# 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 2016-17.

2. Recent research.

4. Publications.

5. Recent talks, both seminars and conference presentations.

6. Research projects for PhD or MPhil students.

7. Research grants for 2008-09.

10. Contact details.

## Teaching

In 2016-17, I give one lecture course. A brief syllabus for this is given below.

Introduction to Statistics (Semester 2): This is a first-year undergraduate course for majors in Mathematics/Statistics.
Descriptive statistics. Summary statistics. Discrete random variables: probability generating functions. Populations and samples: sampling distribution; point estimation. Hypothesis tests on proportions: type I and II errors; one- and two-sided alternative hypotheses. Continuous random variables: probability density functions; monotone transformations. Normal random variables. Joint probability density functions: covariance, correlation and independence. Laws of large numbers and central limit theorem. One-sample z test: significance levels and p-values. Confidence intervals for a mean. Conditioning on a continuous random variable.

The course material for Spring Semester 2017 is available on the Introduction to Statistics 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 two research students, Ashna J. Mohammad and Ayon Mukherjee. 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 opportunities. Details of my previous research students are given below.

Liu, W. (2016): "Group-sequential response-adaptive designs for comparing several treatments". PhD.

Alam, M.I. (2015): "Optimal adaptive designs for dose finding in early phase clinical trials". PhD.

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

"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). Comput. Statist. Data Anal. 111, 183-202 (2017).

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). Statist. Med. 36, 1302-1318 (2017).

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.

"Real-time Bayesian parameter estimation for item response models" (with Ruby Chiu-Hsing Weng). Bayesian Anal. 12, (2017). To appear.

Bayesian item response models have been used in modelling educational testing and Internet ratings data. Typically, the statistical analysis is carried out using Markov Chain Monte Carlo (MCMC) methods. However, MCMC methods may not be computationally feasible when real-time data continuously arrive and online parameter estimation is needed. We develop an efficient algorithm based on a deterministic moment matching method to adjust the parameters in real-time. The proposed online algorithm works well for two real datasets, achieving good accuracy but with considerably less computational time.

"The power of covariate-adaptive randomisation schemes in clinical trials" (with Wai Y. Yeung). Submitted to Clin. Trials.

When one or more covariates affect patients' responses to different treatments, they can be included both in the randomisation stage and in the analysis stage. In the randomisation stage, covariate-adaptive randomisation schemes can be used. Such schemes have been studied when two treatments are under comparison. The randomisation schemes are applied to patients classified by their prognostic factors to ensure that those with the same prognostic profile are balanced between the two treatments. In the analysis stage, analysis of covariance can be used to compare the mean responses for the two treatments. In this paper, three covariate-adaptive randomisation schemes are studied when either global or marginal balance is sought. By considering a fixed-effects model for the treatment responses when there are several covariates, an analysis of covariance t test is carried out. Numerical values of the power are simulated for the three randomisation schemes for both global and marginal balance when there is an interaction between the covariates. It is shown that the covariate-adaptive adjustable biased coin design produces the highest power among the three and that the power gain under global balance is higher than under marginal balance. In addition, the accuracy of normal approximations to the power is assessed by simulations for different scenarios. Numerical values for the simulated powers by the two-sample t test and the analysis of covariance t test are compared with the power obtained by normal approximations.

"Group-sequential response-adaptive designs for censored survival responses" (with Wenyu Liu). Submitted to Statist. Med.

Previous work on two-treatment comparisons has shown that the use of optimal response-adaptive randomisation with group sequential analysis can allocate more patients to the better-performing treatment while preserving the error rates. However, it focused on immediate responses. The application of the combined approach to censored survival responses is investigated and different optimal response-adaptive randomised procedures are compared by simulation. For a maximum duration trial, the information level at the final look is usually unpredictable. An approximate information time is defined. Group sequential tests and optimal allocations for two measures of treatment difference are given. The simulation results reveal that the existing boundaries derived using the error-spending approach can be applied to the designs to control the overall type I error rate. Compared to the group sequential complete randomisation design, the combined approach is more ethical in terms of reducing the expected numbers of patients and failures and lowering the allocation proportion for the inferior treatment. The two optimal response-adaptive randomisation procedures investigated target the pre-specified optimal allocation well with reasonably small variability. For simplicity, the case of exponential survival responses is considered. A generalisation to the case of Weibull survival times is briefly discussed.

"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

"Statistical inference following covariate-adaptive randomisation: Recent advances". In Modern Adaptive Randomised Clinical Trials: Statistical and Practical Aspects, ed. O. Sverdlov, pp. 155-170 (2015). London: CRC Press.

"Approximate confidence sets for adaptive generalised linear models". In Recent Advances in Applied Mathematics, Modelling and Simulation, eds. N.E. Mastorakis, M. Demiralp, N. Mukhopadhyay and F. Mainardi, pp. 40-42 (2014). Athens: WSEAS Press.

"Corrected confidence intervals based on the signed root transformation for multi-parameter sequentially designed experiments". J. Statist. Plann. Inf. 147, 173-187 (2014).

"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 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 "Sequential Quasi-Monte-Carlo sampling" by M. Gerber and N. Chopin (with R.C. Weng). J. R. Statist. Soc. B 77, 561-562 (2015).

Discussion on "Analysis of forensic DNA mixtures with artefacts" by R.G. Cowell, T. Graversen, S.L. Lauritzen and J. Mortera. Appl. Statist. 64, 40 (2015).

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 June, I am an invited speaker at the Sixth International Workshop in Sequential Methodologies in Rouen, France.

#### Seminars

"Bias calculations for adaptive generalised linear models". University of Southampton (April 2015).

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

#### Conference Presentations

"A combined criterion for dose optimisation in early phase clinical trials". 13th Workshop on Stochastic Models, Statistics and their Applications, Berlin, Germany (February 2017).

"Group sequential monitoring of optimal response-adaptive randomised multi-armed clinical trials". 4th International Conference on Design of Experiments, Memphis, Tennessee (May 2016).

"Improving covariate-adaptive designs". 8th Annual Conference on Adaptive Designs in Clinical Trials, London (April 2016).

## 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.

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, a member of the Committee of Professors of Statistics, the Organiser of the Statistics and Data Analysis Seminars, a Science and Engineering Foundation Programme Advisor and a Study Programme Advisor.

## 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 August and September 2015, I made a three-week trip to Thailand and Malaysia. One of the highlights was a ride on the funicular up Penang Hill west of George Town, which offers a cool retreat from the searing heat below. From the summit, there are spectacular views of the island. Other high points included a visit to Porta de Santiago in Melaka, once the main gate of the Portuguese fortress A'Famosa. A river cruise provides a very pleasant way to appreciate the contrast between the old and new parts of the city, in addition to the many colourful murals painted on the backs of the buildings. One of my other pastimes is learning Thai. I am currently living in Hove.

## Contact Details

Office
W303, Queens' Building
E-mail