This computational study using retrospectively collected data was approved by the University of Pittsburgh Institutional Review Board (STUDY19120054). The requirement for informed consent was waived by the IRB. Data from this urban, high-volume Level 4 Maternity Center were abstracted for all OR activity from July 2019 - June 2020. These OR activities included but were not limited to CD, tubal ligation, double set-up for vaginal twin delivery, dilation and curettage, external cephalic version, cerclage, fetal procedures, post-delivery procedures associated with bleeding such as laceration repairs, peri-delivery cystoscopies, exams under anesthesia with or without uterine balloon tamponade procedures, and procedures for retained placenta. Other information abstracted from the medical record included age, American Society of Anesthesiologists Physical Status (ASA PS), emergency designation by ASA PS, race, and obesity. Operational data were collected from medical records, including room locations, anesthesia start times, room start times, room end times, total room times, time of day, overlap times, and overlap frequencies.
QTA involves persons arriving in a queue, waiting in the queue, receiving service, then departing the system (Fig. 1). QTA has two primary variables of interest: Mean Arrival Rate, calculated as patients per hour λ = number of patients per year divided by the number of hours; and Mean Service Rate µ = average length of cases in hours per patient / hour7. Both λ and µ can be calculated using historical or observed data. We abstracted this data from our medical records as described above. The arrival rate was defined using anesthesia start times; service rates were defined using OR times (anesthesia start and stop times). QTA formulas computed probabilities: P0 = 1-(λ/ µ) and Pn = P0 (λ/µ)n where n = number of patients. P0…n is the probability there are zero (P0) or one (P1) patients in the OR queue at a given time, and the probability that ≥ 2 patients require ORs simultaneously (P2…n). All probabilities add up to 1 (P0 + P1 + P2…Pn = 1). Therefore,
P≥ 2 = 1-(P0 + P1) and
P≥ 2 = 1-((1-λ/ µ) + [(1-λ/ µ)( λ/ µ)])
Utilization ratio (ρ) is defined as a ratio of demand for service to capacity as it changes throughout a workday. It is calculated as ρ = λ/µ and gives an understanding of the demand for resources. When ρ ≥ 1, a backlog develops and worsens. In the context of obstetric operations, an ideal ρ is not universally defined, but should ideally be low to allow minimal wait times and access to operative interventions to minimize risk for maternal or fetal harm. Setting a lower ρ also enables high variability in arrival rates and service times. Other parameters defined in our QTA included: the average number of people in the system (Ls), the average length of the queue or the average number of people in a line waiting for service (Lq), the average time for a patient in the system or waiting time plus service time (Ws), average time spent in the queue (Wq), the probability that the time spent in the queue is zero (Wq(0)), number of patients in the system and number of operating rooms in use in the system (n), and the probability that n patients require simultaneous OR service (Pn). Although an ideal Wq(0) and Pn are not defined for obstetric operations, we defined a Pn <1% and a Wq(0) no lower than 99% as acceptable parameters for clinical operations to optimize maternal-fetal safety and minimize the risk associated with delays.
In this study, we used the singular term “server team” to encompass all individuals required to staff one OR. This team consists of an anesthesia provider, circulator nurse, a perinatal nurse, a surgical technician, and an obstetrician with or without an assistant. At our institution, the anesthesia team in the birth center ORs follows a medical direction model consisting of an attending anesthesiologist plus a qualified hands-on provider (QHOP), i.e., resident, fellow, or nurse anesthetist. The anesthesia team is dedicated to the obstetric suite. The anesthesiologist oversees a maximum of 2 rooms when 1 or 2 are staffed with a resident; and, a maximum of 4 rooms if all rooms are staffed with nurse anesthetists. The model was run for the number of ORs in addition to the number of server teams. This model was not designed to speak to the availability of individual server components (e.g., availability of circulator, technician, nurse, etc.) in the ability to mount a surge response. Room turnover procedures, including cleaning and room preparations, are an average of 30 minutes at our institution but were not explicitly included in the model.
Model Assumptions.
Safety parameters were defined by 30 minutes decision-to-incision in unscheduled non-emergent CD; ≤5 minutes for emergent CD; no greater than 8 hours for nil per os time (for elective or non-emergent cases). The model assumed the following. To achieve these safety targets, a < 0.5% probability that a patient would need to wait was assumed. We assumed Pn <1% and a Wq(0) no lower than 99%. Although other centers reported reductions in obstetric care utilization associated with the COVID-19 pandemic, that phenomenon was not observed in our cohort during this study period.
Statistical Analysis.
Summary statistics for demographic information included mean and standard deviation for continuous variables following a standard normal distribution and frequencies with percentages for ordinal data. Multiphase multichannel analysis was used to gain insights on optimal staff and space utilization, assuming a priori assumptions and safety parameters. Target utilization ρ was set at > 0.10. Poisson distribution of total operating room time was examined using histograms. Percentage of ORs overlapping were grouped by time of day and examined by histograms. Time intervals of overlaps were grouped (up to 15-minute overlap, up to a 30-minute overlap, and so on, until greater than 60-minute overlap). Percentages of these overlaps by time interval group were examined by histograms. The number of server teams (s) dedicated to OR activity was varied between 2 to 5 between peak hours to assess the impact on all other model parameters. All analyses were performed using XLSTAT (Microsoft Inc., USA) and Stata SE 15.1 (StataCorp Copyright 1985, College Station, TX).