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Preventing chronic diseases is an essential aspect of medical care. To prevent chronic diseases, physicians focus on monitoring their risk factors and prescribing the necessary medication. The optimal monitoring policy depends on the patient's risk factors and demographics. Monitoring too frequently may be unnecessary and costly; on the other hand, monitoring the patient infrequently means the patient may forgo needed treatment and experience adverse events related to the disease. We propose a finite horizon and finite-state Markov decision process to define monitoring policies. To build our Markov decision process, we estimate stochastic models based on longitudinal observational data from electronic health records for a large cohort of patients seen in the national U.S. Veterans Affairs health system. We use our model to study policies for whether or when to assess the need for cholesterol-lowering medications. We further use our model to investigate the role of gender and race on optimal monitoring policies.

Prediction models are recommended by national guidelines to support clinical decision making in prostate cancer. Existing models to predict pathological outcomes of radical prostatectomy (RP)-the Memorial Sloan Kettering (MSK) models, Partin tables, and the Briganti nomogram-have been developed using data from tertiary care centers and may not generalize well to other settings.Data from a regional cohort (Michigan Urological Surgery Improvement Collaborative [MUSIC]) were used to develop models to predict extraprostatic extension (EPE), seminal vesicle invasion (SVI), lymph node invasion (LNI), and nonorgan-confined disease (NOCD) in patients undergoing RP. The MUSIC models were compared against the MSK models, Partin tables, and Briganti nomogram (for LNI) using data from a national cohort (Surveillance, Epidemiology, and End Results [SEER] registry).We identified 7,491 eligible patients in the SEER registry. The MUSIC model had good discrimination (SEER AUC EPE: 0.77; SVI: 0.80; LNI: 0.83; NOCD: 0.77) and was well calibrated. While the MSK models had similar discrimination to the MUSIC models (SEER AUC EPE: 0.76; SVI: 0.80; LNI: 0.84; NOCD: 0.76), they overestimated the risk of EPE, LNI, and NOCD. The Partin tables had inferior discrimination (SEER AUC EPE: 0.67; SVI: 0.76; LNI: 0.69; NOCD: 0.72) as compared to other models. The Briganti LNI nomogram had an AUC of 0.81 in SEER but overestimated the risk.New models developed using the MUSIC registry outperformed existing models and should be considered as potential replacements for the prediction of pathological outcomes in prostate cancer.

We used data-analytics approaches to develop, calibrate, and validate predictive models, to help urologists in a large statewide collaborative make prostate cancer staging decisions on the basis of individual patient risk factors. The models were validated using statistical methods based on bootstrapping and evaluation on out-of-sample data. These models were used to design guidelines that optimally weigh the benefits and harms of radiological imaging for the detection of metastatic prostate cancer. The Michigan Urological Surgery Improvement Collaborative, a statewide medical collaborative, implemented these guidelines, which were predicted to reduce unnecessary imaging by more than 40% and limit the percentage of patients with missed metastatic disease to be less than 1%. The effects of the guidelines were measured after implementation to confirm their impact on reducing unnecessary imaging across the state of Michigan.

We consider the problem of decision-making in Markov decision processes (MDPs) when the reward or transition probability parameters are not known with certainty. We study an approach in which the d...

Surgical nurses are essential resources in the surgery delivery system. However, staffing decisions present a challenge due to the stochastic nature of surgical demand, nurse availability, skill re...

This article describes two versions of the chance-constrained stochastic bin-packing (CCSBP) problem that consider item-to-bin allocation decisions in the context of chance constraints on the total item size within the bins. The first version is a stochastic CCSBP (SP-CCSBP) problem, which assumes that the distributions of item sizes are known. We present a two-stage stochastic mixed-integer program (SMIP) for this problem and a Dantzig–Wolfe formulation suited to a branch-and-price (B&P) algorithm. We further enhance the formulation using coefficient strengthening and reformulations based on probabilistic packs and covers. The second version is a distributionally robust CCSBP (DR-CCSBP) problem, which assumes that the distributions of item sizes are ambiguous. Based on a closed-form expression for the DR chance constraints, we approximate the DR-CCSBP problem as a mixed-integer program that has significantly fewer integer variables than the SMIP of the SP-CCSBP problem, and our proposed B&P algorithm can directly solve its Dantzig–Wolfe formulation. We also show that the approach for the DR-CCSBP problem, in addition to providing robust solutions, can obtain near-optimal solutions to the SP-CCSBP problem. We implement a series of numerical experiments based on real data in the context of surgery scheduling, and the results demonstrate that our proposed B&P algorithm is computationally more efficient than a standard branch-and-cut algorithm, and it significantly improves upon the performance of a well-known bin-packing heuristic.

