Rademacher and Gaussian complexities: Risk bounds and structural results

We investigate the use of certain data-dependent estimates of the complexity of a function class, called Rademacher and Gaussian complexities. In a decision theoretic setting, we prove general risk bounds in terms of these complexities. We consider function classes that can be expressed as combinations of functions from basis classes and show how the Rademacher and Gaussian complexities of such a function class can be bounded in terms of the complexity of the basis classes. We give examples of the application of these techniques in finding data-dependent risk bounds for decision trees, neural networks and support vector machines.

Common variation in the fibroblast growth factor receptor 2 gene is not associated with endometriosis risk

BACKGROUND Endometriosis is a polygenic disease with a complex and multifactorial aetiology that affects 8-10% of women of reproductive age. Epidemiological data support a link between endometriosis and cancers of the reproductive tract. Fibroblast growth factor receptor 2 (FGFR2) has recently been implicated in both endometrial and breast cancer. Our previous studies on endometriosis identified significant linkage to a novel susceptibility locus on chromosome 10q26 and the FGFR2 gene maps within this linkage region. We therefore hypothesized that variation in FGFR2 may contribute to the risk of endometriosis. METHODS We genotyped 13 single nucleotide polymorphisms (SNPs) densely covering a 27 kb region within intron 2 of FGFR2 including two SNPs (rs2981582 and rs1219648) significantly associated with breast cancer and a total 40 tagSNPs across 150 kb of the FGFR2 gene. SNPs were genotyped in 958 endometriosis cases and 959 unrelated controls. RESULTS We found no evidence for association between endometriosis and FGFR2 intron 2 SNPs or SNP haplotypes and no evidence for association between endometriosis and variation across the FGFR2 gene. CONCLUSIONS Common variation in the breast-cancer implicated intron 2 and other highly plausible causative candidate regions of FGFR2 do not appear to be a major contributor to endometriosis susceptibility in our large Australian sample.

The impact of nonlinear exposure risk relationships on seasonal time series data: modelling danish neonatal birth anthropometric data

Background Birth weight and length have seasonal fluctuations. Previous analyses of birth weight by latitude effects identified seemingly contradictory results, showing both 6 and 12 monthly periodicities in weight. The aims of this paper are twofold: (a) to explore seasonal patterns in a large, Danish Medical Birth Register, and (b) to explore models based on seasonal exposures and a non-linear exposure-risk relationship. Methods Birth weight and birth lengths on over 1.5 million Danish singleton, live births were examined for seasonality. We modelled seasonal patterns based on linear, U- and J-shaped exposure-risk relationships. We then added an extra layer of complexity by modelling weighted population-based exposure patterns. Results The Danish data showed clear seasonal fluctuations for both birth weight and birth length. A bimodal model best fits the data, however the amplitude of the 6 and 12 month peaks changed over time. In the modelling exercises, U- and J-shaped exposure-risk relationships generate time series with both 6 and 12 month periodicities. Changing the weightings of the population exposure risks result in unexpected properties. A J-shaped exposure-risk relationship with a diminishing population exposure over time fitted the observed seasonal pattern in the Danish birth weight data. Conclusion In keeping with many other studies, Danish birth anthropometric data show complex and shifting seasonal patterns. We speculate that annual periodicities with non-linear exposure-risk models may underlie these findings. Understanding the nature of seasonal fluctuations can help generate candidate exposures.