Ph.D. Thesis Public Lecture (DSAS) - Yawo Kobara

"Statistical Applications to the Management of Intensive Care and Step-down Units"

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 ICUs.

Secondly, an investigation of the length of stay (LOS) competition between the ICU and the 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.