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Statistical underpinnings of mutational signature analyses


Project Description

Mutational signatures have been one of the hot topics of cancer research for the past six years. The idea that one can take the mutational profile of a sample and infer the processes that have acted on the tumour over time is an extremely attractive one. One successful approach using non-negative matrix factorization has become extremely popular [1].
We can consider a generalized approach that proceeds as follows: Somatic mutations are identified in samples and sorted into c classes. An n x c contingency table (M) is then constructed by counting the numbers of mutations in each class for each of n patients. We then decompose the matrix M into W x S where S is a Signature matrix of dimension s x c, and W is a weights matrix of dimension n x s. The interpretation being that each column of S represents the mutation signature of a real physical process (e.g. Smoking, UV light exposure) and the row of W indicates how much weight that signature has for a particular patient.
While these methods have been hugely successful, there are a number of statistical questions such as 1) How do we incorporate uncertainty in the measurements M? 2) How do we estimate and report uncertainty about W and S? 3) How do we determine the power of a data set to estimate W and S? 4) How do we ensure a minimal distance between columns of S? 5) How do we incorporate prior information about S? 6) How do we deal with population structures? 7) Can we allow for non-additive contributions of signatures?
This project is to resolve some of the statistical underpinnings of this important methodology.

Funding Notes

Multiple sources of scholarship funding are potentially available, including university, research council (EPSRC) and research group (CREEM). Some are open to international students, some to EU and some UK only.

Applicants should have a good first degree in mathematics, statistics or another discipline with substantial numerical component. Applicants with degrees in other subjects (e.g., biology) should have the equivalent of A-level/Higher mathematics, and experience using statistical methods; such candidates should discuss their qualifications with the Postgraduate Officer. A masters-level degree is an advantage.

Further details of the application procedure, including contact details for the Postgraduate Officer, are available at View Website

References

[1] Alexandrov et al. Cell Rep. 2013 Jan 31; 3(1): 246–259.

How good is research at University of St Andrews in Mathematical Sciences?

FTE Category A staff submitted: 30.60

Research output data provided by the Research Excellence Framework (REF)

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