Welcome to Steve Coad's homepage!

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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 2013-14.

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 2013-14.

9. Further information.

10. Contact details.


Teaching

In 2013-14, 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 2013 is available on the Time Series web page.

2. Statistical Theory (Semester 6): This is a third-year undergraduate course for majors in Mathematics/Statistics.
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 2014 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

At present, I have one research student, Hsiao Yin Liu. However. I am interested in recruiting another research student. Details of two possible research projects are given below. Other possibilities exist, and I would be happy to discuss them with anyone who is interested. For UK and EU students, there are funding possibilities. Details of my previous research students are given below.

Yeung, W.Y. (2013): "Inference following biased coin designs in clinical trials". PhD.

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". J. Statist. Plann. Inf. 147, 173-187 (2014).

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.

"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.

"Pharmacokinetically guided optimum adaptive dose selection in early phase clinical trials" (with M. Iftakhar Alam and Barbara Bogacka). Submitted to Statist. Med.

This paper introduces a new statistical method for dose finding in phase I/II trials, which, along with efficacy and toxicity as endpoints, also considers pharmacokinetic information in the dose-selection procedure. Following the assignment of a current best dose to a cohort of patients, the concentration of a drug in the blood is measured at the locally D-optimal time points. The dose-response outcomes are also observed for each patient. Based on the updated information, a new dose is selected for the next cohort so that the estimated probability of efficacy is maximum, subject to the condition that the estimated probability of toxicity is not more than a target value. Another condition for the dose selection is related to the total exposure of the drug in the body so that the curative purpose is likely to be achieved. This is expressed by the area under the concentration curve over time. The purpose of this study was to investigate the gain in efficiency of using pharmacokinetic measures in the dose escalation. The proposed method is found to identify the optimal dose accurately without exposing many patients to toxic doses and therefore can be used as a reliable dose-finding procedure.

"Imbalance properties of centre-stratified permuted-block and complete randomisation for several treatments in a clinical trial" (with Vladimir V. Anisimov and Wai Y. Yeung). Submitted to Ann. Appl. Statist.

Randomisation schemes are rules that assign patients to treatments in a clinical trial. Many of these schemes have the common aim of maintaining balance in the numbers of patients across treatment groups. The properties of imbalance that have been investigated in the literature are based on two treatment groups. In this paper, their properties for K > 2 treatments are studied for two randomisation schemes, centre-stratified permuted-block randomisation and complete randomisation. For both randomisation schemes, analytical approaches are investigated assuming that the patient recruitment process follows a Poisson-gamma model. When the number of centres involved in a trial is large, the imbalance for both schemes is approximated by a multivariate normal distribution. The accuracy of the approximations is assessed by simulation. A test for treatment differences is also considered for normal responses and numerical values for its power are presented for centre-stratified permuted-block randomisation. To speed up the calculations, a combined analytical/approximate approach is used.

"Statistical inference following covariate-adaptive randomisation: Recent advances". Under revision for Modern Adaptive Randomised Clinical Trials: Statistical, Operational and Regulatory Aspects, ed. O. Sverdlov. London: CRC Press.

When comparing treatments in a clinical trial, balance is often sought across treatment groups with respect to important covariates. Until recently, the impact of covariate-adaptive randomisation upon inference following the trial had received limited attention in the literature. The purpose of this paper is to review some of these randomisation rules and their inferential properties. Although the main focus will be on normal linear models, the corresponding properties for other types of models will be briefly discussed. To illustrate the results, simulation results for power will be presented for the two-sample t test and the analysis of covariance t test for various covariate-adaptive randomisation rules when different types of balance are sought. The accuracy of some normal approximations to the power of these tests will also be assessed.

"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

"Inference following designs which adjust for imbalances in prognostic factors" (with Y. Barbáchano). Clin. Trials 10, 540-551 (2013).

"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).

"Sequential allocation involving several treatments". In Adaptive Designs, eds. N. Flournoy and W.F. Rosenberger, pp. 95-109 (1995). Hayward, California: Institute of Mathematical Statistics.

"Sequential estimation for two-stage and three-stage clinical trials". J. Statist. Plann. Inf. 43, 343-351 (1994).

"Estimation following sequential tests involving data-dependent treatment allocation". Statist. Sinica 4, 693-700 (1994).

"Sequential tests with covariates with an application to censored survival data". Commun. Statist. - Theor. Meth. 23, 277-287 (1994).

