Electronic Thesis and Dissertation Repository

Thesis Format

Integrated Article

Degree

Doctor of Philosophy

Program

Statistics and Actuarial Sciences

Supervisor

David Andrew Stanford

2nd Supervisor

Camila de Souza

Co-Supervisor

3rd Supervisor

Felipe Rodrigues

Affiliation

King's University

Co-Supervisor

Abstract

This thesis proposes three contributing manuscripts related to patient flow management, server decision-making, and ventilation time in the intensive care and step-down units system.

First, a Markov decision process (MDP) model with a Monte Carlo simulation was performed to compare two patient flow policies: prioritizing premature step-down and prioritizing rejection of patients when the intensive care unit is congested. The optimal decisions were obtained under the two strategies. The simulation results based on these optimal decisions show that a premature step-down strategy contributes to higher congestion downstream. Counter-intuitively, premature step-down should be discouraged, and patient rejection or divergence actions should be further explored as a viable alternative for congested intensive care units (ICUs).

Secondly, an investigation of the length of stay (LOS) competition between the intensive care unit (ICU) and the step-down unit (SDU), two servers in tandem without a buffer between them was proposed using queuing games. Analysis of the competition was done under four different scenarios: (i) both servers cooperate; (ii) the servers do not cooperate and make decisions simultaneously; (iii) the servers do not cooperate but the first server, the ICU is the leader; (iv) the servers do not cooperate, the second server the SDU is the leader. Finally, a numerical analysis was performed. The results show that the length of stay decisions of each server depends critically on the payoff function’s form and the exogenous demand. Secondly, with a linear payoff function, the SDU is only beneficial to the system if the unit cost is greater than its unit reward at the ICU. Perhaps most importantly, the critical care pathway performs better under coordination and or leadership at the ICU level.

Finally, first-day ventilated patients' ventilation time was analyzed using survival analysis. The probabilistic behaviour of the ventilation time duration was analyzed and the predictors of the ventilation time duration were determined based on available first-day covariates. Data were obtained from the Critical Care Information System (CCIS) about patients admitted to the ICUs in Ontario between July 2015 and December 2016. The log-logistic AFT model was found to be the best to relate the association between first-day covariates and the ventilation time.

Summary for Lay Audience

In this thesis, I used statistics to address certain ICU-SDU server decision-making and ventilation time in the intensive care and step-down unit system.

First, when the critical care unit was overcrowded, a Markov decision process (MDP) model with Monte Carlo simulation was utilized to evaluate two patient flow strategies: prioritizing premature step-down and prioritizing patient rejection. Under the two techniques, the best decisions were made. The simulation findings based on these optimum judgments reveal that a premature step-down method leads to increased downstream congestion. Premature step-down should be avoided, and patient rejection or divergence measures should be investigated further as a possible solution for overcrowded intensive care units (ICUs).

Second, utilizing queuing games, an analysis of the length of stay (LOS) rivalry between the intensive care unit (ICU) and the step-down unit (SDU) was proposed. Four scenarios were used to analyze the competition: both servers collaborate; (ii) both servers cooperate but the first server, the ICU, is the leader; (iv) both servers cooperate but the second server, the SDU, is the leader. After then, there was a numerical analysis. The findings reveal that the payout function's shape and exogenous demand have a significant impact on each server's length-of-stay decisions. The SDU, on the other hand, has a linear payout function.

Finally, survival analysis was used to look at the ventilation time of first-day ventilated patients. Based on available first-day factors, the probabilistic behaviour of ventilation time duration was studied, and predictors of ventilation time duration were identified. Patients hospitalized to ICUs in Ontario between July 2015 and December 2016 were studied using data from the Critical Care Information System (CCIS). The best model for relating the connection between first-day variables and ventilation time was determined to be the log-logistic AFT model.

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