Welcome to Steve Coad's homepage!

I am a Reader in Statistics in the School of Mathematical Sciences at Queen Mary, University of London. On this page, you will find information on the following:

1. Teaching for 2012-13.

2. Recent research.

3. Current preprints.

4. Publications.

5. Recent talks, both seminars and conference presentations.

6. Research projects for PhD or MPhil students.

7. Research grants for 2008-09.

8. Administrative responsibilities for 2012-13.

9. Further information.

10. Contact details.

Teaching

In 2012-13, I give two lecture courses. Brief syllabi for these are given below.

1. Time Series (Semester 5): This is a third-year undergraduate course for majors in Mathematics/Statistics.

Trends and seasonality: time plots; smoothing by moving averages; differencing; elimination of trends and seasonality. Stationary time series models: weak and strict stationarity; autocovariance and autocorrelation functions; moving average (AR) and autoregressive (AR) models. Estimation of the mean and autocovariance function: Bartlett's formula; approximate confidence bounds. ARMA models: parameter redundancy; causality and invertibility; autocorrelation and partial autocorrelation functions; forecasting; parameter estimation. Autoregressive integrated moving average (ARIMA) models: model fitting; seasonal ARIMA models.

The course material for Autumn Semester 2012 is available on the Time Series web page.

Point estimation: likelihood; bias; Cramér-Rao lower bound; efficiency; sufficiency; Neyman's factorisation theorem; Rao-Blackwell theorem; completeness; minimum variance unbiased estimators; exponential families. Methods of estimation: method of moments; maximum likelihood; least squares; properties of estimators obtained from these methods. Interval estimation: confidence intervals; methods of obtaining confidence intervals using pivots; likelihood confidence intervals. Hypothesis testing: power; simple and composite hypotheses; Neyman-Pearson lemma; uniformly most powerful tests; likelihood ratio tests; Wilks' theorem.

The course material for Spring Semester 2013 is available on the Statistical Theory web page.

Research

Topics

My current research is mainly in the area of sequential analysis, with particular emphasis on medical applications. The main topics that I have recently been working on are briefly described below.

1. Inference following Sequentially Designed Experiments.

My current research in this area is concerned with the construction of corrected confidence sets for an adaptive normal nonlinear model. There are many examples of such models in chemometrics, such as the Michaelis-Menten model and the first-order growth or decay model. With these models, the design points are chosen sequentially based on the previous data, which complicates the analysis. My research is joint work with M.B. Woodroofe at the University of Michigan and builds on our earlier papers on adaptive normal linear models.

2. Sequential Procedures for Multi-Armed Clinical Trials.

When there are more than two treatments being compared in a clinical trial, the use of a sequential procedure can sometimes require substantially fewer patients than a fixed-sample design to achieve the same error probabilities. My most recent research in this area, which is joint work with A. Biswas at the Indian Statistical Institute, is concerned with the development of a general elimination rule for comparing several treatments with responses which are multivariate, continuous and dependent on prognostic factors.

3. Response-Adaptive Designs in Clinical Trials.

These designs use the accumulating data in a clinical trial to skew the allocation probabilities in favour of the treatment which is performing better thus far in the trial. The simplest such designs, from a mathematical point of view, are adaptive urn designs and my most recent research in this area, which is joint work with A. Ivanova at the University of North Carolina, addresses the problem of bias following such a design. Current work includes the use of a stopping time and the consideration of more than two treatments.

4. Testing for the Number of Components in Mixture Models.

The determination of the number of components in a finite mixture distribution is an important, but difficult, problem. A number of approaches have been proposed in the literature for tackling the case of a normal mixture, such as the use of posterior Bayes factors and bootstrapping. In joint work with M.N. Goria at the University of Trento, a detailed comparison is being carried out of these methods for the normal case and we then plan to develop analogous approaches for the determination of the number of components in a gamma mixture.

5. Inference for Secondary Parameters following Sequential Tests.

When carrying out estimation following a sequential clinical trial, methods are available for constructing corrected confidence intervals for primary parameters. However, in practice, there is often also interest in secondary parameters. In joint work with R.C. Weng at the National Chengchi University, corrected confidence intervals are being developed for secondary parameters. This work builds on existing work for primary parameters and complements recent work in the literature based on related techniques.

Research Students

Barbáchano, Y. (2007): "Adaptive designs for clinical trials which adjust for imbalances in prognostic factors". DPhil.

Bailey, S.M. (2007): "Sequential adaptive designs for early phase clinical trials". DPhil.

Halimeh, A.A. (2004): "Sequential procedures for comparing several normal means". MPhil.

Morgan, C.C. (2003): "Group-sequential response-adaptive designs for clinical trials". DPhil.