Introduction:We compared cumulative reimbursement to urologists following implementation of surveillance vs immediate treatment. Active surveillance for prostate cancer is widely considered...

Objective Occupational injuries (OIs) cause an immense burden on the US population. Prediction models help focus resources on those at greatest risk of a delayed return to work (RTW). RTW depends on factors that develop over time; however, existing methods only utilize information collected at the time of injury. We investigate the performance benefits of dynamically estimating RTW, using longitudinal observations of diagnoses and treatments collected beyond the time of initial injury. Materials and Methods We characterize the difference in predictive performance between an approach that uses information collected at the time of initial injury (baseline model) and a proposed approach that uses longitudinal information collected over the course of the patient’s recovery period (proposed model). To control the comparison, both models use the same deep learning architecture and differ only in the information used. We utilize a large longitudinal observation dataset of OI claims and compare the performance of the two approaches in terms of daily prediction of future work state (working vs not working). The performance of these two approaches was assessed in terms of the area under the receiver operator characteristic curve (AUROC) and expected calibration error (ECE). Results After subsampling and applying inclusion criteria, our final dataset covered 294 103 OIs, which were split evenly between train, development, and test datasets (1/3, 1/3, 1/3). In terms of discriminative performance on the test dataset, the proposed model had an AUROC of 0.728 (90% confidence interval: 0.723, 0.734) versus the baseline’s 0.591 (0.585, 0.598). The proposed model had an ECE of 0.004 (0.003, 0.005) versus the baseline’s 0.016 (0.009, 0.018). Conclusion The longitudinal approach outperforms current practice and shows potential for leveraging observational data to dynamically update predictions of RTW in the setting of OI. This approach may enable physicians and workers’ compensation programs to manage large populations of injured workers more effectively.

To assess the temporary health impact of prostate multiparametric MRI (mpMRI) and transrectal prostate biopsy in an active surveillance prostate cancer population.A two-arm institutional review board-approved HIPAA-compliant prospective observational patient-reported outcomes study was performed from November 2017 to July 2018. Inclusion criteria were men with Gleason 6 prostate cancer in active surveillance undergoing either prostate mpMRI or transrectal prostate biopsy. A survey instrument was constructed using validated metrics in consultation with the local patient- and family-centered care organization. Study subjects were recruited at the time of diagnostic testing and completed the instrument by phone 24 to 72 hours after testing. The primary outcome measure was summary testing-related quality of life (summary utility score), derived from the testing morbidities index (TMI) (scale: 0 = death and 1 = perfect health). TMI is stratified into seven domains, with each domain scored from 1 (no health impact) to 5 (extreme health impact). Testing-related quality-of-life measures in the two cohorts were compared with Mann-Whitney U test.In all, 122 subjects were recruited, and 90% (110 of 122 [MRI 55 of 60, biopsy 55 of 62]) successfully completed the survey instrument. The temporary quality-of-life impact of transrectal biopsy was significantly greater than that of prostate mpMRI (0.82, 95% confidence interval [CI] 0.79-0.85, versus 0.95, 95% CI 0.94-0.97; P.001). The largest mean domain-level difference was for intraprocedural pain (transrectal biopsy 2.6, 95% CI 2.4-2.8, versus mpMRI 1.3, 95% CI 1.1-1.5; P.001).Transrectal prostate biopsy has greater temporary health impact (lower testing-related quality-of-life measure) than prostate mpMRI.

