Markov Models of Breast Tumor Progression: Some Age-Specific Results

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Abstract
Researchers have noted that mammographic screening has a reduced effect on breast cancer mortality in women in their forties compared to older women. Explanations for this include poorer sensitivity in younger women due to denser breast tissue, as well as more rapid tumor progression, giving a shorter mean sojourn time (the average duration of the preclinical screen-detectable period). To test these hypotheses, we developed a series of Markov-chain models to estimate tumor progression rates and sensitivity. Parameters were estimated using tumor data from the Swedish two-county trial of mammographic screening for breast cancer. The mean sojourn time was shorter in women aged 40-49 compared to women aged 50-59 and 60-69 (2.44, 3.70, and 4.17 years, respectively). Sensitivity was lower in the 40-49 age group compared to the two older groups (83%, 100%, and 100%, respectively). Thus, both rapid progression and poorer sensitivity are associated with the 40-49 age group. We also modeled tumor size, node status, and malignancy grade together with subsequent breast cancer mortality and found that, to achieve a reduction in mortality commensurate with that in women over 50, the interscreening interval for women in their forties should be less than two years. We conclude that Markov models and the use of tumor size, node status, and malignancy grade as surrogates for mortality can be useful in design and analysis of future studies of breast cancer screening.

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