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# ARTICLE IN PRESS

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### ARTICLE IN PRESS

3. 3. ARTICLE IN PRESS American Heart Journal Volume 0, Number 0 Levin et al 3 Table I. Telemetry hazard model Time interval Variables Coefficient P 95% CI 0-3 h OR × CATH LAB −3.79 b.001 −4.47 to −3.10 TELEMETRY −1.99 b.001 −2.79 to −1.18 OTHER −1.62 .089 −3.48 to −0.24 CVICU −1.18 b.001 −1.78 to −0.57 3-28 h HOSP −3.56 b.001 −4.85 to −2.26 TELEMETRY −3.04 b.001 −3.80 to −2.27 CVICU −1.85 b.001 −2.57 to −1.12 The OR × CATH LAB variable was a weighted combination (see equation below) of both variables because of high collinearity (r = 0.76). The weights, WO = 5.9% for OR and WC = 29.2% for CATH LAB, were equivalent to the corresponding patient inflow fractions to telemetry. Other, Other hospital units. WO Â OR WC Â CATH LAB OR Â CATH LAB ¼ þ WC þ WO WC þ WO Patient flow between the cardiology macrosystem units flowing in from the OR/PACU (5.9%), the CATH LAB (Figure 1) was modeled using basic queuing principles that (29.2%), the CVICU (16.0%), other remaining hospital classified each location. Telemetry and CVICU units were units (14.8%), and home (14.0%). Patients boarded for modeled as reactive, that is, these units reacted to time- telemetry had a mean boarding time of 5.3 (median 3.1, dependent fluctuations in demand coming from all inflow interquartile range [IQR] 1.5-6.9) hours. Patients boarded sources. The ORs, PACU, and the CATH LAB were modeled as proactive, that is, these units directed patient flow with highest for the CVICU had a mean boarding time of 2.7 (median priority to and from other locations in the model. Most proactive 1.7, IQR 0.8-3.0) hours. In comparison, the mean ED unit patients were electively scheduled. The ED was modeled treatment time, excluding boarding time, was 4.1 purely as an input source in relation to all other locations. The (median 1.9, [IQR] 3.2-5.3 hours). The average occu- remainder of inpatient hospital beds was modeled as a single pancy of the telemetry and CVICU units was 88% and input/output source to represent the cross-service sharing of 77%, respectively. The independent variables used to beds that existed within the hospital. predict boarding time measured demand in the following Input probability distributions generated from actual patient units: TELEMETRY, CVICU, OTHER remaining hospital flow information were used to drive the timing of arrivals and units, OR, and CATH LAB. The effect of each clinical and departures at each simulated clinical location. Length-of-stay demographic variable on boarding time was examined. within the simulation was defined as the time interval from Interestingly, none of these variables were found to be when a patient entered a unit from any location to when the patient exited that unit to any other location or home. Mann- significant predictors of boarding time to telemetry or the Whitney U tests were used to assess differences between input CVICU. The final model for telemetry-bound patients is and output probability distributions for the simulated versus real seen in Table I. The TELEMETRY, CVICU, and OTHER system. Correlation coefficients were used to compare the variables measured the number of beds occupied at their simulated versus real weekly temporal pattern in minute-by- respective locations. The OR and CATH LAB variables minute census for each location modeled. combined the number of beds occupied at each location Patients were directed to various locations within the model plus the number of procedures scheduled 3 hours into based on transfer probabilities generated from real system data. the future. A 3-hour window capturing future demand in These transfer probabilities were dependent on patients' the OR and CATH LAB was used as a result of insights previous locations. For example, a common surgical patient's gained from several interviews conducted on bed pathway through the system was to (1) arrive in the OR; (2) move to the CVICU postoperatively; (3) move to the telemetry management personnel. unit; and (4) be discharged home. By guiding location transfer The telemetry hazard model (Table I) was used to probabilities based on previous locations, common patient flow predict expected boarding time by creating a unique pathways, as such, were preserved. Boarding time to telemetry, probability distribution of boarding time for each patient location census distributions, and temporal patterns were the based on the covariates collected at the time the major output variables validated against the real system. admission order was placed. An important assumption of Cox regression is that the covariates have the same effect on the hazard function for all values of time. Variables Results capturing demand within the OR and the CATH LAB were Modeling ED boarding time found to have a nonproportional effect on the hazard During the 1-year study period, the cardiac telemetry function. Thus, the strategy of creating models over 2 units received 7,901 separate visits with 1,591 (20.1%) of disjoint periods with equal sample sizes was used.22 The these visits coming from the ED. Emergency department reader is referred to prior published work for further patients compete for telemetry beds with patients details on the boarding prediction methodology.19