A prospective single-arm clinical trial was conducted to determine whether (18)F-choline PET/mpMRI can improve the specificity of multiparametric MRI (mpMRI) of the prostate for Gleason ≥ 3+4 prostate cancer. Methods: Before targeted and systematic prostate biopsy, mpMRI and (18)F-choline PET/CT were performed on 56 evaluable subjects with 90 Likert score 3–5 mpMRI target lesions, using a (18)F-choline target-to-background ratio of greater than 1.58 to indicate a positive (18)F-choline result. Prostate biopsies were performed after registration of real-time transrectal ultrasound with T2-weighted MRI. A mixed-effects logistic regression was applied to measure the performance of mpMRI (based on prospective Likert and retrospective Prostate Imaging Reporting and Data System, version 2 [PI-RADS], scores) compared with (18)F-choline PET/mpMRI to detect Gleason ≥ 3+4 cancer. Results: The per-lesion accuracy of systematic plus targeted biopsy for mpMRI alone was 67.8% (area under receiver-operating-characteristic curve [AUC], 0.73) for Likert 4–5 and 70.0% (AUC, 0.76) for PI-RADS 3–5. Several PET/MRI models incorporating (18)F-choline with mpMRI data were investigated. The most promising model selected all high-risk disease on mpMRI (Likert 5 or PI-RADS 5) plus low- and intermediate-risk disease (Likert 4 or PI-RADS 3–4), with an elevated (18)F-choline target-to-background ratio greater than 1.58 as positive for significant cancer. Using this approach, the accuracy on a per-lesion basis significantly improved to 88.9% for Likert (AUC, 0.90; P < 0.001) and 91.1% for PI-RADS (AUC, 0.92; P < 0.001). On a per-patient basis, the accuracy improved to 92.9% for Likert (AUC, 0.93; P < 0.001) and to 91.1% for PI-RADS (AUC, 0.91; P = 0.009). Conclusion: (18)F-choline PET/mpMRI improved the identification of Gleason ≥ 3+4 prostate cancer compared with mpMRI, with the principal effect being improved risk stratification of intermediate-risk mpMRI lesions.

Surgery planning decisions include which operating rooms (ORs) to open, allocation of surgeries to ORs, sequence, and time to start each surgery. They are often made under uncertain surgery durations with limited data that lead to unknown distributional information. Moreover, cost parameters for criteria such as overtime and surgery delays are often difficult or impossible to estimate in practice. In this paper, we formulate distributionally robust (DR) chance constraints on surgery waiting and OR overtime, which recognize practical limitations on data availability and cost parameter accuracy. We use [Formula: see text]-divergence measures to build an ambiguity set of possible distributions of random surgery durations, and derive a branch-and-cut algorithm for optimizing a mixed-integer linear programming reformulation based on finite samples of the random surgery durations. We test instances generated from real hospital-based surgery data. The results show computational efficacy of our approaches, and provide insights for DR surgery planning.

The GG (Grade Group) system was introduced in 2013. Data from academic centers suggest that GG better distinguishes between prostate cancer risk groups than the Gleason score (GS) risk groups. We compared the performance of the 2 systems to predict pathological/recurrence outcomes using data from the MUSIC (Michigan Urological Surgery Improvement Collaborative).Patients who underwent biopsy and radical prostatectomy in the MUSIC from March 2012 to June 2017 were classified according to GG and GS. Outcomes included the presence or absence of extraprostatic extension, seminal vesical invasion, positive lymph nodes, positive surgical margins and time to cancer recurrence (defined as postoperative prostate specific antigen 0.2 ng/ml or greater). Logistic and Cox regression models were used to compare the difference in outcomes.A total of 8,052 patients were identified. When controlling for patient characteristics, significantly higher risks of extraprostatic extension, seminal vesical invasion and positive lymph nodes were observed for biopsy GG 3 vs 2 and for GG 5 vs 4 (p0.001). Biopsy GGs 3, 4 and 5 also showed shorter time to biochemical recurrence than GGs 2, 3 and 4, respectively (p0.001). GGs 3, 4 and 5 at radical prostatectomy were each associated with a greater probability of recurrence compared to the next lower GG (p0.001). GG (vs GS) had better predictive power for extraprostatic extension, seminal vesical invasion, positive lymph nodes and biochemical recurrence.GG at biopsy and radical prostatectomy allows for better discrimination of recurrence-free survival between individual risk groups than GS risk groups with GGs 2, 3, 4 and 5 each incrementally associated with increased risk.

