Quantile regression forests for individualized surgery scheduling.

Determining the optimal surgical case start times is a challenging stochastic optimization problem that shares a key feature with many other healthcare operations problems. Namely, successful problem solutions require using a vast array of available historical data to create distributions that accurately capture a case duration's uncertainty for integration into an optimization model. Distribution fitting is the conventional approach to generate these distributions, but it can only employ a limited, aggregate portion of the detailed patient features available in Electronic Medical Records systems today. If all the available information can be taken advantage of, then distributions individualized to every case can be constructed whose precision would support higher quality solutions in the presence of uncertainty. Our individualized stochastic optimization framework shows how the quantile regression forest (QRF) method predicts individualized distributions that are integrable into sample-average approximation, robust optimization, and distributionally robust optimization models for problems like surgery scheduling. In this paper, we present some related theoretical performance guarantees for each formulation. Numerically, we also study our approach's benefits relative to three other traditional models using data from Memorial Sloan Kettering Cancer Center in New York, NY, USA.

Predicting rapid progression phases in glaucoma using a soft voting ensemble classifier exploiting Kalman filtering.

In managing patients with chronic diseases, such as open angle glaucoma (OAG), the case treated in this paper, medical tests capture the disease phase (e.g. regression, stability, progression, etc.) the patient is currently in. When medical tests have low residual variability (e.g. empirical difference between the patient's true and recorded value is small) they can effectively, without the use of sophisticated methods, identify the patient's current disease phase; however, when medical tests have moderate to high residual variability this may not be the case. This paper presents a framework for handling the latter case. The framework presented integrates the outputs of interacting multiple model Kalman filtering with supervised learning classification. The purpose of this integration is to estimate the true values of patients' disease metrics by allowing for rapid and non-rapid phases; and dynamically adapting to changes in these values over time. We apply our framework to classifying whether a patient with OAG will experience rapid progression over the next two or three years from the time of classification. The performance (AUC) of our model increased by approximately 7% (increased from 0.752 to 0.819) when the Kalman filtering results were incorporated as additional features in the supervised learning model. These results suggest the combination of filters and statistical learning methods in clinical health has significant benefits. Although this paper applies our methodology to OAG, the methodology developed is applicable to other chronic conditions.

Data-driven optimization methodology for admission control in critical care units.

The decision of whether to admit a patient to a critical care unit is a crucial operational problem that has significant influence on both hospital performance and patient outcomes. Hospitals currently lack a methodology to selectively admit patients to these units in a way that patient health risk metrics can be incorporated while considering the congestion that will occur. The hospital is modeled as a complex loss queueing network with a stochastic model of how long risk-stratified patients spend time in particular units and how they transition between units. A Mixed Integer Programming model approximates an optimal admission control policy for the network of units. While enforcing low levels of patient blocking, we optimize a monotonic dual-threshold admission policy. A hospital network including Intermediate Care Units (IMCs) and Intensive Care Units (ICUs) was considered for validation. The optimized model indicated a reduction in the risk levels required for admission, and weekly average admissions to ICUs and IMCs increased by 37% and 12%, respectively, with minimal blocking. Our methodology captures utilization and accessibility in a network model of care pathways while supporting the personalized allocation of scarce care resources to the neediest patients. The interesting benefits of admission thresholds that vary by day of week are studied.

Personalized Prediction of Glaucoma Progression Under Different Target Intraocular Pressure Levels Using Filtered Forecasting Methods.

PURPOSE: To generate personalized forecasts of how patients with open-angle glaucoma (OAG) experience disease progression at different intraocular pressure (IOP) levels to aid clinicians with setting personalized target IOPs. DESIGN: Secondary analyses using longitudinal data from 2 randomized controlled trials. PARTICIPANTS: Participants with moderate or advanced OAG from the Collaborative Initial Glaucoma Treatment Study (CIGTS) or the Advanced Glaucoma Intervention Study (AGIS). METHODS: By using perimetric and tonometric data from trial participants, we developed and validated Kalman Filter (KF) models for fast-, slow-, and nonprogressing patients with OAG. The KF can generate personalized and dynamically updated forecasts of OAG progression under different target IOP levels. For each participant, we determined how mean deviation (MD) would change if the patient maintains his/her IOP at 1 of 7 levels (6, 9, 12, 15, 18, 21, or 24 mmHg) over the next 5 years. We also model and predict changes to MD over the same time horizon if IOP is increased or decreased by 3, 6, and 9 mmHg from the level attained in the trials. MAIN OUTCOME MEASURES: Personalized estimates of the change in MD under different target IOP levels. RESULTS: A total of 571 participants (mean age, 64.2 years; standard deviation, 10.9) were followed for a mean of 6.5 years (standard deviation, 2.8). Our models predicted that, on average, fast progressors would lose 2.1, 6.7, and 11.2 decibels (dB) MD under target IOPs of 6, 15, and 24 mmHg, respectively, over 5 years. In contrast, on average, slow progressors would lose 0.8, 2.1, and 4.1 dB MD under the same target IOPs and time frame. When using our tool to quantify the OAG progression dynamics for all 571 patients, we found no statistically significant differences over 5 years between progression for black versus white, male versus female, and CIGTS versus AGIS participants under different target IOPs (P > 0.05 for all). CONCLUSIONS: To our knowledge, this is the first clinical decision-making tool that generates personalized forecasts of the trajectory of OAG progression at different target IOP levels. This approach can help clinicians determine appropriate, personalized target IOPs for patients with OAG.