"Sequential procedures for comparing several medical treatments" (with J.A. Bather). Sequential Anal. 11, 339-376 (1992).

"Some results on estimation for two-stage clinical trials". Sequential Anal. 11, 299-311 (1992).

"A comparative study of some data-dependent allocation rules for Bernoulli data". J. Statist. Comput. Simul. 40, 219-231 (1992).

"Sequential estimation with data-dependent allocation and time trends". Sequential Anal. 10, 91-97 (1991).

"Sequential tests for an unstable response variable". Biometrika 78, 113-121 (1991).

Discussion and Other Contributions

Discussion on "Analysis of forensic DNA mixtures with artefacts" by R.G. Cowell, T. Graversen, S.L. Lauritzen and J. Mortera. Appl. Statist. 63, (2014). To appear.

Discussion on "Multiscale change point inference" by K. Frick, A. Munk and H. Sieling. J. R. Statist. Soc. B 76, 552 (2014).

Discussion on "Large covariance estimation by thresholding principal orthogonal complements" by J. Fan, Y. Liao and M. Mincheva (with H. Maruri-Aguilar). J. R. Statist. Soc. B 75, 660-661 (2013).

Discussion on "How to find an appropriate clustering for mixed type variables with application to socio-economic stratification" by C. Hennig and T.F. Liao (with H. Maruri-Aguilar). Appl. Statist. 62, 346 (2013).

Discussion on "A Bayesian approach to complex clinical diagnoses: A case-study in child abuse" by N. Best, D. Ashby, F. Dunstan, D. Foreman and N. McIntosh (with L.I. Pettit). J. R. Statist. Soc. A 176, 89 (2013).

Discussion on "Group sequential tests for delayed responses" by L.V. Hampson and C. Jennison. J. R. Statist. Soc. B 75, 47 (2013).

Discussion on "A hybrid selection and testing procedure with curtailment for comparative clinical trials" by E.M. Buzaianu and P. Chen. Sequential Anal. 28, 26-29 (2009).

Discussion on "Second guessing clinical trial designs" by J.J. Shuster and M.N. Chang. Sequential Anal. 27, 21-23 (2008).

"Sequential testing". In Encyclopedia of Statistics in Behavioral Science, eds. B.S. Everitt and D.C. Howell, pp. 1819-1820 (2005). Chichester: Wiley.

Comment on "Randomised urn models and sequential design" by W.F. Rosenberger (with C.C. Morgan). Sequential Anal. 21, 29-32 (2002).

Comment on "Statistical and ethical issues in monitoring clinical trials" by S.J. Pocock. Statist. Med. 12, 1473 (1993).

Comment on "Investigating therapies of potentially great benefit: ECMO" by J.H. Ware (with P. Armitage). Statist. Sci. 4, 322-323 (1989).

Book Reviews

Review of Mathematical Statistics: Basic Ideas and Selected Topics, Volume I, 2nd edition, by P.J. Bickel and K.A. Doksum. Biometrics 58, 691-692 (2002).

Review of Asymptotic Statistics by A.W. van der Vaart. Biometrics 57, 645-646 (2001).

Review of Optimal Sequentially Planned Decision Procedures by N. Schmitz. J. R. Statist. Soc. A 156, 511 (1993).

Review of Applied Multivariate Analysis by B.S. Everitt and G. Dunn. The Statistician 42, 325-326 (1993).


Recent Talks

My most recent talks are listed below. In November, I am an invited speaker at the 8th International Conference on Applied Mathematics, Simulation, Modelling in Florence, Italy, and, in February, I am an invited speaker at the 12th Workshop on Stochastic Models, Statistics and their Applications in Wroclaw, Poland.

Seminars

"Group-sequential response-adaptive designs". Academia Sinica (July 2014).

"Bias calculations for adaptive generalised linear models". National Chengchi University (July 2014).

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

Conference Presentations

"The use of group sequential tests with designs which adjust for imbalances in prognostic factors". Joint Statistical Meetings, Boston, Massachusetts (August 2014).

"Estimation of parameters of the absolute autoregressive model". Fourth International Workshop in Sequential Methodologies, Athens, Georgia (July 2013).

"Group-sequential response-adaptive designs". Seventh International Workshop on Simulation, Rimini, Italy (May 2013).


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 a London Taught Course Centre Representative and a member of the Committee of Professors of Statistics.


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 7882 7684 (from outside UK +44 20 7882 7684)
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]