M illions of Americans undergo colonoscopy screening for colorectal cancer (CRC) prevention and surveillance every year. The efficiency of colonoscopy operations depends on how often patients are screened, which is a complex and controversial decision, as reflected by the discrepancy between clinical practice and guidelines. We develop a partially observable Markov decision process to optimize colonoscopy screening policies for the objective of maximizing total quality-adjusted life years. Our model incorporates age, gender, and risk of having CRC into the screening decisions and therefore provides a novel framework for personalized CRC screening. In addition to deriving the maximum attainable benefit from colonoscopy screening, which reflects the opportunity cost of following current guidelines, our results have several policy implications. Using clinical data, we show that the optimal colonoscopy screening policies may be more aggressive than the guidelines under some conditions. Optimal screening policies recommend that females with CRC history undergo colonoscopy more frequently than males. In contrast, females without CRC history should be screened less frequently than males. This result, which was not recognized before, signifies the role of gender in optimal CRC screening decisions.

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We consider the problem of designing an efficient system for allocating donated livers to patients waiting for transplantation. The trade-off between medical urgency and efficiency is at the heart of the liver allocation problem. We model the transplant waiting list as a multiclass fluid model of overloaded queues, which captures the disease evolution by allowing the patients to switch between classes, i.e., health levels. We consider the bicriteria objective of minimizing total number of patient deaths while waiting for transplantation (NPDWT) and maximizing total quality-adjusted life years (QALYs) through a weighted combination. On one hand, under the objective of minimizing NPDWT, the current policy of United Network for Organ Sharing (UNOS) emerges as the optimal policy, providing a theoretical justification for the current practice. On the other hand, under the metric of maximizing QALYs, the optimal policy is an intuitive dynamic index policy that ranks patients based on their marginal benefit from transplantation, i.e., the difference in benefit with versus without transplantation. Finally, we perform a detailed simulation study to compare the performances of our proposed policies and the current UNOS policy along the following metrics: total QALYs, NPDWT, number of patient deaths after transplantation, number of total patient deaths, and number of wasted livers. Numerical experiments show that our proposed policy for maximizing QALYs outperforms the current UNOS policy along all metrics except the NPDWT.

Objectives Some aspects of the natural history of metachronous colorectal cancer (MCRC), such as the rate of progression from adenomatous polyp to MCRC, are unknown. The objective of this study is to estimate a set of parameters revealing some of these unknown characteristics of MCRC. Methods The authors developed a computer simulation model that mimics the progression of MCRC for a 5-year period following the treatment of primary colorectal cancer (CRC). They obtained the inputs of the simulation model using longitudinal data for 284 CRC patients from the Mayo Clinic, Rochester. Results Five-year MCRC incidence and all-cause mortality were 7.4% and 12.7% in the patient cohort, respectively. Statistical analysis showed that 5-year MCRC incidence was associated with gender (P = 0.05), whereas both all-cause and CRC-related mortalities were associated with age (P < 0.001 and P = 0.01). Estimated annual probabilities of progression from adenomatous polyp to MCRC and from MCRC to metastatic MCRC were 0.14 and 0.28, respectively. Annual probabilities of mortality after MCRC and metastatic MCRC treatments were estimated to be 0.06 and 0.26, respectively. The estimated annual probability of mortality due to undetected MCRC was 0.16. Conclusions The results imply that MCRC, especially in women, may be more common than suggested by previous studies. In addition, statistics derived from the clinical data and results of the simulation model indicate that gender and age affect the progression of MCRC.