Bayesian model search and multilevel inference for SNP association studies

Technological advances in genotyping have given rise to hypothesis-based association studies of increasing scope. As a result, the scientific hypotheses addressed by these studies have become more complex and more difficult to address using existing analytic methodologies. Obstacles to analysis include inference in the face of multiple comparisons, complications arising from correlations among the SNPs (single nucleotide polymorphisms), choice of their genetic parametrization and missing data. In this paper we present an efficient Bayesian model search strategy that searches over the space of genetic markers and their genetic parametrization. The resulting method for Multilevel Inference of SNP Associations, MISA, allows computation of multilevel posterior probabilities and Bayes factors at the global, gene and SNP level, with the prior distribution on SNP inclusion in the model providing an intrinsic multiplicity correction. We use simulated data sets to characterize MISA's statistical power, and show that MISA has higher power to detect association than standard procedures. Using data from the North Carolina Ovarian Cancer Study (NCOCS), MISA identifies variants that were not identified by standard methods and have been externally ``validated'' in independent studies. We examine sensitivity of the NCOCS results to prior choice and method for imputing missing data. MISA is available in an R package on CRAN.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS322 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

MULTIPLE MODEL EVALUATION ABSENT THE GOLD STANDARD VIA MODEL COMBINATION

We describe a method for evaluating an ensemble of predictive models given a sample of observations comprising the model predictions and the outcome event measured with error. Our formulation allows us to simultaneously estimate measurement error parameters, true outcome — aka the gold standard — and a relative weighting of the predictive scores. We describe conditions necessary to estimate the gold standard and for these estimates to be calibrated and detail how our approach is related to, but distinct from, standard model combination techniques. We apply our approach to data from a study to evaluate a collection of BRCA1/BRCA2 gene mutation prediction scores. In this example, genotype is measured with error by one or more genetic assays. We estimate true genotype for each individual in the dataset, operating characteristics of the commonly used genotyping procedures and a relative weighting of the scores. Finally, we compare the scores against the gold standard genotype and find that Mendelian scores are, on average, the more refined and better calibrated of those considered and that the comparison is sensitive to measurement error in the gold standard

Hosts of avian brood parasites have evolved egg signatures with elevated information content.

Hosts of brood-parasitic birds must distinguish their own eggs from parasitic mimics, or pay the cost of mistakenly raising a foreign chick. Egg discrimination is easier when different host females of the same species each lay visually distinctive eggs (egg 'signatures'), which helps to foil mimicry by parasites. Here, we ask whether brood parasitism is associated with lower levels of correlation between different egg traits in hosts, making individual host signatures more distinctive and informative. We used entropy as an index of the potential information content encoded by nine aspects of colour, pattern and luminance of eggs of different species in two African bird families (Cisticolidae parasitized by cuckoo finches Anomalospiza imberbis, and Ploceidae by diederik cuckoos Chrysococcyx caprius). Parasitized species showed consistently higher entropy in egg traits than did related, unparasitized species. Decomposing entropy into two variation components revealed that this was mainly driven by parasitized species having lower levels of correlation between different egg traits, rather than higher overall levels of variation in each individual egg trait. This suggests that irrespective of the constraints that might operate on individual egg traits, hosts can further improve their defensive 'signatures' by arranging suites of egg traits into unpredictable combinations.EMC was supported by the Pomona College-Downing College Student Exchange Scholarship, MS by a BBSRC David Phillips Research Fellowship (BB/G022887/1), and CNS by a Royal Society Dorothy Hodgkin Fellowship, a BBSRC David Phillips Research Fellowship (BB/J014109/1), and the DST-NRF Centre of Excellence at the Percy FitzPatrick Institute.This is the final version of the article. It first appeared from Royal Society Publishing via http://dx.doi.org/10.1098/rspb.2015.059

Effects of Stone Size on the Comminution Process and Efficiency in Shock Wave Lithotripsy