Markov decision processes (MDPs) have found success in many application areas that involve sequential decision making under uncertainty, including the evaluation and design of treatment and screening protocols for medical decision making. However, the data used to parameterize the model can influence what policies are recommended, and multiple competing data sources are common in many application areas, including medicine. In this article, we introduce the Multi-model Markov decision process (MMDP) which generalizes a standard MDP by allowing for multiple models of the rewards and transition probabilities. Solution of the MMDP generates a single policy that maximizes the weighted performance over all models. This approach allows the decision maker to explicitly trade-off conflicting sources of data while generating a policy of the same level of complexity for models that only consider a single source of data. We study the structural properties of this problem and show that it is at least NP-hard. We develop exact methods and fast approximation methods supported by error bounds. Finally, we illustrate the effectiveness and the scalability of our approach using a case study in preventative blood pressure and cholesterol management that accounts for conflicting published cardiovascular risk models.

This study aimed to estimate the rates of biopsy undersampling and progression for four prostate cancer (PCa) active surveillance (AS) cohorts within the Movember Foundation's Global Action Plan Prostate Cancer Active Surveillance (GAP3) consortium. We used a hidden Markov model (HMM) to estimate factors that define PCa dynamics for men on AS including biopsy under‐sampling and progression that are implied by longitudinal data in four large cohorts included in the GAP3 database. The HMM was subsequently used as the basis for a simulation model to evaluate the biopsy strategies previously proposed for each of these cohorts. For the four AS cohorts, the estimated annual progression rate was between 6%–13%. The estimated probability of a biopsy successfully sampling undiagnosed non‐favorable risk cancer (biopsy sensitivity) was between 71% and 80%. In the simulation study of patients diagnosed with favorable risk cancer at age 50, the mean number of biopsies performed before age 75 was between 4.11 and 12.60, depending on the biopsy strategy. The mean delay time to detection of non‐favorable risk cancer was between 0.38 and 2.17 years. Biopsy undersampling and progression varied considerably across study cohorts. There was no single best biopsy protocol that is optimal for all cohorts, because of the variation in biopsy under‐sampling error and annual progression rates across cohorts. All strategies demonstrated diminishing benefits from additional biopsies., There was no single best biopsy protocol in prostate cancer active surveillance that is optimal for all cohorts. The optimal biopsy strategy depends on biopsy under‐sampling error and cancer progression rate, which vary significantly across cohorts.

The weighted-sum method is a commonly used technique in Multi-objective optimization to represent different criteria considered in a decision-making and optimization problem. Weights are assigned to different criteria depending on the degree of importance. However, even if decision-makers have an intuitive sense of how important each criteria is, explicitly quantifying and hand-tuning these weights can be difficult. To address this problem, we propose the Pareto-Weighted-Sum-Tuning algorithm as an automated and systematic way of trading-off between different criteria in the weight-tuning process. Pareto-Weighted-Sum-Tuning is a configurable online-learning algorithm that uses sequential discrete choices by a decision-maker on sequential decisions, eliminating the need to score items or weights. We prove that utilizing our online-learning approach is computationally less expensive than batch-learning, where all the data is available in advance. Our experiments show that Pareto-Weighted-Sum-Tuning is able to achieve low relative error with different configurations.