Coordinating clinic and surgery appointments to meet access service levels for elective surgery.

Providing timely access to surgery is crucial for patients with high acuity diseases like cancer. We present a methodological framework to make efficient use of scarce resources including surgeons, operating rooms, and clinic appointment slots with a goal of coordinating clinic and surgery appointments so that patients with different acuity levels can see a surgeon in the clinic and schedule their surgery within a maximum wait time target that is clinically safe for them. We propose six heuristic scheduling policies with two underlying ideas behind them: (1) proactively book a tentative surgery day along with the clinic appointment at the time an appointment request is received, and (2) intelligently space out clinic and surgery appointments such that if the patient does not need his/her surgery appointment there is sufficient time to offer it to another patient. A 2-stage stochastic discrete-event simulation approach is employed to evaluate the six scheduling policies. In the first stage of the simulation, the heuristic policies are compared in terms of the average operating room (OR) overtime per day. The second stage involves fine-tuning the most-effective policy. A case study of the division of colorectal surgery (CRS) at the Mayo Clinic confirms that all six policies outperform the current scheduling protocol by a large margin. Numerical results demonstrate that the final policy, which we refer to as Coordinated Appointment Scheduling Policy considering Indication and Resources (CASPIR), performs 52% better than the current scheduling policy in terms of the average OR overtime per day under the same access service level. In conclusion, surgical divisions desiring stratified patient urgency classes should consider using scheduling policies that take the surgical availability of surgeons, patients' demographics and indication of disease into consideration when scheduling a clinic consultation appointment.

Using filtered forecasting techniques to determine personalized monitoring schedules for patients with open-angle glaucoma.

PURPOSE: To determine whether dynamic and personalized schedules of visual field (VF) testing and intraocular pressure (IOP) measurements result in an improvement in disease progression detection compared with fixed interval schedules for performing these tests when evaluating patients with open-angle glaucoma (OAG). DESIGN: Secondary analyses using longitudinal data from 2 randomized controlled trials. PARTICIPANTS: A total of 571 participants from the Advanced Glaucoma Intervention Study (AGIS) and the Collaborative Initial Glaucoma Treatment Study (CIGTS). METHODS: Perimetric and tonometric data were obtained for AGIS and CIGTS trial participants and used to parameterize and validate a Kalman filter model. The Kalman filter updates knowledge about each participant's disease dynamics as additional VF tests and IOP measurements are obtained. After incorporating the most recent VF and IOP measurements, the model forecasts each participant's disease dynamics into the future and characterizes the forecasting error. To determine personalized schedules for future VF tests and IOP measurements, we developed an algorithm by combining the Kalman filter for state estimation with the predictive power of logistic regression to identify OAG progression. The algorithm was compared with 1-, 1.5-, and 2-year fixed interval schedules of obtaining VF and IOP measurements. MAIN OUTCOME MEASURES: Length of diagnostic delay in detecting OAG progression, efficiency of detecting progression, and number of VF and IOP measurements needed to assess for progression. RESULTS: Participants were followed in the AGIS and CIGTS trials for a mean (standard deviation) of 6.5 (2.8) years. Our forecasting model achieved a 29% increased efficiency in identifying OAG progression (P<0.0001) and detected OAG progression 57% sooner (reduced diagnostic delay) (P = 0.02) than following a fixed yearly monitoring schedule, without increasing the number of VF tests and IOP measurements required. The model performed well for patients with mild and advanced disease. The model performed significantly more testing of patients who exhibited OAG progression than nonprogressing patients (1.3 vs. 1.0 tests per year; P<0.0001). CONCLUSIONS: Use of dynamic and personalized testing schedules can enhance the efficiency of OAG progression detection and reduce diagnostic delay compared with yearly fixed monitoring intervals. If further validation studies confirm these findings, such algorithms may be able to greatly enhance OAG management.

