Abstract 161: Heart Failure Care Transitions: A Queuing Theory Approach to Match Variable Hospital Discharge Rate With Outpatient Clinic Capacity
Authors: Mutharasan R. Kannan , Kansal Preeti , Abecassis Michael M , Alphs Jackson Hannah , Anderson Allen S , Benacka Corrine , Berry Jaeker Jillian A , Davidson Charles , Gurvich Itai , Navarro Daniel , Noskin Gary A , Schaeffer-Pettigrew Christine , Soulakis Nicholas D , Van Mieghem Jan , Yancy Clyde W 
Published: March 2022

Background:
Heart failure (HF) readmissions remain a major driver of cost and health care utilization. Timely follow-up of patients post-discharge represents an evidence-based intervention proven to reduce readmission rates. A previously unexplored characteristic of hospital discharges is variability in discharge caseload. This variability thwarts the timeliness of follow-up, negates the benefit of transition care planning and may lead to a higher risk of HF readmissions. Queuing theory is the mathematical study of waiting times. We opted to use queuing theory to determine if caseload can be determined more precisely in a manner that sufficiently accommodates HF discharge variability.

Objective:
To analyze the impact of hospital discharge rate variability on outpatient clinic capacity needs using HF hospitalization discharge data and operations management approaches.

Methods:
Higher risk hospitalizations requiring active transitional care heart failure management were detected using an enterprise data warehouse-supported process over the study period. Queuing theory approaches were used to model the impact of HF discharge clinic capacity on wait time to an appointment. Discharge clinic was modeled as a single 7-day follow-up appointment, with an acceptable scheduling window of 5 to 9 days post-discharge.

Results:
During the study period of 100 days, 566 HF discharges were made, for a median of 5.66 discharges daily, or 39.6 discharges weekly. The distribution of daily discharges was skewed rightward (mode = 3, range = 0 to 18, standard deviation = 3.3, coefficient of variation = 0.58). Current clinic design: Providing one discharge slot for every hospital discharge (100% utilization) leads to an average wait of 18.3 days prior to an appointment, with only 31.9% of appointments scheduled within 7 days, and 38.9% of appointments scheduled within 9 days. Clinic re-design (queuing theory): Providing five extra discharge appointment slots per week (88% utilization or 13.6% excess capacity) reduces the expected waiting period to 1.1 days, with 99.8% of patients seen within 7 days, and virtually all patients seen within 9 days of discharge.

Conclusions:
Deployment of queuing theory allows for a more precise quantification of needed clinical capacity to accomplish appropriate HF follow-up with a reasonable degree of certainty. Our simplified model demonstrates that variability in hospital discharge rates leads to excessive clinic wait times in the absence of a modest capacity buffer and consequently exposes patients to a higher risk of HF readmission. We show using single center HF discharge data that a 10-15% increase in capacity is needed to ensure an adequate follow-up service level. Ongoing process of care work will demonstrate if optimization of clinic load yields a significant reduction in HF readmissions.