The objective of this study was to evaluate the cost-effectiveness of (18)F-choline PET/multiparametric MRI (mpMRI) versus mpMRI alone for the detection of primary prostate cancer with a Gleason score of greater than or equal to 3 + 4 in men with elevated prostate-specific antigen levels. Methods: A Markov model of prostate cancer onset and progression was used to estimate the health and economic consequences of (18)F-choline PET/mpMRI for the detection of primary prostate cancer with a Gleason score of greater than or equal to 3 + 4 in men with elevated prostate-specific antigen levels. Multiple simultaneous hybrid (18)F-choline PET/mpMRI strategies were evaluated using Likert or Prostate Imaging Reporting and Data System version 2 (PI-RADSv2) scoring; the first was biopsy for Likert 5 mpMRI lesions or Likert 3–4 lesions with (18)F-choline target-to-background ratios of greater than or equal to 1.58, and the second was biopsy for PI-RADSv2 5 mpMRI lesions or PI-RADSv2 3–4 mpMRI lesions with (18)F-choline target-to-background ratios of greater than or equal to 1.58. These strategies were compared with universal standard biopsy, mpMRI alone with biopsy only for PI-RADSv2 3–5 lesions, and mpMRI alone with biopsy only for Likert 4–5 lesions. For each mpMRI strategy, either no biopsy or standard biopsy could be performed after negative mpMRI results were obtained. Deaths averted, quality-adjusted life years (QALYs), cost, and incremental cost-effectiveness ratios were estimated for each strategy. Results: When the results of (18)F-choline PET/mpMRI were negative, performing a standard biopsy was more expensive and had lower QALYs than performing no biopsy. The best screening strategy among those considered in this study performed hybrid (18)F-choline PET/mpMRI with Likert scoring on men with elevated PSA, performed combined biopsy (targeted biopsy and standard 12-core biopsy) for men with positive imaging results, and no biopsy for men with negative imaging results ($22,706/QALY gained relative to mpMRI alone); this strategy reduced the number of biopsies by 35% in comparison to mpMRI alone. When the same policies were compared using PI-RADSv2 instead of Likert scoring, hybrid (18)F-choline PET/mpMRI cost $46,867/QALY gained relative to mpMRI alone. In a threshold analysis, the best strategy among those considered remained cost-effective when the sensitivity and specificity of PET/mpMRI and combined biopsy (targeted biopsy and standard 12-core biopsy) were simultaneously reduced by 20 percentage points. Conclusion: (18)F-choline PET/mpMRI for the detection of primary prostate cancer with a Gleason score of greater than or equal to 3 + 4 is cost-effective and can reduce the number of unneeded biopsies in comparison to mpMRI alone.

OBJECTIVE To determine how best to use magnetic resonance imaging (MRI) and targeted MRI/ultrasonography fusion biopsy for early detection of prostate cancer (PCa) in men with elevated prostate-specific antigen (PSA) concentrations and whether it can be cost-effective. METHODS A Markov model of PCa onset and progression was developed to estimate the health and economic consequences of PCa screening with MRI. Patients underwent PSA screening from ages 55 to 69 years. Patients with elevated PSA concentrations (>4 ng/mL) underwent MRI, followed by targeted fusion or combined (standard + targeted fusion) biopsy on positive MRI, and standard or no biopsy on negative MRI. Prostate Imaging Reporting and Data System (PI-RADS) score on MRI was used to determine biopsy decisions. Deaths averted, quality-adjusted life-years (QALYs), cost and incremental cost-effectiveness ratio (ICER) were estimated for each strategy. RESULTS With a negative MRI, standard biopsy was more expensive and had lower QALYs than performing no biopsy. The optimum screening strategy (ICER $23 483/QALY) recommended combined biopsy for patients with PI-RADS score ≥3 and no biopsy for patients with PI-RADS score

This paper presents a new model for online decision making. Motivated by the healthcare delivery application of dynamically allocating patients to procedure rooms in outpatient procedure centers, the online stochastic extensible bin-packing problem is described. The objective is to minimize the combined costs of opening procedure rooms and utilizing overtime to complete a day’s procedures. The dynamic patient-allocation decisions are made in an uncertain environment where the number of patients scheduled and the procedure durations are not known in advance. The resulting optimization model’s tractability focuses the paper’s attention on approximation methods and a special case that is amenable to decomposition-based solution methods. Theoretical performance guarantees are presented for list-based approximation methods as well as an approximation that is common in practice, where procedure rooms are reserved for patient groups in advance. Numerical results based on a real outpatient procedure center demonstrate the favorable results of the list-based approximations based on their average and worst case performances, as well as their computational requirements. Further, the numerical experiments show that the policy of reserving procedure rooms for patient groups in advance can perform poorly. These results are contrary to common practice and favor alternative, and still easy-to-implement, policies. The online supplement is available at https://doi.org/10.1287/ijoc.2017.0750 .