Augmenting Kalman Filter Machine Learning Models with Data from OCT to Predict Future Visual Field Loss: An Analysis Using Data from the African Descent and Glaucoma Evaluation Study and the Diagnostic Innovation in Glaucoma Study.

Purpose: To assess whether the predictive accuracy of machine learning algorithms using Kalman filtering for forecasting future values of global indices on perimetry can be enhanced by adding global retinal nerve fiber layer (RNFL) data and whether model performance is influenced by the racial composition of the training and testing sets. Design: Retrospective, longitudinal cohort study. Participants: Patients with open-angle glaucoma (OAG) or glaucoma suspects enrolled in the African Descent and Glaucoma Evaluation Study or Diagnostic Innovation in Glaucoma Study. Methods: We developed a Kalman filter (KF) with tonometry and perimetry data (KF-TP) and another KF with tonometry, perimetry, and global RNFL data (KF-TPO), comparing these models with one another and with 2 linear regression (LR) models for predicting mean deviation (MD) and pattern standard deviation values 36 months into the future for patients with OAG and glaucoma suspects. We also compared KF model performance when trained on individuals of European and African descent and tested on patients of the same versus the other race. Main Outcome Measures: Predictive accuracy (percentage of MD values forecasted within the 95% repeatability interval) differences among the models. Results: Among 362 eligible patients, the mean ± standard deviation age at baseline was 71.3 ± 10.4 years; 196 patients (54.1%) were women; 202 patients (55.8%) were of European descent, and 139 (38.4%) were of African descent. Among patients with OAG (n = 296), the predictive accuracy for 36 months in the future was higher for the KF models (73.5% for KF-TP, 71.2% for KF-TPO) than for the LR models (57.5%, 58.0%). Predictive accuracy did not differ significantly between KF-TP and KF-TPO (P = 0.20). If the races of the training and testing set patients were aligned (versus nonaligned), the mean absolute prediction error of future MD improved 0.39 dB for KF-TP and 0.48 dB for KF-TPO. Conclusions: Adding global RNFL data to existing KFs minimally improved their predictive accuracy. Although KFs attained better predictive accuracy when the races of the training and testing sets were aligned, these improvements were modest. These findings will help to guide implementation of KFs in clinical practice.

Comparing Perimetric Loss at Different Target Intraocular Pressures for Patients with High-Tension and Normal-Tension Glaucoma.

PURPOSE: To compare forecasted changes in mean deviation (MD) for patients with normal-tension glaucoma (NTG) and high-tension open-angle glaucoma (HTG) at different target intraocular pressures (IOPs) using Kalman filtering, a machine learning technique. DESIGN: Retrospective cohort study. PARTICIPANTS: From the Collaborative Initial Glaucoma Treatment Study or Advanced Glaucoma Intervention Study, 496 patients with HTG; from Japan, 262 patients with NTG. METHODS: Using the first 5 sets of tonometry and perimetry measurements, each patient was classified as a fast progressor, slow progressor, or nonprogressor. Using Kalman filtering, personalized forecasts of MD changes over 2.5 years' follow-up were generated for fast and slow progressors with HTG and NTG with IOPs maintained at hypothetical IOP targets of 9 to 21 mmHg. Future MD loss with different percentage IOP reductions from baseline (0%-50%) were also assessed for the groups. MAIN OUTCOME MEASURES: Mean forecasted MD change at different target IOPs. RESULTS: The mean (± standard deviation) patient age was 63.5 ± 10.5 years for NTG and 66.5 ± 10.9 years for HTG. Over the 2.5-year follow-up, at target IOPs of 9, 15, and 21 mmHg, respectively, the mean forecasted MD losses for fast progressors with NTG were 2.3 ± 0.2, 4.0 ± 0.2, and 5.7 ± 0.2 dB; for slow progressors with NTG, losses were 0.63 ± 0.02, 1.02 ± 0.03, and 1.49 ± 0.07 dB; for fast progressors with HTG, losses were 1.8 ± 0.1, 3.4 ± 0.1, and 5.1 ± 0.1 dB; and for slow progressors with HTG, losses were 0.55 ± 0.06, 1.04 ± 0.08, and 1.59 ± 0.10 dB. Fast progressors with NTG had greater MD decline than fast progressors with HTG at each target IOP (P ≤ 0.007 for all). The MD decline for slow progressors with HTG and NTG were similar (P ≥ 0.24 for all target IOPs). Fast progressors with HTG had greater MD loss than those with NTG with 0%-10% IOP reduction since baseline (P ≤ 0.01 for all), but not 25% (P = 0.07) or 50% (P = 0.76) reduction since baseline. CONCLUSIONS: Machine learning algorithms using Kalman filtering techniques demonstrate promise at forecasting future MD values at different target IOPs for patients with NTG and HTG.

