. Attention too is given to the question of which behavioural pathways carry the homeostasis effect, and whether those pathways are 'local' to the nature of the change in environmental risk. It is suggested that investigating RHT through this new methodology holds a number of advantages and should be developed further in an attempt to answer the RHT question. It is suggested too that the methodology allows RHT to be seen in a psychological context, rather than the statistical context that has so far characterised its investigation. The experimental findings reported here are in support of hypotheses derived from RHT and would therefore seem to argue for the importance of the individual and collective target level of risk, as opposed to the level of environmental risk, as the major determinant of accident loss.

Bayesian methods for estimation, optimization and experimental design

Mathematical models often contain parameters that need to be calibrated from measured data. The emergence of efficient Markov Chain Monte Carlo (MCMC) methods has made the Bayesian approach a standard tool in quantifying the uncertainty in the parameters. With MCMC, the parameter estimation problem can be solved in a fully statistical manner, and the whole distribution of the parameters can be explored, instead of obtaining point estimates and using, e.g., Gaussian approximations. In this thesis, MCMC methods are applied to parameter estimation problems in chemical reaction engineering, population ecology, and climate modeling. Motivated by the climate model experiments, the methods are developed further to make them more suitable for problems where the model is computationally intensive. After the parameters are estimated, one can start to use the model for various tasks. Two such tasks are studied in this thesis: optimal design of experiments, where the task is to design the next measurements so that the parameter uncertainty is minimized, and model-based optimization, where a model-based quantity, such as the product yield in a chemical reaction model, is optimized. In this thesis, novel ways to perform these tasks are developed, based on the output of MCMC parameter estimation. A separate topic is dynamical state estimation, where the task is to estimate the dynamically changing model state, instead of static parameters. For example, in numerical weather prediction, an estimate of the state of the atmosphere must constantly be updated based on the recently obtained measurements. In this thesis, a novel hybrid state estimation method is developed, which combines elements from deterministic and random sampling methods.

A novel Bayesian approach to drug design with simple and complex enzymes: Use with lens aldehyde dehydrogenase and the glyoxalase pathway

Purpose: Acquiring details of kinetic parameters of enzymes is crucial to biochemical understanding, drug development, and clinical diagnosis in ocular diseases. The correct design of an experiment is critical to collecting data suitable for analysis, modelling and deriving the correct information. As classical design methods are not targeted to the more complex kinetics being frequently studied, attention is needed to estimate parameters of such models with low variance. Methods: We have developed Bayesian utility functions to minimise kinetic parameter variance involving differentiation of model expressions and matrix inversion. These have been applied to the simple kinetics of the enzymes in the glyoxalase pathway (of importance in posttranslational modification of proteins in cataract), and the complex kinetics of lens aldehyde dehydrogenase (also of relevance to cataract). Results: Our successful application of Bayesian statistics has allowed us to identify a set of rules for designing optimum kinetic experiments iteratively. Most importantly, the distribution of points in the range is critical; it is not simply a matter of even or multiple increases. At least 60 % must be below the KM (or plural if more than one dissociation constant) and 40% above. This choice halves the variance found using a simple even spread across the range.With both the glyoxalase system and lens aldehyde dehydrogenase we have significantly improved the variance of kinetic parameter estimation while reducing the number and costs of experiments. Conclusions: We have developed an optimal and iterative method for selecting features of design such as substrate range, number of measurements and choice of intermediate points. Our novel approach minimises parameter error and costs, and maximises experimental efficiency. It is applicable to many areas of ocular drug design, including receptor-ligand binding and immunoglobulin binding, and should be an important tool in ocular drug discovery.

Efficient and accurate experimental design for enzyme kinetics: Bayesian studies reveal a systematic approach

In areas such as drug development, clinical diagnosis and biotechnology research, acquiring details about the kinetic parameters of enzymes is crucial. The correct design of an experiment is critical to collecting data suitable for analysis, modelling and deriving the correct information. As classical design methods are not targeted to the more complex kinetics being frequently studied, attention is needed to estimate parameters of such models with low variance. We demonstrate that a Bayesian approach (the use of prior knowledge) can produce major gains quantifiable in terms of information, productivity and accuracy of each experiment. Developing the use of Bayesian Utility functions, we have used a systematic method to identify the optimum experimental designs for a number of kinetic model data sets. This has enabled the identification of trends between kinetic model types, sets of design rules and the key conclusion that such designs should be based on some prior knowledge of K-M and/or the kinetic model. We suggest an optimal and iterative method for selecting features of the design such as the substrate range, number of measurements and choice of intermediate points. The final design collects data suitable for accurate modelling and analysis and minimises the error in the parameters estimated. (C) 2003 Elsevier Science B.V. All rights reserved.

Bayesian L-optimal exact design of experiments for biological kinetic models

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Bayesian dual threshold design with Dirichlet distribution: An alternative way to frequentist multi-stage phase II designs in oncology

Many phase II clinical studies in oncology use two-stage frequentist design such as Simon's optimal design. However, they have a common logistical problem regarding the patient accrual at the interim. Strictly speaking, patient accrual at the end of the first stage may have to be suspended until all patients have events, success or failure. For example, when the study endpoint is six-month progression free survival, patient accrual has to be stopped until all outcomes from stage I is observed. However, study investigators may have concern when accrual is suspended after the first stage due to the loss of accrual momentum during this hiatus. We propose a two-stage phase II design that resolves the patient accrual problem due to an interim analysis, and it can be used as an alternative way to frequentist two-stage phase II studies in oncology. ^