Analysis of uncertainty in the surgical department: durations, requests and cancellations

Abstract

Objective Analytical techniques are being implemented with increasing frequency to improve the management of surgical departments and to ensure that decisions are well informed. Often these analytical techniques rely on the validity of underlying statistical assumptions, including those around choice of distribution when modelling uncertainty. The aim of the present study was to determine a set of suitable statistical distributions and provide recommendations to assist hospital planning staff, based on three full years of historical data.

Methods Statistical analysis was performed to determine the most appropriate distributions and models in a variety of surgical contexts. Data from 2013 to 2015 were collected from the surgical department at a large Australian public hospital.

Results A log-normal distribution approximation of the total duration of surgeries in an operating room is appropriate when considering probability of overtime. Surgical requests can be modelled as a Poisson process with rate dependent on urgency and day of the week. Individual cancellations could be modelled as Bernoulli trials, with the probability of patient-, staff- and resource-based cancellations provided herein.

Conclusions The analysis presented herein can be used to ensure that assumptions surrounding planning and scheduling in the surgical department are valid. Understanding the stochasticity in the surgical department may result in the implementation of more realistic decision models.

What is known about the topic? Many surgical departments rely on crude estimates and general intuition to predict surgical duration, surgical requests (both elective and non-elective) and cancellations.

What does this paper add? This paper describes how statistical analysis can be performed to validate common assumptions surrounding surgical uncertainty. The paper also provides a set of recommended distributions and associated parameters that can be used to model uncertainty in a large public hospital’s surgical department.

What are the implications for practitioners? The insights on surgical uncertainty provided here will prove valuable for administrative staff who want to incorporate uncertainty in their surgical planning and scheduling decisions.