Access Planning and Resource Coordination for Clinical Research Operations.

This research creates an operations engineering and management methodology to optimize a complex operational planning and coordination challenge faced by sites that perform clinical research trials. The time-sensitive and resource-specific treatment sequences for each of the many trial protocols conducted at a site make it very difficult to capture the dynamics of this unusually complex system. Existing approaches for site planning and participant scheduling exhibit both excessively long and highly variable Time to First Available Visit (TFAV) waiting times and high staff overtime costs. We have created a new method, termed CApacity Planning Tool And INformatics (CAPTAIN) that provides decision support to identify the most valuable set of research trials to conduct within available resources and a plan for how to book their participants. Constraints include (i) the staff overtime costs, and/or (ii) the TFAV by trial. To estimate the site's metrics via a Mixed Integer Program, CAPTAIN combines a participant trajectory forecasting with an efficient visit booking reservation plan to allocate the date for the first visit of every participant's treatment sequence. It also plans a daily nursing staff schedule that is optimized together with the booking reservation plan to optimize each nurse's shift assignments in consideration of participants' requirements/needs.

Dynamic Monitoring and Control of Irreversible Chronic Diseases with Application to Glaucoma.

To manage chronic disease patients effectively, clinicians must know (1) how to monitor each patient (i.e., when to schedule the next visit and which tests to take), and (2) how to control the disease (i.e., what levels of controllable risk factors will sufficiently slow progression). Our research addresses these questions simultaneously and provides the optimal solution to a novel linear quadratic Gaussian state space model. For the objective of minimizing the relative change in state over time (i.e., disease progression), which is necessary for managing irreversible chronic diseases while also considering the cost of tests and treatment, we show that the classical two-way separation of estimation and control holds. This makes a previously intractable problem solvable by decomposition into two separate, tractable problems while maintaining optimality. The resulting optimization is applied to the management of glaucoma. Based on data from two large randomized clinical trials, we validate our model and demonstrate how our decision support tool can provide actionable insights to the clinician caring for a patient with glaucoma. This methodology can be applied to a broad range of irreversible chronic diseases to devise patient-specific monitoring and treatment plans optimally.

Accuracy of Kalman Filtering in Forecasting Visual Field and Intraocular Pressure Trajectory in Patients With Ocular Hypertension.

Importance: Techniques that properly identify patients in whom ocular hypertension (OHTN) is likely to progress to open-angle glaucoma can assist clinicians with deciding on the frequency of monitoring and the potential benefit of early treatment. Objective: To test whether Kalman filtering (KF), a machine learning technique, can accurately forecast mean deviation (MD), pattern standard deviation, and intraocular pressure values 5 years into the future for patients with OHTN. Design, Setting, and Participants: This cohort study was a secondary analysis of data from patients with OHTN from the Ocular Hypertension Treatment Study, performed between February 1994 and March 2009. Patients underwent tonometry and perimetry every 6 months for up to 15 years. A KF (KF-OHTN) model was trained, validated, and tested to assess how well it could forecast MD, pattern standard deviation, and intraocular pressure at up to 5 years, and the forecasts were compared with results from the actual trial. Kalman filtering for OHTN was compared with a previously developed KF for patients with high-tension glaucoma (KF-HTG) and 3 traditional forecasting algorithms. Statistical analysis for the present study was performed between May 2018 and May 2019. Main Outcomes and Measures: Prediction error and root-mean-square error at 12, 24, 36, 48, and 60 months for MD, pattern standard deviation, and intraocular pressure. Results: Among 1407 eligible patients (2806 eyes), 809 (57.5%) were female and the mean (SD) age at baseline was 57.5 (9.6) years. For 2124 eyes with sufficient measurements, KF-OHTN forecast MD values 60 months into the future within 0.5 dB of the actual value for 696 eyes (32.8%), 1.0 dB for 1295 eyes (61.0%), and 2.5 dB for 1980 eyes (93.2%). Among the 5 forecasting algorithms tested, KF-OHTN achieved the lowest root-mean-square error (1.72 vs 1.85-4.28) for MD values 60 months into the future. For the subset of eyes that progressed to open-angle glaucoma, KF-OHTN and KF-HTG forecast MD values 60 months into the future within 1 dB of the actual value for 30 eyes (68.2%; 95% CI, 54.4%-82.0%) and achieved the lowest root-mean-square error among all models. Conclusions and Relevance: These findings suggest that machine learning algorithms such as KF can accurately forecast MD, pattern standard deviation, and intraocular pressure 5 years into the future for many patients with OHTN. These algorithms may aid clinicians in managing OHTN in their patients.