Poor adherence to medication is a serious problem in the United States, leading to complications and preventable hospitalizations, particularly for patients with chronic diseases. Interventions hav...

Background. New cancer biomarkers are being discovered at a rapid pace; however, these tests vary in their predictive performance characteristics, and it is unclear how best to use them. Methods. We investigated 2-stage biomarker-based screening strategies in the context of prostate cancer using a partially observable Markov model to simulate patients’ progression through prostate cancer states to mortality from prostate cancer or other causes. Patients were screened every 2 years from ages 55 to 69. If the patient’s serum prostate-specific antigen (PSA) was over a specified threshold in the first stage, a second stage biomarker test was administered. We evaluated design characteristics for these 2-stage strategies using 7 newly discovered biomarkers as examples. Monte Carlo simulation was used to estimate the number of screening biopsies, prostate cancer deaths, and quality-adjusted life-years (QALYs) per 1000 men. Results. The all-cancer biomarkers significantly underperformed the high-grade cancer biomarkers in terms of QALYs. The screening strategy that used a PSA threshold of 2 ng/mL and a second biomarker test with high-grade sensitivity and specificity of 0.86 and 0.62, respectively, maximized QALYs. This strategy resulted in a prostate cancer death rate within 1% of using PSA alone with a threshold of 2 ng/mL, while reducing the number of biopsies by 20%. Sensitivity analysis suggests that the results are robust with respect to variation in model parameters. Conclusions. Two-stage biomarker screening strategies using new biomarkers with risk thresholds optimized for high-grade cancer detection may increase quality-adjusted survival and reduce unnecessary biopsies.

This article addresses an appointment scheduling problem in which the server responds to congestion of the service system. Using waiting time as a proxy for how far behind schedule the server is running, we characterize the congestion-induced behavior of the server as a function of a customer’s waiting time. Decision variables are the scheduled arrival times for a specific sequence of customers. The objective of our model is to minimize a weighted cost incurred for a customer’s waiting time, server overtime and server speedup in response to congestion. We provide alternative formulations of this problem as a Simulation Optimization (SO) model and a Stochastic Integer Programming (SIP) model, respectively. We show that the SIP model can solve moderate-sized instances exactly under certain assumptions about a server′s response to congestion. We further show that the SO model achieves near-optimal solutions for moderate-sized problems while also being able to scale up to much larger problem instances. We present theoretical results for both models and we carry out a series of experiments to illustrate the characteristics of the optimal schedules and to measure the importance of accounting for a server′s response to congestion when scheduling appointments using a case study for an outpatient clinic at a large medical center. Finally, we summarize the most important managerial insights obtained from this study.

Prostate cancer (PCa) is common in American men with long latent periods during which the disease is asymptomatic. Active surveillance is a monitoring strategy that is commonly used for patients diagnosed with low-risk PCa who may harbor a latent high-risk PCa. The optimal monitoring strategy attempts to minimize the harm of testing while ensuring the patient is detected at the earliest time when the disease progresses. Guidelines for active surveillance of PCa are often one-size-fits-all strategies that ignore the heterogeneity of patients. In contrast, personalized strategies based on partially observable Markov decision process (POMDP) models are challenging to implement in practice because the number of strategies is so large. In contrast, this article presents a two-stage stochastic programming approach that selects a set of strategies of pre-defined cardinality based on patients' disease risks. The first-stage decision variables include binary variables for the selection of periods at which to test patients in each strategy and assignment of patients to strategies. The objective is to maximize a weighted reward function that considers the need for cancer detection, missed detection, and the cost of monitoring patients. We discuss the structure and complexity of the model, and we reformulate a logic-based Bender's decomposition formulation that can solve realistic instances to optimality. We present a case study for active surveillance for PCa and show that our model results in strategies that vary in intensity according to patient disease risk. Finally, we show that our model can generate a small number of strategies that can significantly improve upon the existing "one-size-fits-all'' guideline strategies used in practice.

