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

TL;DR

This study identifies suitable statistical models for key surgical department metrics, enabling more accurate planning and scheduling by understanding the inherent uncertainties based on three years of hospital data.

Contribution

The paper provides a comprehensive analysis of surgical durations, requests, and cancellations, recommending specific statistical distributions for improved hospital management.

Findings

Surgical durations follow a lognormal distribution for overtime prediction.

Requests can be modeled as a Poisson process influenced by urgency and day.

Cancellations are well represented by Bernoulli trials with specific probabilities.

Abstract

BACKGROUND: 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. OBJECTIVE: The objective of the research is 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 has been performed to determine the most appropriate distributions and models in a variety of surgical contexts. Data from 2013 to 2015 was collected from the surgical department at a large Australian public hospital. RESULTS: A lognormal 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. It is found that individual cancellations can be modelled as Bernoulli trials, with the probability of patient, staff, and resource based cancellations provided herein. CONCLUSIONS: The analysis presented here 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.