A sequential Monte Carlo algorithm to incorporate model uncertainty in Bayesian sequential design

Here we present a sequential Monte Carlo (SMC) algorithm that can be used for any one-at-a-time Bayesian sequential design problem in the presence of model uncertainty where discrete data are encountered. Our focus is on adaptive design for model discrimination but the methodology is applicable if one has a different design objective such as parameter estimation or prediction. An SMC algorithm is run in parallel for each model and the algorithm relies on a convenient estimator of the evidence of each model which is essentially a function of importance sampling weights. Other methods for this task such as quadrature, often used in design, suffer from the curse of dimensionality. Approximating posterior model probabilities in this way allows us to use model discrimination utility functions derived from information theory that were previously difficult to compute except for conjugate models. A major benefit of the algorithm is that it requires very little problem specific tuning. We demonstrate the methodology on three applications, including discriminating between models for decline in motor neuron numbers in patients suffering from neurological diseases such as Motor Neuron disease.

A sequential Monte Carlo approach to the sequential design for discriminating between rival continuous data models

Here we present a sequential Monte Carlo approach to Bayesian sequential design for the incorporation of model uncertainty. The methodology is demonstrated through the development and implementation of two model discrimination utilities; mutual information and total separation, but it can also be applied more generally if one has different experimental aims. A sequential Monte Carlo algorithm is run for each rival model (in parallel), and provides a convenient estimate of the marginal likelihood (of each model) given the data, which can be used for model comparison and in the evaluation of utility functions. A major benefit of this approach is that it requires very little problem specific tuning and is also computationally efficient when compared to full Markov chain Monte Carlo approaches. This research is motivated by applications in drug development and chemical engineering.

A pseudo-marginal sequential Monte Carlo algorithm for random effects models in Bayesian sequential design

A computationally efficient sequential Monte Carlo algorithm is proposed for the sequential design of experiments for the collection of block data described by mixed effects models. The difficulty in applying a sequential Monte Carlo algorithm in such settings is the need to evaluate the observed data likelihood, which is typically intractable for all but linear Gaussian models. To overcome this difficulty, we propose to unbiasedly estimate the likelihood, and perform inference and make decisions based on an exact-approximate algorithm. Two estimates are proposed: using Quasi Monte Carlo methods and using the Laplace approximation with importance sampling. Both of these approaches can be computationally expensive, so we propose exploiting parallel computational architectures to ensure designs can be derived in a timely manner. We also extend our approach to allow for model uncertainty. This research is motivated by important pharmacological studies related to the treatment of critically ill patients.

Sequential design of decentralized control systems

Our main result is a new sequential method for the design of decentralized control systems. Controller synthesis is conducted on a loop-by-loop basis, and at each step the designer obtains an explicit characterization of the class C of all compensators for the loop being closed that results in closed-loop system poles being in a specified closed region D of the s-plane, instead of merely stabilizing the closed-loop system. Since one of the primary goals of control system design is to satisfy basic performance requirements that are often directly related to closed-loop pole location (bandwidth, percentage overshoot, rise time, settling time), this approach immediately allows the designer to focus on other concerns such as robustness and sensitivity. By considering only compensators from class C and seeking the optimum member of that set with respect to sensitivity or robustness, the designer has a clearly-defined limited optimization problem to solve without concern for loss of performance. A solution to the decentralized tracking problem is also provided. This design approach has the attractive features of expandability, the use of only 'local models' for controller synthesis, and fault tolerance with respect to certain types of failure.

An adaptive group sequential design for phase II/III clinical trials that select a single treatment from several

There is increasing interest in combining Phases II and III of clinical development into a single trial in which one of a small number of competing experimental treatments is ultimately selected and where a valid comparison is made between this treatment and the control treatment. Such a trial usually proceeds in stages, with the least promising experimental treatments dropped as soon as possible. In this paper we present a highly flexible design that uses adaptive group sequential methodology to monitor an order statistic. By using this approach, it is possible to design a trial which can have any number of stages, begins with any number of experimental treatments, and permits any number of these to continue at any stage. The test statistic used is based upon efficient scores, so the method can be easily applied to binary, ordinal, failure time, or normally distributed outcomes. The method is illustrated with an example, and simulations are conducted to investigate its type I error rate and power under a range of scenarios.