Using Kalman Filtering to Forecast Disease Trajectory for Patients With Normal Tension Glaucoma.

PURPOSE: To determine whether a machine learning technique called Kalman filtering (KF) can accurately forecast future values of mean deviation (MD), pattern standard deviation, and intraocular pressure for patients with normal tension glaucoma (NTG). DESIGN: Development and testing of a forecasting model for glaucoma progression. METHODS: We parameterized and validated a KF (KF-NTG) to forecast MD, pattern standard deviation, and intraocular pressure at 24 months into the future using 263 eyes of 263 Japanese patients with NTG. We determined the proportion of patients with MD forecasts within 0.5, 1.0, and 2.5 dBs of the actual values and calculated the root mean squared error (RMSE) for each forecast. We compared KF-NTG with a previously published KF model calibrated using patients with high-tension open-angle glaucoma (KF-HTG) and to 3 conventional forecasting algorithms. RESULTS: The 263 patients with NTG had mean ± standard deviation age of 63.4 ± 10.5 years. KF-NTG forecasted MD values 24 months ahead within 0.5, 1.0, and 2.5 dBs of the actual value for 78 eyes (32.2%), 122 eyes (50.4%), and 211 eyes (87.2%), respectively. The proportion of eyes with MD values forecasted within 2.5 dB of the actual value for the KF-NTG (87.2%) were similar to KF-HTG (86.0%) and the null model (86.4%), and much better than the 2 linear regression-based models (72.7-74.0%; P < .001). When forecasting MD, KF-NTG (RMSE = 2.71) and KF-HTG (RMSE = 2.68) achieved lower RMSE than the other 3 forecasting models (RMSE = 2.81-3.90), indicating better performance. CONCLUSION: As observed previously for patients with HTG, KF can also effectively forecast disease trajectory for many patients with NTG.

A Capacity Allocation Planning Model for Integrated Care and Access Management.

The prevailing first-come-first-served approach to outpatient appointment scheduling ignores differing urgency levels, leading to unnecessarily long waits for urgent patients. In data from a partner healthcare organization, we found in some departments that urgent patients were inadvertently waiting longer for an appointment than non-urgent patients. This paper develops a capacity allocation optimization methodology that reserves appointment slots based on urgency in a complicated, integrated care environment where multiple specialties serve multiple types of patients. This optimization reallocates network capacity to limit access delays (indirect waiting times) for initial and downstream appointments differentiated by urgency. We formulate this problem as a queueing network optimization and approximate it via deterministic linear optimization to simultaneously smooth workloads and guarantee access delay targets. In a case study of our industry partner we demonstrate the ability to (1) reduce urgent patient mean access delay by 27% with only a 7% increase in mean access delay for non-urgent patients, and (2) increase throughput by 31% with the same service levels and overtime.

An IP-based healthcare provider shift design approach to minimize patient handoffs.

The new Accreditation Council for Graduate Medical Education (ACGME) duty-hour standards for residents and fellows went into effect in 2011. These regulations were designed to reduce fatigue-related medical errors and improve patient safety. The new shift restrictions, however, have led to more frequent transitions in patient care (handoffs), resulting in greater opportunity for communication breakdowns between caregivers, which correlate with medical errors and adverse events. Recent research has focused on improving the quality of these transitions through standardization of the handoff protocols; however, no attention has been given to reducing the number of transitions in patient care. This research leverages integer programming methods to design a work shift schedule for trainees that minimizes patient handoffs while complying with all ACGME duty-hour standards, providing required coverage, and maintaining physician quality of life. In a case study of redesigning the trainees' schedule for a Mayo Clinic Medical Intensive Care Unit (MICU), we show that the number of patient handoffs can be reduced by 23 % and still meet all required and most desired scheduling constraints. Furthermore, a 48 % reduction in handoffs could be achieved if only the minimum required rules are satisfied.