Interaction

The biologic mechanism that leads to the formation of breast cancer is likely to have multiple component causes that interact. In addition to estimating main effects, statistical

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interaction with non-genetic breast cancer risk factors was evaluated in order to estimate the extent to which those factors influence genotype and haplotype associations. WHR and combined parity and lactation were chosen for interaction analyses because parity without lactation and WHR were two strong risk factors for basal-like breast cancer in the CBCS, the association for those factors and luminal A breast cancer was either weaker or in the opposite direction, and the candidate genes were chosen based on biology associated with these two risk factors (9). I hypothesized that candidate gene associations would be modified in the presence of the environmental risk factor.

Evidence for a biological interaction between genotypes or haplotypes was inferred from measures of statistical interaction calculated from regression models. Statistical interaction, or effect measure modification, occurs when the joint effects of two exposures are not additive for difference measures or not multiplicative for ratio measures. Some have argued that independent steps of a multistage process, such as cancer, have multiplicative effects (78). On the other hand, additive interaction on the risk scale may be more reflective of biological interaction in simple systems (78). As Greenland and colleagues note (78), if both exposures have marginal effects, the presence of exact additivity on one scale implies departure from additivity on another scale.

To limit the number of comparisons, potential effect measure modifiers were selected based on the plausibility of biologic interaction. Two-way interactions between the effect measure modifier and SNPs with a main effect OR greater than 1.5 or less than 0.67 were evaluated to determine whether the joint effect is associated with a departure from additivity or multiplicativity. Although there is a chance that synergistic interactions were missed [SNPs have no effect individually, but have a causal effect when both the effect modifier is

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present (78)] by limiting this analysis to SNPs that showed a main effect, it was necessary to limit the number of interaction terms that were evaluated.

Effect measure modification was evaluated through the introduction of a

multiplicative interaction term to the regression model. Departures from the multiplicative null were evaluated using the likelihood ratio test (LRT), which compares the -2 log-

likelihood of nested models under the null hypothesis that the addition of the interaction term does not improve model fit. Likelihood ratio test P-values less than 0.10 were considered evidence of multiplicative interaction, and stratified ORs were calculated for those SNPs.

Departures from the additive null were evaluated by calculating the synergy index (S) and the corresponding 90% CI (79). S compares the excess risk of joint exposure allowing for interaction to the excess risk of joint exposure under the additive null. The null value for S is 1; values less than 1 indicate less than additive interaction and values greater than 1 indicate greater than additive interaction. Although the interaction contrast ratio (ICR) is commonly used to assess additive interaction and may have a more accessible interpretation, the ICR is not valid when covariates are included in the logistic regression model (80). All models in this analysis must be adjusted for age and self-identified race due to frequency matching. This problem may be avoided if the ICR is estimated using a linear odds ratio model instead of a log-linear model (80, 81), however procedures available to fit linear odds ratio models in SAS did not allow for the incorporation of an offset term.

A basic logistic regression model allowing for interaction is: logit[D=1|X=x] = α + β1X1 + β2X2 + β3(X1)(X2) where α = regression model intercept

127 X2 = effect modifier

β1 = effect of exposure on outcome β2 = effect of effect modifier on outcome β3 = excess effect due to joint exposure The synergy index is calculated as:

S= [e(β1 + β2 + β3) – 1]/[(eβ1 -1) + (eβ2 -1)] 2.8.1 Parity and lactation variable definition

Parity was measured by self-report during the study interview. Women were asked how many times they had been pregnant in their lifetime, including the current pregnancy if they were pregnant at the time of the interview. Women were then asked the duration of each pregnancy and the outcome. Parity was defined as the total number of full-term births

reported by the study subject. Lactation was measured by self-report during the study interview. For each live birth reported, women were asked whether they breastfed the baby and for how long (in months). Only 5 subjects with genotyping data were missing

information on lactation history. This constitutes less than 1% of the population and is unlikely to bias the results. There was no missing data for parity.

The association between parity and basal-like breast cancer did not differ for CBCS participants with 1-2 children compared to 3 or more children (where nulliparous women were the referent group) for women with the same lactation status (9). Likewise, the association between parity and lactation and luminal A breast cancer was the same for women with 1-2 children compared to women with 3 or more children for women with the same lactation status (9). Therefore, parity and lactation was defined as a single 3-category variable: nulliparous (controls N=201; all cases N=301; luminal A N=111; basal-like N=24),

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parous/never breastfed (controls N=878; all cases N=983; luminal A N=317; basal-like N=124), and parous/ever breastfed (controls N=694; all cases N=686; luminal A N=251; basal-like N=52).

2.8.2 Waist-hip ratio (WHR) variable definition

WHR was calculated as the ratio of waist circumference to hip circumference. Waist and hip circumference were measured using a tape measure by a trained nurse-interviewer during the study interview and were recorded to the nearest half centimeter. The waist measurement was taken at the natural indentation of the waist. Hip circumference was

measured at the greatest protrusion of the buttocks. Both measurements were taken twice and averaged. If measurements differed by more than 1 cm, a third measurement was taken and the two closest measurements were averaged.

WHR was categorized based on the tertile distribution CBCS controls. Associations between WHR and basal-like breast cancer and WHR and luminal A breast cancer were similar for tertile 2 and tertile 3 (vs. tertile 1) in the CBCS (9), and so the top two tertiles were combined. Data on WHR was missing for 21 controls and 29 cases (5 basal-like cases, 7 luminal A cases). The proportion of missing WHR data was similar for cases compared to controls as well as basal-like cases compared to controls and luminal A cases compared to controls.

2.8.3 Body mass index (BMI) variable definition

Studies suggest that body mass index (BMI, weight in kg/height in m2) is a confounder of the association between WHR and breast cancer in premenopausal women [reviewed by (82, 83)]. Preliminary analyses showed that BMI was a confounder of the association between WHR and breast cancer in the CBCS; ORs estimated from models not

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adjusting for BMI were closer to the null (data not shown). Therefore, all models estimating WHR parameters were adjusted for BMI. BMI was calculated from height and weight measured during the study visit. Weight was the average of two measurements taken using a standardized scale and recorded to the nearest half kilogram. Height was the average of two measurements made to the nearest half centimeter.

BMI data was missing for 78 subjects with genotyping data (37 controls, 41 cases, 5 basal-like cases and 15 luminal A cases), 10 of whom were classified as WHR < 0.77, 30 of whom were classified as WHR ≥ 0.77, and 38 of whom were missing WHR data.

A total of 90 of 3748 (2%) genotyped subjects (40 controls, 50 cases, 6 basal-like cases, 17 luminal A cases) were missing data for either WHR or BMI and were excluded from the WHR effect measure modification analysis. Proportions of subjects missing data for either WHR or BMI did not differ by case status. The low proportion of missing data

combined with the fact that missingness was unrelated to case status strongly indicate that missing WHR or BMI data was not a source of bias in the WHR interaction analyses.