Incorporating tumour pathology information into breast cancer risk prediction algorithms.

INTRODUCTION: Mutations in BRCA1 and BRCA2 confer high risks of breast cancer and ovarian cancer. The risk prediction algorithm BOADICEA (Breast and Ovarian Analysis of Disease Incidence and Carrier Estimation Algorithm) may be used to compute the probabilities of carrying mutations in BRCA1 and BRCA2 and help to target mutation screening. Tumours from BRCA1 and BRCA2 mutation carriers display distinctive pathological features that could be used to better discriminate between BRCA1 mutation carriers, BRCA2 mutation carriers and noncarriers. In particular, oestrogen receptor (ER)-negative status, triple-negative (TN) status, and expression of basal markers are predictive of BRCA1 mutation carrier status. METHODS: We extended BOADICEA by treating breast cancer subtypes as distinct disease end points. Age-specific expression of phenotypic markers in a series of tumours from 182 BRCA1 mutation carriers, 62 BRCA2 mutation carriers and 109 controls from the Breast Cancer Linkage Consortium, and over 300,000 tumours from the general population obtained from the Surveillance Epidemiology, and End Results database, were used to calculate age-specific and genotype-specific incidences of each disease end point. The probability that an individual carries a BRCA1 or BRCA2 mutation given their family history and tumour marker status of family members was computed in sample pedigrees. RESULTS: The cumulative risk of ER-negative breast cancer by age 70 for BRCA1 mutation carriers was estimated to be 55% and the risk of ER-positive disease was 18%. The corresponding risks for BRCA2 mutation carriers were 21% and 44% for ER-negative and ER-positive disease, respectively. The predicted BRCA1 carrier probabilities among ER-positive breast cancer cases were less than 1% at all ages. For women diagnosed with breast cancer below age 50 years, these probabilities rose to more than 5% in ER-negative breast cancer, 7% in TN disease and 24% in TN breast cancer expressing both CK5/6 and CK14 cytokeratins. Large differences in mutation probabilities were observed by combining ER status and other informative markers with family history. CONCLUSIONS: This approach combines both full pedigree and tumour subtype data to predict BRCA1/2 carrier probabilities. Prediction of BRCA1/2 carrier status, and hence selection of women for mutation screening, may be substantially improved by combining tumour pathology with family history of cancer.RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are

A matrix-less and parallel interpolation–extrapolation algorithm for computing the eigenvalues of preconditioned banded symmetric Toeplitz matrices

In the past few years, Bogoya, Bottcher, Grudsky, and Maximenko obtained the precise asymptotic expansion for the eigenvalues of a Toeplitz matrix T-n(f), under suitable assumptions on the generating function f, as the matrix size n goes to infinity. On the basis of several numerical experiments, it was conjectured by Serra-Capizzano that a completely analogous expansion also holds for the eigenvalues of the preconditioned Toeplitz matrix T-n(u)T--1(n)(v), provided f = v/u is monotone and further conditions on u and v are satisfied. Based on this expansion, we here propose and analyze an interpolation-extrapolation algorithm for computing the eigenvalues of T-n(u)T--1(n)(v). The algorithm is suited for parallel implementation and it may be called matrix-less as it does not need to store the entries of the matrix. We illustrate the performance of the algorithm through numerical experiments and we also present its generalization to the case where f = v/u is non-monotone

Fast error analysis of continuous GNSS observations with missing data

One of the most widely used method for the time-series analysis of continuous Global Navigation Satellite System (GNSS) observations is Maximum Likelihood Estimation (MLE) which in most implementations requires O(n3)operations for nn observations. Previous research by the authors has shown that this amount of operations can be reduced to O(n2) for observations without missing data. In the current research we present a reformulation of the equations that preserves this low amount of operations, even in the common situation of having some missing data. Our reformulation assumes that the noise is stationary to ensure a Toeplitz covariance matrix. However, most GNSS time-series exhibit power-law noise which is weakly non-stationary. To overcome this problem, we present a Toeplitz covariance matrix that provides an approximation for power-law noise that is accurate for most GNSS time-series. Numerical results are given for a set of synthetic data and a set of International GNSS Service (IGS) stations, demonstrating a reduction in computation time of a factor of 10–100 compared to the standard MLE method, depending on the length of the time-series and the amount of missing data

Learning detectors quickly with stationary statistics

Computer vision is increasingly becoming interested in the rapid estimation of object detectors. The canonical strategy of using Hard Negative Mining to train a Support Vector Machine is slow, since the large negative set must be traversed at least once per detector. Recent work has demonstrated that, with an assumption of signal stationarity, Linear Discriminant Analysis is able to learn comparable detectors without ever revisiting the negative set. Even with this insight, the time to learn a detector can still be on the order of minutes. Correlation filters, on the other hand, can produce a detector in under a second. However, this involves the unnatural assumption that the statistics are periodic, and requires the negative set to be re-sampled per detector size. These two methods differ chie y in the structure which they impose on the co- variance matrix of all examples. This paper is a comparative study which develops techniques (i) to assume periodic statistics without needing to revisit the negative set and (ii) to accelerate the estimation of detectors with aperiodic statistics. It is experimentally verified that periodicity is detrimental