INPUT MODELING & PARAMETER ESTIMATION

From the ICU data, the group was able to determine the exact patients who stayed in the ICU, these patients' arrival date into the ICU, and their departure date from the ICU. The group was able to calculate the duration of each patient’s ICU stay by calculating the difference between the departure and arrival dates. Each patient’s ICU stay duration was used to calculate the average number of days a patient spends in the ICU.

However, the data provided included people that stay in an ICU bed upon arrival and also people who will transfer to an ICU bed from a regular bed. After sorting the data set by date-time, the group was able to determine the order of beds the patient stayed in (regular vs ICU) and what the next event would be for them based on the calculated probability. Therefore, we have two data sets for the ICU service time depending on the path the patient took between the ICU and regular beds. Following that logic, we have two distributions for ICU bed service time shown below using Arena.

From the hospitalziation dataset, the group determined the number of days that a patient spends in the system by observing the hospital admission time and the end date. This was considered the amount of time that a patient stays in a regular hospital bed. Moreover, similar to the logic of the ICU bed above, we can also create two different distributions of service time depending on the order the patient stays in the ICU beds or regular beds. These distributions were found using Arena software.

After the initial distributions were collected from Arena, this gave the group an idea of which distributions to use for parameter estimation. Originally, the group planned on using moment matching for parameter estimation, however this was discovered to be too complicated as the lognormal distribution requires complex mathematics to solve the equations for the parameters. Instead, the MLE (Most Likely Estimator) process was used as shown in the calculations below.

Figures 2, 4, and 5 all were calculated with the lognormal distribution, while Figure 3 was calculated using the gamma distribution. After the parameters for the respective distributions were calculated, the data was bootstrapped in order to gain more accurate results.