Application of Bivariate Conditional Erlang Distribution to Sequential Medical Procedures

This investigation applied Bivariate Conditional Erlang Distribution (BCED) to model two key sequential medical procedures: Time to Blood Glucose Monitoring (T1) and Time to Follow-Up Treatment (T2). The findings estimated T1 to have a shape parameter of 24.14 and a scale parameter of 0.642, while T2 had a shape parameter of 25.87 and a scale parameter of 0.847. The Goodness-of-fit tests using the Kolmogorov-Smirnov method yielded p-values of 0.9129 for T1 and 0.9462 for T2, confirming that the Erlang distribution adequately describes both processes. A strong positive correlation of 0.983 between T1 and T2, with a highly significant p-value of 3.9 × 10−223.9, indicated a close relationship between the two procedures. These outcomes confirmed that, when the time for blood glucose monitoring increases, the time for follow-up treatment also rises proportionately. Visualizations using bivariate Gaussian kernel density estimates further reinforced these findings by demonstrating the concentration of data points around the joint mode of the two variables. This investigation illuminates the appropriateness of the BCED for modelling real-world dependent stochastic processes, particularly in healthcare where interrelated tasks like T1 and T2 can be adequately trapped. The analysis offers a solid foundation for using the Erlang distribution in healthcare procedure modelling and offers insights for improving time efficiency in sequential medical operations.