PhD position in Applied Statistics in Quantitative Genetics

PhD position in Applied Statistics in Quantitative Genetics
at the Aarhus University, DJF, Department of Genetics and Biotechnology
Research Group for Bioinformatics, Genetics and Statistics

score function of two mixtures of piecewise constant hazard models

Closing date for applications: 15 April 2009 at 12.00 noon

Project summary:
The project will develop mathematical and statistical methods for modelling incompletely observed traits (censored or truncated) and events of low frequency in large-scale quantitative genetic studies. The general idea is to explore the close mathematical connection between modern methods of event-history-analysis and nested case-control techniques to develop a range of statistical tools relevant to applications in quantitative genetics. The project is related to an existing research line on livestock quantitative genetics and breeding value prediction at the Research Group of Bioinformatics, Genetics and Statistics. See further details on the project below.

Supervision:
Rodrigo Labouriau (main supervisor), PhD (Mathematical Statistics)
Per Madsen, PhD (Quantitative Genetics)

Application procedure:

The application should be sent in a single file in pdf format. This file should include the application form and all the documents you want to annex for the evaluation. We will only consider applications meeting all the requirements stated in the official application form
The application form can be found by clicking here.
The closing date for applications is 15 April 2009 at 12.00 noon (Danish time, i.e. +1 GWT)
Applications received after the closing date will not be considered!
Please send your application to the following address: SAFE@agrsci.dk (or click here to send an e-mail applying).

Selection criteria and required qualifications:

Qualifications:

A relevant Master's degree (or equivalent), e.g. a master in mathematics/statistics or a master in genetics (but in this case with a very strong mathematical and statistical background, see the selection criteria below)
Fluent English spoken and written.

Selection criteria:

The project requires a strong background in statistics and probability theory.
It is necessary that the candidate has already had contact with formal probability theory (e.g. axiomatic treatment of probability, stochastic processes) and theoretical statistics (e.g. classic theory of inference in parametric models, multivariate analysis and models for discrete variables as log-linear models), since it will not be possible (due to time limitations) to build-up these basic skills during the PhD program.
Computer skills and some experience with applied statistics are required.
Knowledge of general biology and specifically basic genetics will be considered an advantage, but will not be a necessary condition.

Employment conditions:
For further information on employment conditions are described in the official announcement that can be found by clicking here.

Negative information function of a mixture of piecewise constant hazard models

Further details on the project:

Background:
Event-history- and survival-analysis study the time to occurrence of some specified event of interest. Classical examples are time to death, onset of diseases, observation of certain behaviour, occurrence of the first oestrus, seed germination, flowering, etc. All the above-mentioned examples occurred at least once in real research work at DJF and resulted in at least one published article from the supervisors. Typically the time of occurrence of an event is incompletely observed (e.g. right censoring when the time to occurrence is known to be larger than a given value; or interval censoring, when the time to occurrence is know to fall in an interval) which substantially complicates the analysis. Although some of the classic methods for analysing right-censored data have already been adapted and implemented in animal breeding, including the development of suitable software (e.g. DMU), there is still a need for basic improvements in the area. Unfortunately, the use of these techniques in real examples is limited by a prohibitive computational burden (e.g. calculation of animal breeding values) or lack of generality (e.g. occurrence of interval censoring and informative censoring in plant genetics and animal fertility studies). Recently, a range of methods has been developed for epidemiological and complex clinical studies that are similar to the problems described above. These techniques are based on proper sampling and use of nested case-control and related techniques that are equivalent to classic models of event-history-analysis. This had a strong impact on the area of human epidemiology. Although the mathematics behind those methods is rather sophisticated, its use is relatively simple and might reduce considerably the computation burden. Proper applications of these methods in applied genetics will, of course, require not only the correct use of the mathematical techniques, but also a good understanding of the genetics and physiology involved.

Work description:
The project aims to develop mathematical and statistical methods for modelling incompletely observed traits (censored or truncated) and events with low frequency in large-scale quantitative genetic studies. In both cases the project will aim to develop multivariate extensions allowing simultaneously modelling traits of different nature (e.g. by applying suitable multivariate versions of generalized linear mixed models).
In the case of the incompletely observed traits the typical example is the time to occurrence of an event (e.g. death, conception or disease onset) and the idea is to adapt classic techniques of event-history analysis and survival analysis (Cox proportional models, frailty models, accelerated failure models, etc) to a context of quantitative genetics with complex structure of random components. We will investigate alternative inference methods based on computer intensive re-sampling techniques and suitable U-statistics.
With regards to modelling events with low frequency, the idea is to take advantage of the close mathematical connection between modern methods of event-history-analysis and nested case-control techniques, to develop a range of statistical tools relevant to applications in quantitative genetics. This will make use of the modern theory of counting processes.
The applications of the methods developed in the project will involve genetic studies on longevity of sows, mortality of cows and disease incidence in pigs, among others. The project is related to and extends an existing research line on livestock quantitative genetics and breeding value prediction at the Research Group of Bioinformatics, Genetics and Statistics.

Research environment:
The project is related to an important research line of the Research Group of Bioinformatics, Genetics and Statistics (BGS), namely development and implementation of statistical methods in quantitative genetics (specifically inference on variance components and breeding value prediction). The group has strong expertise in this subject and have developed original research in the use of survival analysis in applied quantitative genetics (including software development, DMU). The group is part of a strong international research network in this subject.