The effects of stone size on the process and comminution efficiency in shock wave lithotripsy (SWL) are investigated by experiments, numerical simulations, and scale analysis. Cylindrical BegoStone phantoms with approximately equal height and diameter of either 4-, or 7- or 10-mm, in a total aggregated mass of about 1.5 g, were treated in an electromagnetic shock wave lithotripter field. The resultant stone comminution (SC) was found to correlate closely with the average peak pressure, P+(avg), incident on the stones. The P+(avg) threshold to initiate stone fragmentation in water increased from 7.9 to 8.8 to 12.7 MPa, respectively, when the stone size decreased from 10 to 7 to 4 mm. Similar changes in the P+(avg) threshold were observed for the 7- and 10-mm stones treated in 1,3-butanediol where cavitation is suppressed, suggesting that the observed size dependency is due to changes in stress distribution within different size stones. Moreover, the slope of the correlation curve between SC and ln(P‒+(avg)) in water increased with decreasing stone size, while the opposite trend was observed in 1,3-butanediol. The progression of stone comminution in SWL showed a size-dependency with the 7- and 10-mm stones fragmented into progressively smaller pieces while a significant portion (> 30%) of the 4-mm stones were stalemated within the size range of 2.8 ~ 4 mm even after 1,000 shocks. Analytical scaling considerations suggest size-dependent fragmentation behaviour, a hypothesis further supported by numerical model calculations that exhibit changing patterns of constructive and destructive wave interference, and thus variations in the maximum tensile stress or stress integral produced in cylindrical and spherical stone of different sizes

OPTIMIZED CROSS-STUDY ANALYSIS OF MICROARRAY-BASED PREDICTORS

Background: Microarray-based gene expression analysis is widely used in cancer research to discover molecular signatures for cancer classification and prediction. In addition to numerous independent profiling projects, a number of investigators have analyzed multiple published data sets for purposes of cross-study validation. However, the diverse microarray platforms and technical approaches make direct comparisons across studies difficult, and without means to identify aberrant data patterns, less than optimal. To address this issue, we previously developed an integrative correlation approach to systematically address agreement of gene expression measurements across studies, providing a basis for cross-study validation analysis. Here we generalize this methodology to provide a metric for evaluating the overall efficacy of preprocessing and cross-referencing, and explore optimal combinations of filtering and cross-referencing strategies. We operate in the context of validating prognostic breast cancer gene expression signatures on data reported by three different groups, each using a different platform. Results: To evaluate overall cross-platform reproducibility in the context of a specific prediction problem, we suggest integrative association, that is the cross-study correlation of gene-specific measure of association with the phenotype predicted. Specifically, in this paper we use the correlation among the Cox proportional hazard coefficients for association of gene expression to relapse free survival (RFS). Gene filtering by integrative correlation to select reproducible genes emerged as the key factor to increase the integrative association, while alternative methods of gene cross-referencing and gene filtering proved only to modestly improve the overall reproducibility. Patient selection was another major factor affecting the validation process. In particular, in one of the studies considered, gene expression association with RFS varied across subsets of patients that differ by their ascertainment criteria. One of the subsets proved to be highly consistent with other studies, while others showed significantly lower consistency. Third, as expected, use of cluster-specific mean expression profiles in the Cox model yielded more generalizable results than expression data from individual genes. Finally, by using our approach we were able to validate the association between the breast cancer molecular classes proposed by Sorlie et al. and RFS. Conclusions: This paper provides a simple, practical and comprehensive technique for measuring consistency of molecular classification results across microarray platforms, without requiring subjective judgments about membership of samples in putative clusters. This methodology will be of value in consistently typing breast and other cancers across different studies and platforms in the future. Although the tumor subtypes considered here have been previously validated by their proponents, this is the first independent validation, and the first to include the Affymetrix platform

Low Concordance Between T-Cell Densities in Matched Primary Tumors and Liver Metastases in Microsatellite Stable Colorectal Cancer

