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Fluence map optimization for intensity-modulated radiation therapy planning can be formulated as a large-scale inverse problem with competing objectives and constraints associated with the tumors and organs at risk. Unfortunately, clinically relevant dose–volume constraints are nonconvex, so standard algorithms for convex problems cannot be directly applied. Although prior work focuses on convex approximations for these constraints, we propose a novel relaxation approach to handle nonconvex dose–volume constraints. We develop efficient, provably convergent algorithms based on partial minimization, and show how to adapt them to handle maximum-dose constraints and infeasible problems. We demonstrate our approach using the CORT data set and show that it is easily adaptable to radiation treatment planning with dose–volume constraints for multiple tumors and organs at risk. Summary of Contribution: This paper proposes a novel approach to deal with dose–volume constraints in radiation treatment planning optimization, which is inherently nonconvex, mixed-integer programming. The authors tackle this NP-hard problem using auxiliary variables and continuous optimization while preserving the problem's nonconvexity. Algorithms to efficiently solve the nonconvex optimization problem presented in this paper yield computation speeds suitable for a busy clinical setting. [ABSTRACT FROM AUTHOR]

There are several different modalities, e.g. surgery, chemotherapy and radiotherapy, that are currently used to treat cancer. It is common practice to use a combination of these modalities to maximize clinical outcomes, which are often measured by a balance between maximizing tumor damage and minimizing normal tissue side effects due to treatment. However, multi-modality treatment policies are mostly empirical in current practice and are therefore subject to individual clinicians' experiences and intuition. We present a novel formulation of optimal multi-modality cancer management using a finite-horizon Markov decision process approach. Specifically, at each decision epoch, the clinician chooses an optimal treatment modality based on the patient's observed state, which we define as a combination of tumor progression and normal tissue side effect. Treatment modalities are categorized as (1) type 1, which has a high risk and high reward, but is restricted in the frequency of administration during a treatment course; (2) type 2, which has a lower risk and lower reward than type 1, but may be repeated without restriction; and (3) type 3, no treatment (surveillance), which has the possibility of reducing normal tissue side effect at the risk of worsening tumor progression. Numerical simulations using various intuitive, concave reward functions show the structural insights of optimal policies and demonstrate the potential applications of using a rigorous approach to optimizing multi-modality cancer management. [ABSTRACT FROM AUTHOR]

Key Points: Question: How does maternal mortality vary by state and race and ethnicity over time in the US? Findings: Long-term trends in maternal mortality ratios from vital registration and census data were estimated. Increases in maternal mortality ratios in specific states were identified and showed previously unmeasured inequities for specific subpopulations. Meaning: Previous research has focused on trends at the national level or in selected states. Comprehensive reporting of disparities in maternal mortality provides evidence to guide intervention policies and benchmark progress for the prevention of maternal deaths. Importance: Evidence suggests that maternal mortality has been increasing in the US. Comprehensive estimates do not exist. Long-term trends in maternal mortality ratios (MMRs) for all states by racial and ethnic groups were estimated. Objective: To quantify trends in MMRs (maternal deaths per 100 000 live births) by state for 5 mutually exclusive racial and ethnic groups using a bayesian extension of the generalized linear model network. Design, Setting, and Participants: Observational study using vital registration and census data from 1999 to 2019 in the US. Pregnant or recently pregnant individuals aged 10 to 54 years were included. Main Outcomes and Measures: MMRs. Results: In 2019, MMRs in most states were higher among American Indian and Alaska Native and Black populations than among Asian, Native Hawaiian, or Other Pacific Islander; Hispanic; and White populations. Between 1999 and 2019, observed median state MMRs increased from 14.0 (IQR, 5.7-23.9) to 49.2 (IQR, 14.4-88.0) among the American Indian and Alaska Native population, 26.7 (IQR, 18.3-32.9) to 55.4 (IQR, 31.6-74.5) among the Black population, 9.6 (IQR, 5.7-12.6) to 20.9 (IQR, 12.1-32.8) among the Asian, Native Hawaiian, or Other Pacific Islander population, 9.6 (IQR, 6.9-11.6) to 19.1 (IQR, 11.6-24.9) among the Hispanic population, and 9.4 (IQR, 7.4-11.4) to 26.3 (IQR, 20.3-33.3) among the White population. In each year between 1999 and 2019, the Black population had the highest median state MMR. The American Indian and Alaska Native population had the largest increases in median state MMRs between 1999 and 2019. Since 1999, the median of state MMRs has increased for all racial and ethnic groups in the US and the American Indian and Alaska Native; Asian, Native Hawaiian, or Other Pacific Islander; and Black populations each observed their highest median state MMRs in 2019. Conclusion and Relevance: While maternal mortality remains unacceptably high among all racial and ethnic groups in the US, American Indian and Alaska Native and Black individuals are at increased risk, particularly in several states where these inequities had not been previously highlighted. Median state MMRs for the American Indian and Alaska Native and Asian, Native Hawaiian, or Other Pacific Islander populations continue to increase, even after the adoption of a pregnancy checkbox on death certificates. Median state MMR for the Black population remains the highest in the US. Comprehensive mortality surveillance for all states via vital registration identifies states and racial and ethnic groups with the greatest potential to improve maternal mortality. Maternal mortality persists as a source of worsening disparities in many US states and prevention efforts during this study period appear to have had a limited impact in addressing this health crisis. This study uses vital registration and census data from 1999 to 2019 to quantify trends in maternal mortality ratios (maternal deaths per 100 000 live births) by state for 5 mutually exclusive racial and ethnic groups in the US using a bayesian extension of the generalized linear model network. [ABSTRACT FROM AUTHOR]