O.R./Analytics in Action Blog

I have had a strong interest in answering screening policy questions associated with breast cancer since 2006. Questions such as when to start and screening or how often to screen women are among the most controversial issues regarding breast cancer, the most common non-skin cancer in US women. Although mammography is the most effective modality for breast cancer screening, it has several potential risks including high false-positive rates. Therefore, the balance of benefits and risks is critical in designing a mammography screening schedule, which requires a formal framework to evaluate these effects such as simulation modeling.

After I got involved in the breast cancer screening problem, I noticed that most of the existing cancer screening guidelines simply provide very generic and static instructions. For example, many medical organizations recommend that women over 40 (over 50, according to some organizations) should have a screening mammogram every 1 to 2 years and should continue to do so for as long as they are in good health.

On the other hand, there are some factors suggesting that a more precise screening program would perform better than population-based screening programs as suggested by existing guidelines. For example, women with a family history of breast cancer is about twice more likely to develop breast cancer than a woman who does not have a family history of breast cancer. Therefore, women with a family history of cancer may need a more aggressive screening protocol than those without a family history. Furthermore, there is strong evidence that breast cancer is less aggressive in older women which suggests a dynamic personalized breast-cancer screening policy, i.e., a policy that prescribes different screening intervals depending on the woman's age and personalized risk of cancer, might be preferable to a population-based screening strategies recommended by the medical organizations.

Obviously, tailoring clothing to fit a woman is straightforward: take measurements and alter accordingly. Similarly, tailoring breast cancer screening to fit a woman needs to account for individual risk factors, such as age, parity, breast density, obesity, family history, etc. and determine a mammogram schedule accordingly. In fact, individualizing mammography screening decisions based on personal risk characteristics of women is identified as crucial to improve breast cancer diagnosis by numerous researchers and several health organizations. On the other hand, no structured protocol exists to individualize this process.

To this end, along with my students I developed a partially observable Markov decision process (POMDP) model that determines the optimal individualized cancer screening strategies for women with different risk groups. Mammography screening is a very natural application area for POMDPs, that are underutilized in health-care area. More specifically, unlike Markov decision processes (MDPs), POMDPs assume a probability distribution around the true states (i.e. true cancer stage of a patient) and use belief states (i.e. probability of cancer estimate) and observations (i.e. screening test result) to update the belief states. Similar to MDPs, POMDPs also consider sequential decision making which is the case in breast cancer screening since screening decisions for patients need to be made every year.

We then used a previously developed and validated simulation model to estimate the input parameters of the model and solved the POMDP optimally, which is rarely done in the literature due to extensive computational requirements. We found several interesting results such as dynamic screening policies generated by our POMDP increase the societal benefit of mammography significantly. For example, the use of personalized screening strategies would save more than two million life-years for the 40-44 age group in the US alone while recommending 60% fewer mammograms than the existing guidelines.

Figure 1. Optimal Probability of Cancer Threshold to Recommend Mammography for Various Ages

We also found that the mammography screening threshold risk changes with age, being lower in younger women and higher in older women (Figure 1). This is consistent with the knowledge that older women are more likely to suffer from other comorbidities; hence, further invasive tests are often less beneficial for these women. On the other hand, while one would expect that older women need to be screened less aggressively than younger women, we find that this is not always the case. Although this finding appears counterintuitive, because breast cancer risk is also higher in older women, mammography decisions should be determined considering this trade-off. We showed that, under this trade-off, screening is less beneficial for most women over age 74 and provides significant QALY gains especially for the high-risk women in the controversial age group 40-49. In addition, one of the key features of the personalized optimal mammography screening strategy proposed in our study is that it considers not only personal risk characteristics but also the personal history of screening when making recommendations for mammography decisions.

To individualize the mammography screening process, I propose a statistic, i.e. the belief state of the POMDP, which captures possible risk factors and screening history. From a clinical standpoint, this new statistic and our results might be useful for communication between the radiologist, patient, and referring physician. Our findings may in turn facilitate shared decision making, decision making within a patient-–clinician partnership, which is especially recommended for complex decisions such as mammography screening.

My research on mammography screening may not only improve breast cancer screening, but also has the potential to provide a framework for developing better screening policies for other cancers such as prostate and colorectal cancers as well as other diseases such as Human papillomavirus (HPV) with some modifications. Any improvement on cancer screening would directly affect millions of people being screened for cancer and indirectly affect almost the whole population being screened for other diseases. Furthermore, the potential life savings and dollar savings of this research are substantial. In summary, OR has a lot to offer to optimize disease screening & diagnosis and improve health outcomes.

Link to the papers related to this research:

http://homepages.cae.wisc.edu/~alagoz/OR-BCPOMDP.pdf

http://www.informs.org/Pubs/Tutorials-in-OR/2011-TutORials-in-Operations-Research-ONLINE/Chapter-5

alagoz at engr dot wisc dot edu

Research supported in part by NSF Grant CMMI-0844423.

