School of Mathematical Sciences Queen Mary, University of London AUTUMN TERM 2000/01 STATISTICS SEMINAR: DESIGN OF EXPERIMENTS All are welcome The talks are held at 16.30, all in the Mathematics Seminar Room (103) on Level 1 of the Mathematics Building, Queen Mary and Westfield College. Tea and coffee are available in the Mathematics Common Room (102) from 15.00. The nearest underground station is Stepney Green. Turn left at the exit and walk 400 yards. ________________________________________________________________________ DATE SPEAKER TITLE ------------------------------------------------------------------------ 26 Oct. 2000 Steven Gilmour Response Surface Designs in QMW Complex Blocking Structures 16 Nov. 2000 Russell Cheng Analysis of Distributions in University of Southampton Simulation Factorial Experiments 30 Nov. 2000 Simon Bate Good change-over designs when Royal Holloway there are fewer subjects than treatments 14 Dec. 2000 Alicja Rudnicka Use of hierarchical models for Christopher Frost normal variations in retinal QMW sensitivity London School of Hygiene & Tropical Medicine ----------------------------------------------------------------------- For more information ask: Barbara Bogacka School of Mathematical Sciences Queen Mary University of Lonodon Mile End Road London E1 4NS Tel: 020 7882 5497 e-mail: [log in to unmask] --------------------------------------------- The seminar information is kept on: http://www.maths.qmw.ac.uk/~rab/seminars.html ______________________________________________________________________ A B S T R A C T S ______________________________________________________________________ Steven Gilmour Response Surface Designs in Complex Blocking Structures In most published response surface experiments the allocation of treatments to units is completely randomised, or randomised in orthogonal blocks. In many applications involving biological materials it is necessary to use smaller, nonorthogonal, blocks in order to control variation efficiently. Sometimes there is more than one blocking factor, so that crossed or nested block structures are needed. In addition, when the experimental units are sequential runs, there are often some factors which are difficult to change, leading to multi-stratum (e.g. split-plot) structures. A series of algorithms for dealing with all of these situations will be described and areas for future research identified. ------------------------------------------------------------------- Russell Cheng Analysis of Distributions in Simulation Factorial Experiments The output from simulation factorial experiments can be complex and may not be amenable to standard methods of estimation like ANOVA. We consider the situation where the simulation output may not satisfy normality or homoscedasticity assumptions and where differences in output at different factor combinations are not simply differences in means. We show that some well known goodness of fit statistics can be generalised to provide a simple analysis that is similar to ANOVA but which is more sensitive. We describe its properties. An advantage is that, whatever the sample size, Monte-Carlo sampling can be used to directly generate arbitrarily accurate critical test null values in online analysis. The method is illustrated with an example based on consultancy work for National Air Traffic Services in real time simulation trials investigating changes in procedures used by air traffic controllers overseeing flights over Britain. ------------------------------------------------------------------ Simon Bate Good change-over designs when there are fewer subjects than treatments Change-over designs are required for practical situations where a set of subjects are given a sequence of treatments in a number of time periods, it is well known that the effect of one treatment may "carry-over" into the following period. Many change-over designs require large numbers of subjects, either greater than or equal to the number of treatments. In this talk, due to the lack of subject materials, we consider the case where the number of subjects is less than the number of treatments. It is shown, by searching through a class of cyclic designs, that designs more efficient than those given in the literature can be constructed. Extensions to when the number of subjects is greater than, but not a multiple of, the number of treatments are also considered. -------------------------------------------------------------------------- Alicja R Rudnicka Christopher Frost Use of hierarchical models for normal variations in retinal sensitivity Aims & objectives: Retinal light sensitivity (RLS) is an important psychophysical measure of visual function and is used as an aid in diagnosis and for monitoring certain ocular pathologies, especially glaucoma. RLS can be evaluated using a visual field test which measures light sensitivity in two dimensional space usually on a hemispherical screen positioned about one-third of a metre from the human eye. The unit of measure is the decibels which is related to the light intensity of the stimulus on a log scale. Most instruments are automated and a single visual field test measures the RLS at approximately 70 locations per eye. Various summary measures have been devised which combine the information from all locations into a single index. Typically, these do not take into consideration the inherent correlation between values from the same eye nor the spatial location. In this study hierarchical models were utilised to identifying important predictors of normal RLS whilst accounting for the correlation and spatial nature of the information from a visual field test and compared with traditional multiple linear regression. Understanding RLS in normal eyes is required before extrapolations can be made to eyes suffering from disease. Methods: A sample of 121 normal individuals had their RLS measured on one eye only, randomly select, at 149 locations per eye, using the Humphrey Field Analyzer 630. Each point tested can be located by its x and y co-ordinate in degrees on the hemispherical testing surface of the instrument. A two level hierarchical model was fitted, the lowest level 1 being the location in the visual field and level 2 denotes the person. The 'person effect' was modelled according to age, sex, and 5 ocular structural factors (axial length, ocular refraction, optic disc area, neuroretinal rim area, peripapillary atrophy area) as fixed effects. The random component at level 2 was designed to take into consideration the spatial location of each RLS value, the expected decline in RLS with increasing radial distance from the centre of the visual field, the increase in between person variance in RLS with radial distance from the centre of the visual field, and the non-independence of RLS values from the same person that are close to each other, (neighbouring points should be more highly correlated than points farther apart). Analysis by traditional multiple linear regression using the same covariates was performed. Results: The hierarchical model captured the desired properties of correlation between points and once the level 2 variation was allowed for axial length and optic disc area were found to be important predictors of RLS. The effects of the latter two factors were masked using traditional multiple linear regression. An extension of the analysis should address the asymmetric decline in RLS with increasing distance from the centre of the visual field. Conclusions: Hierarchical models are more powerful than traditional linear regression models for the type of data used in this study, and the former identified two factors as important predictors of RLS which have not previously been demonstrated to be related to RLS. A thorough understanding of the important predictors of RLS in a normal population is a precursor to evaluating diseased populations. This descriptive analysis demonstrates the application of these more complex statistical models to medical data with a two dimensional structure. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%