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Shape restricted regressions, including isotonic regression and concave regression as special cases, are studied using priors on Bernstein polynomials and Markov chain Monte Carlo methods. These priors have large supports, select only smooth functions, can easily incorporate geometric information into the prior, and can be generated without computational difficulty. Algorithms generating priors and posteriors are proposed, and simulation studies are conducted to illustrate the performance of this approach. Comparisons with the density-regression method of Dette et al. (2006) are included.Comment: Published at http://dx.doi.org/10.1214/074921707000000157 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

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Maternal and environmental factors in the study could not explain the decline in exclusive breastfeeding. The decline in exclusive breastfeeding, accompanying the increase in partial breastfeeding, suggests that more support is needed for mothers who intend to breastfeed exclusively.

Given the functional relevance of many rare variants, their identification is frequently critical for dissecting disease etiology. Functional variants are likely to be aggregated in family studies enriched with affected members, and this aggregation increases the statistical power to detect rare variants associated with a trait of interest. Longitudinal family studies provide additional information for identifying genetic and environmental factors associated with disease over time. However, methods to analyze rare variants in longitudinal family data remain fairly limited. These methods should be capable of accounting for different sources of correlations and handling large amounts of sequencing data efficiently. To identify rare variants associated with a phenotype in longitudinal family studies, we extended pedigree-based burden (BT) and kernel (KS) association tests to genetic longitudinal studies. Generalized estimating equation (GEE) approaches were used to generalize the pedigree-based BT and KS to multiple correlated phenotypes under the generalized linear model framework, adjusting for fixed effects of confounding factors. These tests accounted for complex correlations between repeated measures of the same phenotype (serial correlations) and between individuals in the same family (familial correlations). We conducted comprehensive simulation studies to compare the proposed tests with mixed-effects models and marginal models, using GEEs under various configurations. When the proposed tests were applied to data from the Diabetes Heart Study, we found exome variants of POMGNT1 and JAK1 genes were associated with type 2 diabetes.

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IMPORTANCEThe number of children born through the use of assisted reproductive technology (ART) has been increasing. These children may have higher risks for epigenetic alteration and adverse perinatal outcomes, which may be associated with childhood cancers. OBJECTIVETo determine the associations between different modes of conception and childhood cancers and potential mediation by preterm birth and low birth weight.