Models to Assess the Association of a Semiquantitative Exposure With Outcomes

Newly Identified Gross Human Anatomy: Eight Paired Vestigial Breast Mounds Run along the Embryological Mammary Ridges in Lean Adults

Although isolated accessory breasts have been reported in many locations on the torso, we noted that lean men presenting for liposuction had mounds of fullness in a curvilinear array (axilla to groin) consistent with the configuration of the embryological mammary ridge. We hypothesized that grid mapping and pinch testing would elucidate the pattern of fullness and its relation to the "milk line."

METHODS

Twenty lean participants (10 men, 10 women) each underwent standardized photography and grid mapping of anterior torsos. We then pinch-tested each for subcutaneous fullness in 250 standardized loci. We used plotted pinch values and OLS regression models to determine if focal fullness corresponded to published configurations of the embryologic mammary ridge.

RESULTS

We identified a pattern of paired mounds in all participants running bilaterally in curved linear arrays from axillae to groin in the exact form of milk lines. Regression models applied to the male and female pinch data indicated that focal thickness matched mammary ridge configurations in all subjects (P = 0.023 for men, <0.001 for women). Fatty fullness never appeared elsewhere on the anterior torsos.

CONCLUSIONS

The linear pattern of paired focal fat mounds present on the anterior torsos is consistent with the paths of embryological mammary ridges, suggesting these focal fat pads are of breast origin. The consistent mounds are distinct from general subcutaneous fullness and therefore represent a new finding of gross human anatomy. We recommend further research to define differential physiology of distinct subpopulations of yellow fat and clinical implications.

The minimum intensity of a mixed exposure that increases the risk of an outcome

Semi-quantitative exposures, such as smoking and alcohol consumption, are common in clinical studies. Their association with outcomes is captured using either a single quantitative variable that includes nonexposed with a value of zero, or using two variables by adding an additional binary variable exposed versus not exposed. Herein, we propose two approaches to determine a lower bound on the amount of such an exposure (eg, number of cigarettes smoked per day) that significantly increases the risk of outcomes. Using smoking as illustration, the first approach consists of sequentially testing the effect of 1, 2, and so on, cigarettes per day, which requires an adjustment for multiplicity to protect the overall type-I error. An alternative gatekeeping approach is also described. The proposed methods are illustrated for the association of smoking with clinically confirmed neuropathy in a logistic regression model, and for the association of smoking with the risk of CVD in a Cox PH regression model.