How a sequential design would have affected the GAIN international study of Gavestinel in stroke

While planning the GAIN International Study of gavestinel in acute stroke, a sequential triangular test was proposed but not implemented. Before the trial commenced it was agreed to evaluate the sequential design retrospectively to evaluate the differences in the resulting analyses, trial durations and sample sizes in order to assess the potential of sequential procedures for future stroke trials. This paper presents four sequential reconstructions of the GAIN study made under various scenarios. For the data as observed, the sequential design would have reduced the trial sample size by 234 patients and shortened its duration by 3 or 4 months. Had the study not achieved a recruitment rate that far exceeded expectation, the advantages of the sequential design would have been much greater. Sequential designs appear to be an attractive option for trials in stroke. Copyright 2004 S. Karger AG, Basel

Adaptive and Maladaptive Correlates of Repetitive Behavior and Restricted Interests in Persons with Down Syndrome and Developmentally-Matched Typical Children: A Two-Year Longitudinal Sequential Design

We examined the course of repetitive behavior and restricted interests (RBRI) in children with and without Down syndrome (DS) over a two-year time period. Forty-two typically-developing children and 43 persons with DS represented two mental age (MA) levels: `` younger'' 2-4 years; `` older'' 5-11 years. For typically developing younger children some aspects of RBRI increased from Time 1 to Time 2. In older children, these aspects remained stable or decreased over the two-year period. For participants with DS, RBRI remained stable or increased over time. Time 1 RBRI predicted Time 2 adaptive behavior (measured by the Vineland Scales) in typically developing children, whereas for participants with DS, Time 1 RBRI predicted poor adaptive outcome (Child Behavior Checklist) at Time 2. The results add to the body of literature examining the adaptive and maladaptive nature of repetitive behavior.

Optimal static and sequential design : a critical review

The aim of this thesis is to review and augment the theory and methods of optimal experimental design. In Chapter I the scene is set by considering the possible aims of an experimenter prior to an experiment, the statistical methods one might use to achieve those aims and how experimental design might aid this procedure. It is indicated that, given a criterion for design, a priori optimal design will only be possible in certain instances and, otherwise, some form of sequential procedure would seem to be indicated. In Chapter 2 an exact experimental design problem is formulated mathematically and is compared with its continuous analogue. Motivation is provided for the solution of this continuous problem, and the remainder of the chapter concerns this problem. A necessary and sufficient condition for optimality of a design measure is given. Problems which might arise in testing this condition are discussed, in particular with respect to possible non-differentiability of the criterion function at the design being tested. Several examples are given of optimal designs which may be found analytically and which illustrate the points discussed earlier in the chapter. In Chapter 3 numerical methods of solution of the continuous optimal design problem are reviewed. A new algorithm is presented with illustrations of how it should be used in practice. It is shown that, for reasonably large sample size, continuously optimal designs may be approximated to well by an exact design. In situations where this is not satisfactory algorithms for improvement of this design are reviewed. Chapter 4 consists of a discussion of sequentially designed experiments, with regard to both the philosophies underlying, and the application of the methods of, statistical inference. In Chapter 5 we criticise constructively previous suggestions for fully sequential design procedures. Alternative suggestions are made along with conjectures as to how these might improve performance. Chapter 6 presents a simulation study, the aim of which is to investigate the conjectures of Chapter 5. The results of this study provide empirical support for these conjectures. In Chapter 7 examples are analysed. These suggest aids to sequential experimentation by means of reduction of the dimension of the design space and the possibility of experimenting semi-sequentially. Further examples are considered which stress the importance of the use of prior information in situations of this type. Finally we consider the design of experiments when semi-sequential experimentation is mandatory because of the necessity of taking batches of observations at the same time. In Chapter 8 we look at some of the assumptions which have been made and indicate what may go wrong where these assumptions no longer hold.

Macromolecular engineering via RAFT chemistry : from sequential to modular design

Sequential Design Molecular Weight Range Functional Monomers: Possibilities, Limits, and Challenges Block Copolymers: Combinations, Block Lengths, and Purities Modular Design End-Group Chemistry Ligation Protocols Conclusions

A Sequential Algorithm for the Rigorous Design of Thermally Coupled Distillation Sequences

A sequential design method is presented for the design of thermally coupled distillation sequences. The algorithm starts by selecting a set of sequences in the space of basic configurations in which the internal structure of condensers and reboilers is explicitly taken into account and extended with the possibility of including divided wall columns (DWC). This first stage is based on separation tasks (except by the DWCs) and therefore it does not provide an actual sequence of columns. In the second stage the best arrangement in N-1 actual columns is performed taking into account operability and mechanical constraints. Finally, for a set of candidate sequences the algorithm try to reduce the number of total columns by considering Kaibel columns, elimination of transfer blocks or columns with vertical partitions. An example illustrate the different steps of the sequential algorithm.

Sequential Monte Carlo for Bayesian sequentially designed experiments for discrete data

In this paper we present a sequential Monte Carlo algorithm for Bayesian sequential experimental design applied to generalised non-linear models for discrete data. The approach is computationally convenient in that the information of newly observed data can be incorporated through a simple re-weighting step. We also consider a flexible parametric model for the stimulus-response relationship together with a newly developed hybrid design utility that can produce more robust estimates of the target stimulus in the presence of substantial model and parameter uncertainty. The algorithm is applied to hypothetical clinical trial or bioassay scenarios. In the discussion, potential generalisations of the algorithm are suggested to possibly extend its applicability to a wide variety of scenarios