Symposium on Mathematical and Statistical Methods in the Life
Sciences
November 12, 2004
Abstracts

Richard Cook, University of Waterloo
Assessing Association With Clustered and Truncated Disease Onset
Data
In many epidemiological studies, individuals are sampled subject to
predefined selection criteria. When these selection criteria are based
on the response of interest, the resulting data are said to be truncated.
We consider data from an epidemiological study with the aim of assessing
withinfamily assocation in the onset times of schizophrenia. All cases
hospitalized in a particular 20 year period were documented and data
were then grouped by family dentifiers.
The resulting onset times were therefore clustered by family and truncated
by the selection criteria. We describe approaches for estimating withinfamily
association in this context based on models for multivariate truncated
failure time data. Specifically we consider use of marginal models based
on copula functions and conditional models based on familylevel frailties.
The amount of information available on withinfamily association is
studied as a function of the degree of truncation. EM algorithms are
described for estimation in both the marginal and conditional frameworks.
This is based on joint work with Rinku Sutradhar (University of Waterloo)
and
Jack Kalbfleisch (University of Michigan)
Ross Cressman, Wilfrid Laurier University,
Coevolution, Adaptive Dynamics and the Replicator Equation for a
Continuous Trait Space
Coevolutionary models combine population dynamics (i.e. the aggregate
ecological changes to species densities) with the effects of changing
individual behavior (i.e. the evolution of individual phenotypes or
traits). I will briefly review the adaptive dynamics approach to coevolution
that assumes changes in ecological time occur much faster than evolutionary
changes and that populations are monomorphic. These assumptions lead
to the canonical equation of adaptive dynamics, an evolution equation
for the mean trait of the population. For a single species with onedimensional
trait space, the CSS (Continuously Stable
Strategy) characterize those traits that are dynamically stable.
The main purpose of the talk is to compare the adaptive dynamics method
to another approach that leads to the replicator equation. This is a
dynamical system that models the evolution of the distribution of traits
which, for continuous trait space, becomes a measure dynamics. When
trait space is onedimensional, it is shown that among monomorphisms
(which are now measures supported on a single trait value), the static
CSS condition is equivalent to asymptotic stability of the replicator
equation with respect to all initial measures whose support is an interval
containing this trait value. The relevance of the NIS (Neighborhood
Invader Strategy) concept is also clarified. In the cases where adaptive
dynamics predicts evolutionary branching, convergence to a dimorphism
is established. Extensions to multidimensional trait space are discussed.
The talk is based on recent joint work with Josef Hofbauer (UCL) and
Frank Riedel (Bonn).
Gerarda Darlington, University of Guelph
Analysis of PretestPosttest data in Cluster Randomization Trials
The aim of some randomized trials is to investigate the ability
of an intervention to change patient knowledge, behaviour or health.
Thus, the study outcome will need to be measured prior to random assignment
and following implementation of the intervention. Methods for analyzing
change are explored when data are obtained from cluster randomization
trials where the unit of allocation is a family, school or community.
The use of mixed effects linear regression models is considered. Simulation
study results provide information on the power of these procedures allowing
for variability in cluster size. The discussion is illustrated using
data from a schoolbased smoking prevention trial. (Joint work with
Neil Klar  Cancer Care Ontario)
David Earn, McMaster University
The capacity of modern cities to resist infectious disease invasions
A.H. ElShaarawi, National Water Research
Institute, Burlington, Ontario
and Department of Mathematics and Statistics, McMaster University
Modelling and Analyzing SpatialTemporal Environmental Data
In recent years more efforts have been directed to the development
of statistical methods for the detection, estimation and prediction
of environmental changes. The aim is to generate efficient information
for use in environmental management. In this talk an overview of these
efforts will be presented and areas where further research is needed
will be emphasized. Environmental data are routinely collected from
a fixed set of locations within an ecosystem as a mixture of time series
of discrete and continuous measurements. The interest is to model trend
and seasonality at each location and to combine the locations' models
into an overall model for making inferences about the entire ecosystem.
The results of using quasilikelihood based methods to model Canadian
acid rain and water quality data will be discussed.
Igor Jurisica (Ontario Cancer Institute)
Avoiding fusion of illusion and confusion.Integrated computational
biology.
The accumulation of data from systematic highthroughput experiments
has brought the potential to construct models of how biological systems
work at the whole cell or whole organism level. How to integrate multiple
information levels to achieve this task is not trivial, and we discuss
some of the possible approaches.
Our goal is to understand cancer at molecular level to develop early
detection methods, accurate prognosis and effective therapies. We can
increase our understanding of the disease origin and tumorigenesis by
integrating existing large scale genomic and proteomic data sets. This
requires new analysis methods to combine, consolidate and interpret
heterogeneous data. No single database or algorithm will be successful
at solving these complex analytical problems.
Lindi Wahl, University of Western Ontario
Information theory reveals functional domains in proteins.
In a Multiple Sequence Alignment (MSA), rows of amino acid sequences
from related proteins are aligned such that the amino acid identity
in each column is preserved as much as possible. If a column is completely
conserved, that is, if the same amino acid occurs in the same position
in all of the related proteins, we assume that this position is functionally
important. Experimental studies, however, have shown that many nonconserved
positions are also critical to protein function. In particular, positions
may coevolve, such that a mutation in one column is typically matched
by a compensating mutation in another column. Unfortunately, the experimental
identification of such positions is prohibitively difficult for typical
MSAs. We use mutual information, a measure based on Shannon's entropy,
to identify nonconserved but coevolving positions in an MSA. Since
mutual information is correlated with the entropy of the column, we
study a number of possible normalizations, using {\it in silico} evolution
to evaluate contributions from shared evolutionary history. MSAs collected
from a range of real proteins indicate that normalized mutual information
identifies functionally important positions in the protein with high
significance.
Jianhong Wu, York University
Modelling Spatiotemporal Patterns in Biological Invasion and Diseases
Spread
The interaction between spatial dispersal and temporal reaction/reproduction
delay plays an important role in describing patterns of biological invasion
and spatial spreads of infectious diseases. Mathematical modelling and
analysis of the impact of such an interaction on the spatialtemporal
pattern formation requires advancement in a new class of partial functional
differential equations with nonlocal delayed nonlinearities. We shall
provide a short survey of the motivation, the current theoretical progress
and its relevance to West Nile virus propagation.