Current Preprints

My current preprints, together with abstracts, are listed below. Please contact me for paper copies.

"Corrected confidence intervals based on the signed root transformation for multi-parameter sequentially designed experiments". Under revision for J. Statist. Plann. Inf.

A two-parameter model is studied in which there is a parameter of interest and a nuisance parameter. Corrected confidence intervals are constructed for the parameter of interest for data from a sequentially designed experiment. This is achieved by considering the distribution of the first component of the bivariate signed root transformation, and then by applying a version of Stein's identity and very weak expansions to determine the correction terms. The accuracy of the approximations is assessed by simulation for three nonlinear regression models with normal errors, a two-population normal model, a logistic model and a Poisson model. An extension of the approach to higher dimensions is briefly discussed.

"Inference following designs which adjust for imbalances in prognostic factors" (with Yolanda Barbáchano). Clin. Trials 10, (2013). To appear.

When minimisation is used to balance treatment groups across prognostic factors, a problem arises at the time of analysing the results. Since minimisation is essentially a deterministic method, any statistical test based on the assumption of complete randomisation should not be used in the analysis. Previous papers have shown that analysis of covariance produces valid tests. In this paper, these results are extended to trials with more prognostic factors and more treatments. An alternative design to minimisation which makes use of optimum design theory is also considered, with two choices of biased coin. Simulation is used to study the effect on the power and the coverage probabilities of the usual tests and confidence intervals when these different allocation methods are applied. The results are then illustrated using data from an actual clinical trial. Simulation shows that, when analysis of covariance is used, it is sometimes more powerful with these designs than with minimisation and produces slightly conservative confidence intervals for the treatment mean differences. The increase in power and conservativeness is more pronounced when there are more prognostic factors. The possibility of treatment-covariate interactions is also addressed. When a covariate-adaptive design is used, the use of analysis of covariance yields a test which can be slightly more powerful than when complete randomisation is used. Moreover, the increase in power is greater for designs based on optimum design theory than for minimisation.

"The use of group sequential tests with designs which adjust for imbalances in prognostic factors" (with Yolanda Barbáchano). Under revision for Statist. Med.

Minimisation and methods that make use of optimum design theory have been suggested to balance treatment groups across prognostic factors. Although the problem of analysing a trial when one of these methods has been used has been looked at in the fixed-sample case, it has so far not been considered in the group sequential setting. In this paper, simulation is used to explore the consequences of adapting for prognostic factors in a group sequential trial. Both Pocock's test and the O'Brien and Fleming test are considered and three methods of adjusting for covariates are studied. When the variance of the response variables is unknown, the critical values are obtained using those in the known variance case and the significance level approach. The resulting tests have approximately the required type I error probability. To maintain the desired power, sample size re-estimation is incorporated. Simulation shows that the tests satisfy the power requirement for moderate sample sizes, with those using complete randomisation being less powerful than those using the adaptive methods. The results are then illustrated using data from an actual clinical trial. Repeated confidence intervals for the mean treatment effects are also calculated.

"A bivariate design for a combined phase I/II clinical trial in oncology" (with S.M. Bailey).

This paper reviews the current state of research on bivariate adaptive designs for early phase clinical trials with two competing outcomes, often known as combined phase I/II trials. Such trials aim to find the maximum tolerated dose (MTD) of a new drug, whilst assuring that the efficacious effects of the drug remain above a given level. A new Bayesian design is presented addressing shortfalls of previous designs of this type for these combined trials. The main features of the design are the use of separate response curves for toxicity and efficacy, the modelling of the joint events of toxicity and efficacy using the bivariate Gumbel model, and the incorporation of stopping rules for early termination and identification of incorrect doses ranges. It is shown via simulation that the new design targets the doses most closely associated with the MTD, whose efficacious effects are above a given threshold, with high probability. Comparisons with two recently proposed bivariate designs show that the new design performs favourably with regard to MTD targeting and patient allocation within the trials. A description of the techniques used within the simulation structure is also outlined.

Publications

Refereed Publications

"Response adaptive randomisation". In Encyclopedia of Clinical Trials, Volume 4, eds. R. D'Agostino, L. Sullivan and J. Massaro, pp. 113-119 (2008). New York: Wiley.

"Predictability of designs which adjust for imbalances in prognostic factors" (with Y. Barbáchano and D.R. Robinson). J. Statist. Plann. Inf. 138, 756-767 (2008).

"The duplicate method of uncertainty estimation: Are eight targets enough?" (with J.A. Lyn, M.H. Ramsey, A.P. Damant, R. Wood and K.A. Boon). Analyst 132, 1147-1152 (2007).

