May 28, 2018

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



Richard Cook, University of Waterloo

Assessing Association With Clustered and Truncated Disease Onset Data
In many epidemiological studies, individuals are sampled subject to pre-defined 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 within-family 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 within-family 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 family-level frailties. The amount of information available on within-family 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 one-dimensional 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 one-dimensional, 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 multi-dimensional 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 Pretest-Posttest 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 school-based 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. El-Shaarawi, National Water Research Institute, Burlington, Ontario
and Department of Mathematics and Statistics, McMaster University

Modelling and Analyzing Spatial-Temporal 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 quasi-likelihood 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 high-throughput 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 non-conserved positions are also critical to protein function. In particular, positions may co-evolve, 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 non-conserved but co-evolving 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 Spatio-temporal 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 spatial-temporal pattern formation requires advancement in a new class of partial functional differential equations with non-local delayed nonlinearities. We shall provide a short survey of the motivation, the current theoretical progress and its relevance to West Nile virus propagation.