Markov decision processes (MDPs) are models for sequential decision-making that inform decision making in many fields, including healthcare, manufacturing, and others. However, the optimal policy for an MDP may be sensitive to the reward and transition parameters which are often uncertain because parameters are typically estimated from data or rely on expert opinion. To address parameter uncertainty in MDPs, it has been proposed that multiple models of the parameters be incorporated into the solution process, but solving these problems can be computationally challenging. In this article, we propose a policy-based branch-and-bound approach that leverages the structure of these problems and numerically compare several important algorithmic designs. We demonstrate that our approach outperforms existing methods on test cases from the literature including randomly generated MDPs, a machine maintenance MDP, and an MDP for medical decision making.

Chemotherapy infusion treatments for cancer have significant and unpredictable variability in duration. This variability can have negative impact on operations – both patient wait time and staff overtime – if not managed well. From an appointment scheduling optimization perspective, this problem has a unique structure because a single server (a nurse) attends to multiple customers (patients) at one time. Based on our observations at the University of Michigan Comprehensive Cancer Center (UMCCC) and collaborations with clinicians there, we present a two-stage stochastic integer program for designing patient appointment schedules under uncertainty in treatment times. The objective is to minimize a trade-off between expected patient wait times and expected total time required to treat patients. We show that solving this optimization problem exactly requires a prohibitive computational time, so we develop a heuristic algorithm to find approximate solutions. We also present an approach to compute lower...

In rare situations, stochastic programs can be solved analytically. Otherwise, approximation is necessary to solve stochastic programs with a large or infinite number of scenarios to a desired level of accuracy. This involves statistical sampling or deterministic selection of a finite set of scenarios to obtain a tractable deterministic equivalent problem. Some of these approaches rely on bounds for primal and dual decision variables of the second stage. We develop new algorithms to improve these bounds and reduce the deterministic approximation error. Experiments were conducted to compare a sequential approximation approach with and without these new algorithms. Each algorithm is applied to a set of test instances for a problem of managing semiconductor inventory with downward substitutions, where random variables only appear in the right-hand side of the second stage. Experiments were also conducted using a sample average approximation (SAA) algorithm. The sequential approximation and SAA algorithm generate a feasible solution upon termination. We directly compare the quality of these solutions using a paired student t-test.

According to data from the Surveillance, Epidemiology, and End Results (SEER) program in the United States, approximately 15% of men will be diagnosed with prostate cancer during their lifetimes. Over the past 15 years, the battle against prostate cancer has been joined by researchers and practitioners who have used a wide variety of operations research (OR) models and methods to investigate decisions involving screening, detection, and treatment of prostate cancer. We provide a narrative review of articles falling into the following five categories: decision analysis, machine learning, optimization, simulation, and statistics. We identified a total of 523 archival journal articles describing the use of methods in these categories in the context of prostate cancer since 2000. We categorize and annotate 49 of these articles in order to provide representative examples of the use of OR models and methods in each of these areas. We conclude with a summary of the trends in research using OR methods in the context of prostate cancer over the past 15 years, and a discussion about how these trends will influence future research.

Background Clinical registries provide physicians with a means for making data-driven decisions but few opportunities exist for patients to interact with registry data to help make decisions. Objective We sought to develop a web-based system that uses a prostate cancer (CaP) registry to provide newly diagnosed men with a platform to view predicted treatment decisions based on patients with similar characteristics. Design, setting, and participants The Michigan Urological Surgery Improvement Collaborative (MUSIC) is a quality improvement consortium of urology practices that maintains a prospective registry of men with CaP. We used registry data from 45 MUSIC urology practices from 2015 to 2017 to develop and validate a random forest machine learning model. After fitting the random forest model to a derivation cohort consisting of a random two-thirds sample of patients after stratifying by practice location, we evaluated the model performance in a validation cohort consisting of the remaining one-third of patients using a multiclass area under the curve (AUC) measure and calibration plots. Results and limitations We identified 7543 men diagnosed with CaP, of whom 45% underwent radical prostatectomy, 30% surveillance, 17% radiation therapy, 5.6% androgen deprivation, and 1.8% watchful waiting. The personalized prediction for patients in the validation cohort was highly accurate (AUC 0.81). Conclusions Using clinical registry data and machine learning methods, we created a web-based platform for patients that generates accurate predictions for most CaP treatments. Patient summary We have developed and tested a tool to help men newly diagnosed with prostate cancer to view predicted treatment decisions based on similar patients from our registry. We have made this tool available online for patients to use.

