AbstractIntroductionPercentage mammographic density has long been recognised as a marker of breast cancer risk and of mammography sensitivity. There may be other image markers of screening sensitivity and efficient statistical approaches would be helpful for establishing them from large scale epidemiological and screening data.MethodsWe compare a novel random effects continuous tumour growth model (which includes a screening sensitivity submodel) to logistic regression (with interval vs. screen-detected cancer as the dependent variable) in terms of statistical power to detect image markers of screening sensitivity. We do this by carrying out a simulation study. We also use continuous tumour growth modelling to quantify the roles of dense tissue scatter (measured as skewness of the intensity gradient) and percentage mammographic density in screening sensitivity. This is done by using mammograms and information on tumour size, mode of detection and screening history from 1,845 postmenopausal women diagnosed with invasive breast cancer, in Sweden between 1993 and 1995.ResultsThe statistical power to detect a marker of screening sensitivity was larger for our continuous tumour growth model than it was for logistic regression. For the settings considered in this paper, the percentage increase in power ranged from 34 to 56%. In our analysis of data from Swedish breast cancer patients, using our continuous growth model, when including both percentage mammographic density and dense tissue scatter in the screening sensitivity submodel, only the latter variable was significantly associated with sensitivity. When included one at a time, both markers were significantly associated (p-values of 5.7 × 10−3 and 1.0 × 10−5 for percentage mammographic density and dense tissue scatter, respectively).ConclusionsOur continuous tumour growth model is useful for finding image markers of screening sensitivity and for quantifying their role, using large scale epidemiological and screening data. Clustered dense tissue is associated with low mammography screening sensitivity.
Numerical Solution of a Two Dimensional Tumour Growth Model with Moving Boundary
