In modern genetic epidemiology studies, the association between the disease and a genomic region, such as a candidate gene, is often investigated using multiple SNPs. We propose a multilocus test of genetic association that can account for genetic effects that might be modified by variants in other genes or by environmental factors. We consider use of the venerable and parsimonious Tukey's 1-degree-of-freedom model of interaction, which is natural when individual SNPs within a gene are associated with disease through a common biological mechanism; in contrast, many standard regression models are designed as if each SNP has unique functional significance. On the basis of Tukey's model, we propose a novel but computationally simple generalized test of association that can simultaneously capture both the main effects of the variants within a genomic region and their interactions with the variants in another region or with an environmental exposure. We compared performance of our method with that of two standard tests of association, one ignoring gene-gene/gene-environment interactions and the other based on a saturated model of interactions. We demonstrate major power advantages of our method both in analysis of data from a case-control study of the association between colorectal adenoma and DNA variants in the NAT2 genomic region, which are well known to be related to a common biological phenotype, and under different models of gene-gene interactions with use of simulated data.

Breast cancer is a morphologically and clinically heterogeneous disease; however, it is less clear how risk factors relate to tumour features. We evaluated risk factors by tumour characteristics (histopathologic type, grade, size, and nodal status) in a populationbased case -control of 2386 breast cancers and 2502 controls in Poland. Use of a novel extension of the polytomous logistic regression permitted simultaneous modelling of multiple tumour characteristics. Late age at first full-term birth was associated with increased risk of large (42 cm) tumours (odds ratios (95% confidence intervals) 1.19 (1.07 -1.33) for a 5-year increase in age), but not smaller tumours (P for heterogeneity adjusting for other tumour features (P het ) ¼ 0.007). On the other hand, multiparity was associated with reduced risk for small tumours (0.76 (0.68 -0.86) per additional birth; P het ¼ 0.004). Consideration of all tumour characteristics simultaneously revealed that current or recent use of combined hormone replacement therapy was associated with risk of small (2.29 (1.66 -3.15)) and grade 1 (3.36 (2.22 -5.08)) tumours (P het ¼ 0.05 for size and 0.0008 for grade 1 vs 3), rather than specific histopathologic types (P het ¼ 0.63 for ductal vs lobular). Finally, elevated body mass index was associated with larger tumour size among both pre-and postmenopausal women (P het ¼ 0.05 and 0.0001, respectively). None of these relationships were explained by hormone receptor status of the tumours. In conclusion, these data support distinctive risk factor relationships by tumour characteristics of prognostic relevance. These findings might be useful in developing targeted prevention efforts.

Family-based case-control studies are popularly used to study the effect of genes and gene-environment interactions in the etiology of rare complex diseases. We consider methods for the analysis of such studies under the assumption that genetic susceptibility (G) and environmental exposures (E) are independently distributed of each other within families in the source population. Conditional logistic regression, the traditional method of analysis of the data, fails to exploit the independence assumption and hence can be inefficient. Alternatively, one can estimate the multiplicative interaction between G and E more efficiently using cases only, but the required population-based G-E independence assumption is very stringent. In this article, we propose a novel conditional likelihood framework for exploiting the within-family G-E independence assumption. This approach leads to a simple and yet highly efficient method of estimating interaction and various other risk parameters of scientific interest. Moreover, we show that the same paradigm also leads to a number of alternative and even more efficient methods for analysis of family-based case-control studies when parental genotype information is available on the case-control study participants. Based on these methods, we evaluate different family-based study designs by examining their relative efficiencies to each other and their efficiencies compared to a population-based case-control design of unrelated subjects. These comparisons reveal important design implications. Extensions of the methodologies for dealing with complex family studies are also discussed.

In case-control studies of inherited diseases, participating subjects (probands) are often interviewed to collect detailed data about disease history and age-at-onset information in their family members. Genotype data are typically collected from the probands, but not from their relatives. In this article, we introduce an approach that combines case-control analysis of data on the probands with kin-cohort analysis of disease history data on relatives. Assuming a marginally specified multivariate survival model for joint risk of disease among family members, we describe methods for estimating relative risk, cumulative risk, and residual familial aggregation. We also describe a variation of the methodology that can be used for kin-cohort analysis of the family history data from a sample of genotyped cases only. We perform simulation studies to assess performance of the proposed methodologies with correct and mis-specified models for familial aggregation. We illustrate the proposed methodologies by estimating the risk of breast cancer from BRCA1/2 mutations using data from the Washington Ashkenazi Study.

Evidence suggests that breast cancer hormone receptor status varies by etiologic factors, but studies have been inconsistent. In a population-based case-control study in Poland that included 2,386 cases and 2,502 controls, we assessed ER-a and PR status of tumors based on clinical records according to etiologic exposure data collected via interview. For 842 cancers, we evaluated ER-a, ER-b, PR and HER2 levels by semiquantitative microscopic scoring of immunostained tissue microarrays and a quantitative immunofluorescence method, automated quantitative analysis (AQUA TM ). We related marker levels in tumors to etiologic factors, using standard regression models and novel statistical methods, permitting adjustment for both correlated tumor features and exposures. Results obtained with different assays were generally consistent. Receptor levels varied most significantly with body mass index (BMI), a factor that was inversely related to risk among premenopausal women and directly related to risk among postmenopausal women with larger tumors. After adjustment for correlated markers, exposures and pathologic characteristics, PR and HER2 AQUA levels were inversely related to BMI among premenopausal women ( p-trend 5 0.01, both comparisons), whereas among postmenopausal women, PR levels were associated directly with BMI ( p-trend 5 0.002). Among postmenopausal women, analyses demonstrated that BMI was related to an interaction of PR and HER2: odds ratio (OR) 5 0.86 (95% CI 5 0.69-1.07) for low PR and HER2 expression vs. OR 5 1.78 (95% CI 5 1.25-2.55) for high expression (p-heterogeneity 5 0.001). PR and HER2 levels in breast cancer vary by BMI, suggesting a heterogeneous etiology for tumors related to these markers. ' 2007 Wiley-Liss, Inc.Key words: breast; etiology; hormones; epidemiology Amassing data suggest that breast cancers are characterized by ''molecular portraits'' that are established at inception, remain stable over time and represent critical determinants of tumor biology.1 Hormone receptor status is a key parameter in molecular classifications of breast cancer, 2,3 which serves as a marker of hormone-dependent growth and predictor of responsiveness to hormonal treatments. Consequently, researchers have hypothesized that etiologic factors mediated by hormones might be more strongly associated with breast cancers that express hormone receptors when compared with those that are receptor-negative. 4,5 A recent literature review found evidence that nulliparity, late age at first birth and postmenopausal obesity are associated with greater risk for estrogen receptor-a (ER-a)-positive cancers when compared with ER-a-negative tumors, and that early menarche was more strongly linked to tumors coexpressing ER-a and progesterone receptor (PR). 4 Subsequently, a metaanalysis updating this review affirmed the heterogeneous associations for nulliparity and late age at first birth, but not for age at menarche. 5 However, results of studies have not been entirely consistent, especially when limited by small sample sizes,...