## Research themes in Statistics

The main topics worked on by the statisticians in the School of Mathematical Sciences at Queen Mary, University of London, are described below. Within each topic, our work covers applications, the foundational theory of statistics, general methodology, and the underlying mathematics.

### Design and analysis of experiments

No matter what the field of experimentation, certain questions are always pertinent to the design of the study. How many treatments are there? Are they qualitative or quantitative? If quantitative, is the assumed model for the response a linear one (such as a polynomial) or a non-linear one (such as occur in chemical kinetics)? Are there some factors whose levels cannot be changed very often? Are there inherent differences between the experimental units? Why and how should we randomize? How does the proposed data analysis impinge on the design?

Designs with two or more treatment factors are said to be *factorial*. R. A. Bailey and H. Maruri-Aguilar use algebraic methods to construct factorial designs.
R. A. Bailey, B. Bogacka, and H. Großmann work on factorial designs for multi-stratum experiments, such as those where one factor's levels cannot often be changed.

Models for quantitative factors are sometimes called *response surfaces*. B. Bogacka and H. Großmann work on designs for non-linear response curve and response surface models.

For all of these, we investigate the analysis based on the assumption that some factors are fixed and others random, and also the analysis based on the model justified by the randomization employed. This links to the question of how much the randomization can be restricted without destroying the validity of the proposed analysis.

R. A. Bailey and H. Großmann use combinatorial methods to investigate the optimality of incomplete-block designs and isomorphism classes of factorial design, and to construct factorial designs with many strata. This links us to Queen Mary's pure mathematicians through the design theory research project.

Members of the group have recently held a four-year EPSRC grant on `Unifying approaches to design of experiments'. They were co-organizers of the one-month programme Design of Experiments held at the Isaac Newton Institute in Cambridge in July–August 2008. They ran a further programme Design and Analysis of Experiments there from 18 July to 21 December 2011.

This research is motivated by, and applied to, problems in choice experiments, clinical and pre-clinical trials, food technology, agricultural field trials, microarray experiments, computer experiments, the pharmaceutical industry, and engineering.

### Sequential analysis

It is sometimes more natural and efficient to design an experiment sequentially, since the data may accrue gradually as the experiment proceeds and a sequential one may require fewer resources. A prime example of this is in clinical trials, where interest is often in comparing a new treatment with an existing one. By designing the trial sequentially, a decision on the relative efficacies of the two treatments can often be made much earlier, and hence fewer patients exposed to a possibly inferior treatment.

Although it is not difficult to design an experiment sequentially, there are many issues that need to be addressed. How do we construct the design? For example, is there some form of optimal allocation of resources? In the context of clinical trials, we may wish to randomize patients to treatments in order to maximize power or to identify which of several competing treatments may be dropped from further consideration. The most efficient use of the data is also important in gene association analysis.

One of D. S. Coad's long-standing interests is in inference following sequential designs, and particularly those incorporating some form of adaptive treatment allocation. To appreciate some of the issues involved, consider the use of likelihood-based inference. Although the use of a sequential design does not affect the form of the likelihood function, the sampling distributions of the usual estimators are affected. However, high-order asymptotic theory can be used to carry out approximately valid inference.

Research students in the School are working on estimation of secondary parameters following sequential tests, and inference following biased coin designs for clinical trials.

### Bayesian methods

Bayesian methods are increasingly being used. They allow for the inclusion
of relevant prior knowledge in an analysis. L. I. Pettit is particularly
interested in how individual observations, or groups of observations, can
affect inferences. He is also interested in how to detect, or allow for,
*outliers*, that is observations which seem to be out of line with the mass of the data. He has recently considered outliers in circular data, the effect
of outliers on the Box-Cox transformation and degradation models for
progression of diabetes.

Research students in the School are working on problems of loss functions and optimal sample sizes based on different loss functions; adaptive designs for phase 1 trials; measuring conflict between data and the prior; dealing with outliers for response surface designs. PhD student A.M. Saiful Islam had his PhD thesis accepted in April 2011.

### Statistics in health care

As well as the work on clinical trials and observational studies on the efficacy of screening for breast cancer conducted by our honorary members in CRUK, group members within the Mathematics Research Centre are also involved in research in the design and analysis of clinical trials.

D. S. Coad works on the design and analysis of clinical trials where patients are recruited sequentially: see above.

Following the incident in London in March 2006 when eight healthy volunteers in a Phase I clinical trial of a new drug were taken seriously ill, the Royal Statistical Society set up a working party to investigate Statistical Issues in First-in-Man Studies. R. A. Bailey and B. Bogacka were members of that working party, and have continued to do research into the design of such trials.

D. S. Coad was awarded a joint research grant with Y. Zhou at the University of Reading by the Medical Research Council to hold a three-day workshop on dose-finding methodology in early phase clinical trials in March 2010.

### Collaboration with researchers in other disciplines.

See this page.