4. 4. ARTICLE IN PRESS American Heart Journal 4 Levin et al Month Year Table II. Simulation verification and validation Figure 2 Real system Simulated system Comparison median (IQR) median (IQR) measure Mann- Arrivals Per Whitney Location Week U (P) ED 882 (855-899) 883 (863-904) .35 ED boarders 242 (226-256) 241 (232-252) .95 Telemetry 30 (23-36) 31 (24-37) .27 boarders CVICU 6 (5-8) 7 (4-9) .56 boarders Telemetry unit 152 (141-161) 153 (142-161) .53 CVICU 56 (50-64) 58 (54-62) .25 CATH LAB 123 ( (110-133) 122 (111-129) .38 OR 298 (278-323) 297 (279-316) .52 Cardiac 32 (24-39) 32 (25-37) .28 Boarding time probability distribution comparison. surgeries Mann- Whitney each location were validated against the real system Length of stay (h) U (P) (Table II). Pearson correlation coefficients ranged from ED treatment 3.2 (1.9-5.3) 3.2 (1.9-5.3) .96 0.78 to 0.99 for weekly temporal patterns between the ED boarding 2.1 (0.7-5.8) 2.1 (0.8-5.9) .19 simulated versus real systems. (all) Telemetry 3.1 (1.5-6.9) 3.3 (1.7-7.0) .33 Artificial variability boarders Telemetry bed management is a difficult task given CVICU 1.7 (0.8-3.0) 1.7 (0.9-3.0) .62 boarders several sources of uncertainty. Demand uncertainty is Telemetry unit 32.3 (17.2-61.4) 33.1 (18.4-61.6) .35 created by variation in patient inflow coming from a CVICU 42.1 (20.3-75.2) 43.1 (21.3-74.9) .42 multiple sources as well as variation in length-of-stay CATH LAB 5.4 (3.1-7.7) 5.5 (3.1-8.1) .34 (outflow). A common misconception is that the OR 2.5, (1.5-4.0) 2.6 (1.6-4.4) b.05 unscheduled environment of the ED produces much of Cardiac 6.1 (3.3-8.9) 6.1 (3.4-9.0) b.05 surgeries the variability in inpatient demand. The opposite was true for the system studied. Weekly variability in unscheduled Census distributions Correlation patients arriving to the ED (coefficient of variation [CV] (minute-by-minute) coefficient (r) 0.03) was significantly lower than variability associated with electively scheduled surgeries (CV 0.09) and CATH ED 32 (26-37) 32 (24-38) 0.97 ED boarding 7 (4-11) 7 (4-11) 0.96 LAB procedures (CV 0.10). Weekly variability in demand Telemetry unit 42 (37-45) 42 (36-45) 0.78 is being increased artificially by elective surgical and CVICU 20 (17-22) 20 (17-23) 0.86 catheterization scheduling practices.23 Demand uncer- CATH LAB 3, (1-10) 3 (1-9) 0.94 tainty must be managed effectively to optimize capacity OR 2 (0-11) 3 (1-12) 0.99 and reduce ED boarding. Other hospital 731 (696-756) 731 (691-761) 0.97 units Simulation model results Results of the telemetry hazard model display that demand coming from the OR and the CATH LAB (OR × Discrete event simulation verification and validation CATH LAB) was the strongest driver of boarding time. The Simulation input distributions capturing arrivals per CATH LAB is most influential because of the weighting week and length-of-stay were verified to match the real scheme used. Electively scheduled patients coming from system (Table II). The simulated OR length-of-stay home represent the CATH LAB's biggest source (64.2%) of distribution did not meet the null hypothesis of coming inflow. However, the outflow for these scheduled from the corresponding real-system distribution. Char- patients is quite uncertain; 50.5% were discharged home, acteristics of these distributions were compared and 30.1% were directed to a telemetry bed, 8.2% went to the determined to be accurate enough for the intended OR, 6.2% went to the CVICU, and 5.0% were transferred application. The probability distribution of boarding time to another location within the hospital. The hospital's bed for patients telemetry bound was validated against the management practice required that a telemetry bed be real system in Figure 2. Output census distributions for reserved for all scheduled catheterization patients
5. 5. ARTICLE IN PRESS American Heart Journal Volume 0, Number 0 Levin et al 5 Figure 3 Cardiology macrosystem patient flow patterns on a typical weekday (6:00 AM to 6:00 AM). Curves represent the probability of the event occurring by hour of day. coming from home. Thus, unoccupied telemetry beds (Figure 4, A). All other inputs being constant, moving one were held for these potential patients, blocking access to afternoon scheduled elective catheterization case to ED patients. before noon on the weekdays resulted in a 6.4% or 20- Scheduling and bed management practices drive minute reduction in average boarding time. In compar- patterns of patient flow through the cardiology macro- ison, increasing telemetry unit capacity (Figure 4, B) by system. A telemetry admission request from the ED has one additional bed resulted in a 2.9% or 9-minute the highest probability of occurring at around 6:00 PM on reduction in average boarding time. A subtle low cost a typical weekday (Figure 3). At this time, N40.0% of scheduling solution aimed at optimizing capacity out- patients scheduled to undergo CATH LAB procedures that performs the higher cost alternative of adding capacity. day have not yet been discharged. The CATH LAB is the largest source of telemetry demand uncertainty as late as 6:00 PM. Uncertainty does not subside to a level allowing Discussion ED patients' access until almost 11:00 PM. This is This study demonstrates a systems engineering demonstrated by the peak in ED transfers to telemetry approach to analyze a hospital macrosystem's relation- (Figure 3). The interval between the admission request ship with the ED. We developed a novel modeling peak and the telemetry transfer peak reflects patient technique to analyze prospective strategies aimed at boarding time. reducing ED boarding time. A low-cost scheduling Examining the repetitive weekday pattern of patient strategy designed to offset unscheduled arrivals (ie, ED flow led to the hypothesis that reducing CATH LAB admission requests) with elective arrivals from the CATH outflow during the period when ED admission requests LAB was superior to a higher cost capacity increase. A were most likely to occur would reduce boarding time for systems approach to managing elective schedules to telemetry-bound patients. Such an intervention would improve interdepartment patient flow is likely to be a shift the CATH LAB discharge curve to the left (ie, earlier more effective and feasible than expanding hospital in the day) in Figure 3. Currently, 70.4% of CATH LAB capacity. Simulation construction and resulting analysis arrivals occur before noon. The simulation demonstrates supported this by providing insights about how sub- the results of having a higher percentage of patients optimal management practices may be rectified to arrive to the CATH LAB before noon on a typical weekday increase efficiency and decrease ED boarding.