OBJECTIVE Our objective was to understand the reliability of profiling surgeons on average health care spending. SUMMARY OF BACKGROUND DATA Under its Merit-based Incentive Payment System (MIPS), Medicare will measure surgeon spending and tie performance to payments. Although the intent of this cost-profiling is to reward low-cost surgeons, it is unknown whether surgeons can be accurately distinguished from their peers. METHODS We used Michigan Medicare and commercial payer claims data to construct episodes of surgical care and to calculate average annual spending for individual surgeons. We then estimated the "reliability" (ie, the ability to distinguish surgeons from their peers) of these cost-profiles and the case-volume that surgeons would need in order to achieve high reliability [intraclass correlation coefficient (ICC) >0.8]. Finally, we calculated the reliability of 2 alternative methods of profiling surgeons (ie, using multiple years of data and grouping surgeons by hospitals). RESULTS We found that annual cost-profiles of individual surgeons had poor reliability; the ICC ranged from

The optimal strategy for the vaccinating against herpes zoster (HZ) vaccine remains unknown. Cost-effectiveness analyses provide insight to the most cost-effective age groups but results vary across studies. The optimal strategy is important given that vaccine efficacy and duration vary depending on vaccination age. Therefore, small changes from the optimal age can affect long-term outcomes and produce sub-optimal results. The objective of this research was to determine the optimal timing policy for HZ vaccination. We simulated cohorts of men and women and use stochastic dynamic programming to evaluate the decision to vaccinate or defer each year from age 50 to 100. If the decision was to defer, the cohort risked developing HZ. If HZ occurred, the cohort was subjected to cost and quality-adjusted life year (QALY) loss for a typical HZ infection (including complications) at that age. If HZ did not occur, the decision was evaluated at the next age. Then, we extend the model to consider the case in which a booster vaccine is available. A set of probabilistic sensitivity analyses were conducted to check model robustness. Results show the optimal policy for women is to vaccinate between ages 66 and 77, and for men between ages 66 and 74, assuming a willingness to pay (WTP) of $100,000 per QALY. It becomes optimal to vaccinate earlier if a booster vaccine is available, and women have a wider range of ages than men. This research is the first to examine exactly when the HZ vaccine should be administered. It is also the first study, to our knowledge, that used stochastic dynamic programming to examine the question of a second dose for any vaccine. This research provides the first simple policy on when to vaccinate and re-vaccinate against HZ.

Objective To determine how well demographic and clinical factors predict the initiation of Active Surveillance (AS). Methods AS has been suggested as a way to reduce overtreatment of men who have prostate cancer; however, factors associated with the decision to choose AS are poorly quantified. Using the Michigan Urological Surgery Improvement Collaborative registry, we identified 2977 men with prostate cancer who made treatment decisions from January 1, 2012, through December 31, 2013. We used chi-square and Wilcoxon tests to examine the association between factors and initiation of AS. Logistic regression models were fit for D'Amico risk categories. Measures of model discrimination and calibration were estimated, including area under the curve (AUC) and Brier score (BS). Results Patient age, Gleason score, clinical T-stage, urology practice, and tumor volume (greatest percent of a core involved with cancer and proportion of positive cores) were associated with the decision to choose AS in the intermediate-risk cohort (AUC = 0.875, BS = 0.07) and the complete cohort (AUC = 0.89, BS = 0.10). Patient age, urology practice, and tumor volume were significant in the low-risk cohort (AUC = 0.71, BS = 0.22). The addition of urology practice increased AUC in the low-risk cohort from 0.71 to 0.76 and reduced BS from 0.22 to 0.21. Conclusion The urology practice at which a patient is seen is an important predictor for whether patients will initiate AS. Predictions were least accurate for low-risk patients, suggesting that factors such as patient preference play a role in treatment decisions.