Regressive logistic and proportional hazards disease models for within-family analyses of measured genotypes, with application to a CYP17 polymorphism and breast cancer

Various statistical methods have been proposed to evaluate associations between measured genetic variants and disease, including some using family designs. For breast cancer and rare variants, we applied a modified segregation analysis method that uses the population cancer incidence and population-based case families in which a mutation is known to be segregating. Here we extend the method to a common polymorphism, and use a regressive logistic approach to model familial aggregation by conditioning each individual on their mother's breast cancer history. We considered three models: 1) class A regressive logistic model; 2) age-of-onset regressive logistic model; and 3) proportional hazards familial model. Maximum likelihood estimates were calculated using the software MENDEL. We applied these methods to data from the Australian Breast Cancer Family Study on the CYP17 5UTR TC MspA1 polymorphism measured for 1,447 case probands, 787 controls, and 213 relatives of case probands found to have the CC genotype. Breast cancer data for first- and second-degree relatives of case probands were used. The three methods gave consistent estimates. The best-fitting model involved a recessive inheritance, with homozygotes being at an increased risk of 47% (95% CI, 28-68%). The cumulative risk of the disease up to age 70 years was estimated to be 10% or 22% for a CYP17 homozygote whose mother was unaffected or affected, respectively. This analytical approach is well-suited to the data that arise from population-based case-control-family studies, in which cases, controls and relatives are studied, and genotype is measured for some but not all subjects.