A few years ago, I attended a seminar where I learned that in external beam radiotherapy, radiation beams that are used to kill tumor cells also pass through and damage healthy tissue nearby. Thus the goal is to maximize tumor cell-kill while minimizing toxic effects of radiation on healthy tissue. As shown in the schematic below, this is achieved in part by optimizing the radiation intensity profile so that it conforms, as much as possible, to the tumor’s shape. Operations Research (OR) has played an important role in this spatial aspect of radiotherapy. Numerous formulations of the above optimization problem have been developed over the last fifteen years and efficient algorithms for their solution have been incorporated into commercial treatment planning systems.

Figure 1. A schematic of intensity modulation in radiotherapy. A cashew nut shaped tumor and a round healthy tissue are depicted. Three radiation beams are shown. Their intensity profiles are tuned so that high radiation is delivered to the tumor whereas low radiation is delivered to the healthy tissue. Long arrows=high intensity radiation; short arrows=low intensity radiation.

As I got more interested in this application of OR, and started working with my former doctoral student Minsun Kim who is a medical physicist, I found that radiotherapy is typically administered daily over several weeks. This gives the healthy tissue, which has better damage-repair capability than tumors, sufficient time to recover between consecutive treatment sessions. It also allows tumor cells to reorganize into more radiosensitive phases of the cell cycle. More generally, it is believed that the efficacy of radiotherapy depends, among many other factors, on patient- and tumor-specific complex biological processes that occur in the cancerous region over several weeks of treatment.

However, I observed, to my surprise, that optimization formulations used in treatment planning were “static”. That is, they did not explicitly model changes in the tumor’s condition over time. At that time, I thought, “but surely, there must be some health benefit in dynamically optimizing treatment plans over time based on biological information acquired over the treatment course and on the patient’s actual response to radiation.” However, I was a bit disappointed when I soon realized that several hurdles would need to be overcome before this idea can be implemented in practice. For instance, it has traditionally been very difficult to model tumor-response and to accurately image spatiotemporal evolution of intra-tumor biological processes. I thus abandoned the idea of working on dynamic optimization in radiotherapy. Well, almost – until I learned from Minsun that functional images can now provide quantitative biological information such as the density of active tumor cells, their radiosensitivity and rate of proliferation. Such biological information could be further utilized to develop patient-specific tumor-response models. In fact, some medical physicists and doctors now believe that spatiotemporally adaptive individualized treatment plans that utilize such response models and functional imaging techniques will be feasible in the not-so-distant future. But we noticed that all existing research in this area was clinical and a mathematical framework for this futuristic treatment paradigm was missing.

Some of our work in applied OR now focuses on building a rigorous mathematical foundation for adaptive individualized radiotherapy. Our goal is to build optimization models and algorithms that deliver the right radiation to the right location at the right time. In Minsun’s doctoral dissertation, we took an initial step[1] toward this objective. We formulated dynamic optimization models that account for uncertainty in tumor-response and let treatment planners tune beam intensities depending on the tumor’s condition, as observed in functional images acquired prior to each treatment session. Exact solution of these optimization models was intractable. We therefore designed approximate solution techniques, and demonstrated, using computer generated medium-scale test cases, that this stochastic dynamic approach to treatment planning can reduce the number of tumor cells by as much as 98% compared to the traditional static approach. Minsun won the Bonder award and the Dantzig dissertation prize for this work and my NSF CAREER grant award further builds upon these ideas. But this is just the tip of the iceberg.

I believe that OR can help make adaptive individualized radiotherapy a reality. This approach to treatment planning will generate a rich array of challenging stochastic control problems[2]. There will be much room for creativity in coming up with sufficiently realistic and yet tractable formulations. For truly patient-specific treatment, these will need to be integrated with methods to estimate the parameters of tumor-response models. The stochastic control problems in our aforementioned preliminary work were solved using approximate control schemes called open loop control, certainty equivalent control, and open loop feedback control. These methods were computationally efficient for our medium-scale test problems because our original model was formulated such that the resulting nonlinear programming sub-problems were convex. In the future, as we attempt to tackle much larger-scale treatment planning problems, we will need to develop specialized nonlinear programming algorithms and approximate control schemes, and thus there will great opportunities for methodological work. In the end, these dynamic optimization models and algorithms will have a real impact on radiotherapy practice only if they can achieve a demonstrable improvement in health outcomes and if they are embedded into commercial treatment planning systems. Thus the pursuit of mathematically rigorous, radiobiologically and clinically sound, and cost-effective adaptive individualized radiotherapy will call for a close collaboration and knowledge-exchange among doctors, medical physicists, radiobiologists, industry, and optimization experts. The 2008 World Cancer Report predicts that by 2030 there could be 17 million cancer deaths annually worldwide. Thus, if clinically successful, this interdisciplinary application of OR has the potential for significant societal impact.

Research supported in part by NSF Grant CMMI-1054026

-Post by Prof Archis Ghate, University of Washington, Seattle

archis at u dot washington dot edu

[1] M Kim, A Ghate, and M H Phillips, A stochastic control formalism for dynamic biologically conformal radiation therapy, forthcoming in European Journal of Operational Research, 2011.

[2] A Ghate, Dynamic optimization in radiotherapy, forthcoming in TutORials in Operations Research, INFORMS 2011.