"A comparison of adaptive allocation rules for group-sequential binary response clinical trials" (with C.C. Morgan). Statist. Med. 26, 1937-1954 (2007).

"Corrected confidence intervals for secondary parameters following sequential tests" (with R.C. Weng). In Recent Developments in Nonparametric Inference and Probability: Festschrift for Michael Woodroofe, eds. J. Sun, A. DasGupta, V. Melfi and C. Page, pp. 80-104 (2006). Hayward, California: Institute of Mathematical Statistics.

"Sequential procedures for comparing several normal means" (with A.A. Halimeh). J. Statist. Comput. Simul. 76, 519-537 (2006).

"Sequential urn designs with elimination for comparing K ≥ 3 treatments" (with A. Ivanova). Statist. Med. 24 , 1995-2009 (2005).

"The use of the triangular test with response-adaptive treatment allocation" (with A. Ivanova). Statist. Med. 24 , 1483-1493 (2005).

"A general multi-treatment adaptive design for multivariate responses" (with A. Biswas). Sequential Anal. 24, 139-158 (2005).

"Corrected confidence intervals for adaptive nonlinear regression models" (with M.B. Woodroofe). J. Statist. Plann. Inf. 130, 63-83 (2005).

"Bias calculations for adaptive urn designs" (with A. Ivanova). Sequential Anal. 20, 91-116 (2001).

"Corrected confidence intervals following a sequential adaptive clinical trial with binary responses" (with Z. Govindarajulu). J. Statist. Plann. Inf. 91, 53-64 (2000).

"Corrected confidence sets for sequentially designed experiments: Examples" (with M. Woodroofe). In Multivariate Analysis, Design of of Experiments and Survey Sampling: A Tribute to Jagdish N. Srivastava, ed. S. Ghosh, pp. 135-161 (1999). New York: Marcel Dekker. Reprinted in Sequential Anal. 21, 191-218 (2002).

"A comparison of the randomised play-the-winner rule and the triangular test for clinical trials with binary responses" (with W.F. Rosenberger). Statist. Med. 18, 761-769 (1999).

"Approximate bias calculations for sequentially designed experiments" (with M.B. Woodroofe). Sequential Anal. 17, 1-31 (1998).

"Approximate confidence intervals after a sequential clinical trial comparing two exponential survival curves with censoring" (with M.B. Woodroofe). J. Statist. Plann. Inf. 63, 79-96 (1997).

"Corrected confidence sets for sequentially designed experiments" (with M. Woodroofe). Statist. Sinica 7, 53-74 (1997).

"Corrected confidence intervals after sequential testing with applications to survival analysis" (with M.B. Woodroofe). Biometrika 83, 763-777 (1996).

"Sequential allocation rules for multi-armed clinical trials". J. Statist. Comput. Simul. 52, 239-251 (1995).

Recent Talks

My most recent talks are listed below. In May, I am an invited speaker at the Seventh International Workshop on Simulation in Rimini, Italy, and, in July, I am an invited speaker at the Fourth International Workshop in Sequential Methodologies in Athens, Georgia.

Seminars

"The use of group sequential tests with designs which adjust for imbalances in prognostic factors". Columbia University (June 2011).

"Corrected confidence intervals based on the signed root transformation for multi-parameter sequentially designed experiments". University of Southampton (April 2009).

"Predictability of designs which adjust for imbalances in prognostic factors". University of Warwick (April 2009).

Conference Presentations

"Imbalance properties of adaptive biased coin designs for K > 2 treatments". International Workshop on Sequential Methods and their Applications, Rouen, France (June 2012).

"Estimation following adaptively randomised clinical trials". 58th World Statistics Congress of the International Statistical Institute, Dublin (August 2011).

"Inference following adaptive biased coin designs". 20th Annual International Chinese Statistical Association Applied Statistics Symposium, New York City (June 2011).

Research Projects for PhD or MPhil Students

Here are details of two possible projects. As mentioned earlier, others are possible, and anyone interested is welcome to contact me. For general information about postgraduate research in Statistics and Probability in the School of Mathematical Sciences at Queen Mary, University of London, please look at our Postgraduate Admissions web page.

Project 1: Inference following Selection and Testing Designs

In combined phase II/III trials, several experimental treatments are compared to a control in the selection stage and the selected experimental treatment is then further compared to the control during the testing stage. Since bias is introduced by treatment selection, estimation of the effect of the selected treatment raises a number of issues. For example, it is not clear how best to estimate the effect of the selected treatment based on the first-stage data, because Cohen and Sackrowitz (1989, Statist. Prob. Lett. 8, 273-278) have shown that a conditionally unbiased estimator does not exist. However, such an estimator with uniformly minimum variance can be constructed at the end of the testing stage by combining the data from the two stages. There are many potential extensions to this work. Is it possible to apply these designs when there are delayed responses by incorporating data on an intermediate outcome? Can a conditionally unbiased estimator be constructed for designs with more than two stages? A good starting point would be to consider the bivariate normal case when there are two stages.