Background: The subtype, density and location of tumor infiltrating T-cells are being explored as prognostic and predictive biomarkers in primary colorectal cancer (pCRC) and colorectal liver metastases (CLM). Very limited data exist comparing findings in pCRC and matched CLM. Patients and methods: Fifty-eight patients with available pCRC and matched CLM (57/58 microsatellite stable) were included in this OSLO-COMET substudy. In immunohistochemically stained sections, total (Ttot), helper (TH), cytotoxic (CTL), and regulatory (Treg) T-cells were manually counted in hotspots from the invasive margin (IM), intratumor (IT), and tumor adjacent regions to determine T-cell densities. Results: A striking accumulation of T-cells was found in IM of both pCRC and CLM with much lower densities in the IT region, exemplified by Ttot of 2838 versus 340 cells/mm2, respectively, in CLM. The correlation at the individual level between T-cell densities in pCRC and corresponding CLM was poor for all regions and T-cell subtypes; for instance, the correlation coefficient (R2) for IM Ttot was 0.07. The IT TH : CTL and Treg : TH ratios were 2.94 and 0.44, respectively, in pCRC, and 1.84 and 0.24, respectively, in CLM. Conclusion: The observed accumulation of T-cells in the IM regions of pCRC and CLM with low penetration to the IT regions, combined with high TH : CTL and Treg : TH ratios, point to the presence of an immune suppressive microenvironment. T-cell densities of CLM differed markedly from the matched pCRC, indicating that to evaluate T-cell biomarkers in metastasis, the commonly available pCRC cannot serve as a surrogate for the metastatic tumor

Regular Multivitamin Supplement Use, Single Nucleotide Polymorphisms in ATIC, SHMT2, and SLC46A1, and Risk of Ovarian Carcinoma

ATIC, SHMT2, and SLC46A1 have essential roles in one-carbon (1-C) transfer. The authors examined whether associations between ovarian carcinoma and 15 variants in these genes are modified by regular multivitamin use, a source of 1-C donors, among Caucasian participants from two US case–control studies. Using a phased study design, variant-by-multivitamin interactions were tested, and associations between variants and ovarian carcinoma were reported stratified by multivitamin supplement use. Per-allele risk associations were modified by multivitamin use at six variants among 655 cases and 920 controls (Phase 1). In a larger sample of 968 cases and 1,265 controls (Phases 1 and 2), interactions were significant (P ≤ 0.03) for two variants, particularly among regular multivitamin users: ATIC rs7586969 [odds ratio (OR) = 0.7, 95% confidence interval (CI) = 0.6–0.9] and ATIC rs16853834 (OR = 1.5, 95% CI = 1.1–2.0). The two ATIC single nucleotide polymorphisms (SNPs) did not share the same haplotype; however, the haplotypes they comprised mirrored their SNP risk associations among regular multivitamin supplement users. A multi-variant analysis was also performed by comparing the observed likelihood ratio test statistic from adjusted models with and without the two ATIC variant-by-multivitamin interaction terms with a null distribution of test statistics generated by permuting case status 10,000 times. The corresponding observed P value of 0.001 was more extreme than the permutation-derived P value of 0.009, suggesting rejection of the null hypothesis of no association. In summary, there is little statistical evidence that the 15 variants are independently associated with risk of ovarian carcinoma. However, the statistical interaction of ATIC variants with regular multivitamin intake, when evaluated at both the SNP and gene level, may support these findings as relevant to ovarian health and disease processes

Hormonal Risk Factors for Ovarian Cancer in Premenopausal and Postmenopausal Women

Ovarian cancer is most frequently diagnosed in postmenopausal women; however, the strongest risk predictors, pregnancy and oral contraceptive use, occur in most women in their twenties and thirties. Relatively few studies have examined how reproductive risk factors vary between pre- and postmenopausal ovarian cancer. The authors used data from a population-based, case-control study of ovarian cancer (896 cases, 967 controls) conducted in North Carolina from 1999 to 2006. Odds ratios and 95% confidence intervals were calculated by using unconditional logistic regression. Inverse associations with ovarian cancer were observed with duration of oral contraceptive use, later age at last use, and more recent use among premenopausal women; no significant associations were found for postmenopausal women. Analyses limited to oral contraceptive users showed that duration was a more significant predictor of risk than was timing of use. Parity was inversely associated with premenopausal but not postmenopausal ovarian cancer. Later age at pregnancy was associated with reduced risk for both pre- and postmenopausal women. Analyses among parous women showed that pregnancy timing was a stronger risk predictor than number of pregnancies. Findings suggest that associations between ovarian cancer and reproductive characteristics vary by menopausal status. Additional research is needed to further elucidate risk factors for postmenopausal disease