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.
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DATE SPEAKER TITLE
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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
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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]
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The seminar information is kept on:
http://www.maths.qmw.ac.uk/~rab/seminars.html
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A B S T R A C T S
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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.
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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.
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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.
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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.
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