During the course of the project, it would be necessary to learn about theoretical techniques in treatment selection designs and to gain experience of Monte Carlo methods.

Project 2: Efficient Multiple Tests with Applications to Genetics

There are often a large number of hypotheses of interest in gene association analysis, but limited numbers of observations available. Consequently, multiple testing procedures are sought which make the most efficient use of the data whilst controlling the false discovery rate. Most of the proposed procedures are based on one-stage designs, which often lead to tests with poor power, since there is only a small number of observations for each hypothesis. Zehetmayer, Bauer and Posch (2005, Bioinformatics 21, 3771-3777) showed that, for normally distributed data, a two-stage design based on combining the p-values from a screening stage and a testing stage can significantly improve the power. However, there are a number of open problems. Can the power of these designs be further improved by allowing unequal allocation during the testing stage? Is there a worthwhile improvement in power if three stages are used? Can analogous designs be developed for other response types, such as binary data? A good starting point would be to study the effect of unequal allocation on a one-stage design.

During the course of the project, it would be necessary to learn about adaptive testing based on p-values and to gain experience of Monte Carlo methods.

Research Grants

During 2008-09, I was awarded a joint research grant with Y. Zhou at the University of Reading by the Medical Research Council (MRC). Details of this are given below.

MRC Workshop on Dose-Finding Methodology in Early Phase Clinical Trials

This is a Fast Tracking Drug Development Initiative Grant to hold a three-day workshop at the University of Reading. More information about the workshop is available here. The project deliverables are as follows:

1. To provide an intensive programme of talks from world experts on current trends in dose-finding methodology for early phase clinical trials, together with small-group discussions, where open problems can be addressed and progress made.

2. Participants will be able to learn about state-of-the-art adaptive designs for early phase clinical trials and related ethical issues, exchange research ideas, establish collaborative research links and discuss how to implement the methodology in practice.

3. To provide a report on the outcomes, which will highlight the main issues raised on each of the topics covered and summarise the current status of any open problems, and thus emphasise researchable areas of interest and important methodological gaps.

4. By exchanging research ideas and establishing collaborative links, the workshop will lead to joint grant applications for funding, preparation of papers for presentation at future international conferences and publication in relevant leading statistical journals.

Administrative Responsibilities

I am currently a member of the Editorial Board for Sequential Analysis and an Associate Editor for Statistical Methodology.

For the School of Mathematical Sciences, I am the programme director for the BSc degree in Mathematics, Statistics and Financial Economics, and a London Taught Course Centre Representative.

Further Information

I have a BSc degree from Portsmouth Polytechnic, and MSc and DPhil degrees from the University of Oxford. I came to my present job at Queen Mary in 2005, and immediately before that was a Senior Lecturer in Statistics at the University of Sussex. During 1993-95, I was a Visiting Assistant Professor at the University of Michigan and was awarded a Fulbright Scholarship Grant in connection with the visit. Since 1993, I have been a Chartered Statisticican, and, since 1998, a Chartered Mathematician. I am a Fellow of the Royal Statistical Society and of the Institute of Mathematics and its Applications, and a Member of the Biometric Society, the International Society for Clinical Biostatistics and the Bernoulli Society.

One of my favourite pastimes is travelling. During June and July 2012, I made a three-week trip to Thailand and Cambodia. One of the highlights was a visit to the abandoned seaside resort of Kep near Kampot, where freshly caught crab cooked with locally produced pepper can be enjoyed at one of the oceanfront crab shacks. Other high points included a visit to the hilltop temple of Wat Banan south of Battambang, with its incredible views across the surrounding countryside. A ride on the local bamboo train provides a wonderful way of seeing some of the beautiful countryside. The train is powered by an engine at the back and accelerates very quickly. One of my other pastimes is learning Thai. I am currently living in Hove.

Contact Details

Steve Coad

Office

352, Mathematics Building

E-mail

D.S.Coad@qmul.ac.uk

Phone

020 7882 5484 (from outside UK +44 20 7882 5484)

Fax

020 8981 9587 (from outside UK +44 20 8981 9587)

Postal Address

Dr. D.S. Coad
School of Mathematical Sciences
Queen Mary, University of London
Mile End Road
London E1 4NS
United Kingdom

The contents of this Home Page are my own responsibility, not those of Queen Mary, University of London, or any of its Units.

[School of Mathematical Sciences] [Queen Mary, University of London]