Studying the relationship between a woman's reproductive lifespan and age at menarche using a Bayesian multivariate structured additive distributional regression model

Studies addressing breast cancer risk factors have been looking at trends relative to age at menarche and menopause. These studies point to a downward trend of age at menarche and an upward trend for age at menopause, meaning an increase of a woman's reproductive lifespan cycle. In addition to studying the effect of the year of birth on the expectation of age at menarche and a woman's reproductive lifespan, it is important to understand how a woman's cohort affects the correlation between these two variables. Since the behavior of age at menarche and menopause may vary with the geographic location of a woman's residence, the spatial effect of the municipality where a woman resides needs to be considered. Thus, a Bayesian multivariate structured additive distributional regression model is proposed in order to analyze how a woman's municipality and year of birth affects a woman's age of menarche, her lifespan cycle, and the correlation of the two. The data consists of 212,517 postmenopausal women, born between 1920 and 1965, who attended the breast cancer screening program in the central region of Portugal