Adoption of 2% probability of breast cancer as a threshold for biopsy has been useful from a practical practice standpoint but until now, has not been supported by decision analytic theory. Our MDP model demonstrates that 2% is the optimal breast biopsy threshold for most women of screening age (between 42 and 75) based on the desire to maximize QALYs. However age is important in determining an optimal biopsy threshold: for younger patients (<42) biopsy thresholds given by our MDP model are lower than for older patients because younger patients accrue more QALYs as a result of early diagnosis and cure. We must carefully consider several aspects of our model including sensitivity analysis, modeling decisions, and assumptions as we judge its clinical accuracy and applicability.
After age, the disutility of biopsy most profoundly affects the optimal biopsy threshold. In our sensitivity analysis, anytime we increase the disutility of biopsy (at age 40 or by increasing the factor that accelerates increases by age) the threshold for biopsy also increases because the “harm” of biopsy increases as the benefit remains the same. However, even if the disutility of biopsy is the same for younger and older patients, the biopsy threshold still increases with age because of the limited benefit in terms of QALYs for older patients. When we increase the fraction of invasive cancers or increase the treatment effectiveness factor, biopsy threshold decreases because an early diagnosis is more valuable for increased length of life and overcomes the disutility of biopsy. However, underlying the details of our sensitivity analysis, a larger theme emerges: if in fact personalized breast cancer screening is a desired goal 
, perhaps we should be tailoring the biopsy threshold to individual patients based on their unique risk tolerance and their judgment of the “harm” of biopsy. Our MDP model provides the framework to offer that individualized threshold.
We decided to adopt the patient’s perspective and not model costs in our MDP in contradistinction to prior literature which concentrated on the cost-effectiveness of interventions from the societal perspective 
. We chose to include only biopsy related disutility to estimate rewards, and exclude disutilities associated with malignancy, treatment and age for several reasons. Our approach allows us to explicitly capture the influence (harm or benefit) of breast biopsy on the expected life years in isolation. Second, there are no well accepted utility weights for breast cancer treatment and a wide range has been reported 
. Third, since our model compares the lump-sum post-biopsy rewards with the sum of intermediate post-mammography rewards to inform a policy, the inclusion of other disutilities would require the calibration of the utility weights in both rewards for a fair comparison, which is beyond the scope of this work. In general, our approach will have the tendency to conservatively estimate the difference in optimal biopsy threshold between older and younger women. Decreasing the value of life with breast cancer disutility during treatment or in older age groups would disproportionately lower the value (increase the threshold) of biopsy in older age groups making the discrepancy between the biopsy threshold in older versus younger women more pronounced.
The limitations of any decision analytic model lie in the assumptions made. We have made several assumptions to simplify our MDP which abbreviate the full complexity inherent in clinical breast imaging practice. For example, we do not consider other screening or follow-up methods like breast MRI, ultrasound or mammographic watchful waiting (short-term interval follow-up). Furthermore, of the demographic risk factors that we evaluated in our logistic regression model (age, family history of breast cancer, personal history of breast cancer, hormone replacement therapy, and prior breast surgery) only patient age and personal history of breast cancer were found to be statistically significant and were ultimately included in the logistic regression model. However, breast density, prior history of atypia on breast biopsy, and BRCA mutations, among other risk factors have certainly been found to confer breast cancer risk from an epidemiologic standpoint in the larger medical literature. Including a more extensive list of breast cancer risk factors would be interesting to include in a risk prediction model to determine if they influence the threshold of biopsy.
We have not incorporated any risk-aversion into the model and therefore do not observe the effect on optimal policies. We do not consider that a patient’s utilities may change if she has undergone more than one biopsy (true-positive or false-positive) or incorporate the possibility that a patient may not adhere to the radiologist recommendation. All of these modeling decisions may influence conclusions and we hope to incorporate such scenarios in our model in the future.
Based on our analysis, a 2% threshold for breast biopsy appears to be optimal for most women of screening age with the important caveat that age and biopsy disutility influence this threshold most profoundly. If personalized care is our goal, we need accurate estimates for malignancy risk and evidence-based, optimal decision thresholds for interventions to most effectively diagnose disease. Decision analytic models, like MDPs, are critically important in defining these levels and are increasingly pervasive.
Our future work will include increasing the complexity of our model to more accurately reflect actual clinical practice. For example, including six-month follow-up and other imaging procedures like breast ultrasound and breast MRI will more adequately reflect the myriad of current tools available for breast cancer diagnosis. In addition, we also plan to include costs in our model to evaluate the cost-effectiveness of current and proposed policies to perform breast biopsy. Once our model is sufficiently validated, we plan to make it available to radiologists and patients in order to aid decisions to biopsy breast findings. While validation will entail testing the generalizability of the model on a wide range of breast imaging practices, ideally in the form of a multi-institutional trial, this validation will represent a critical next step for translation of our methodologies to clinical practice.