Project Management

      MATH PROJECT The premise of the project is closely related to the aspect of the course material but may explore an avenue, specifically in Excel, that was not discussed in class. You are free to use internet resources to strengthen your Excel skill and apply it to tackle your project. • A typed report addressing the questions of the project. No handwritten report is acceptable. • Excel file displaying your work. Use multiple sheets of one Excel _le for multiple tasks rather than using multiple Excel _les. 1.1 Data Data is available for this project on the course website in Canvas with the title Sepsis Data MIMIC Phase 2. This is a real-world healthcare data extracted from Medical Information Mart for Intensive Care III (MIMIC III). MIMIC is a relational database containing tables of data relating to patients who stayed within the intensive care units at Beth Israel Deaconess Medical Center. The data set for this project includes patients who had the diagnosis of sepsis. Your instructor had already cleaned the data and prepared it for the statistical analysis. The data includes 1,072 observations. This dataset has less data points than the Phase 1 of the project (1132). The definition of each column in the data is explained as follows: SUBJECT ID Patient Identification number HADM ID Admission number of the patient. (Remember a patient can have multiple hospital admissions) ADMITTIME Admission time. Because of the privacy reasons, the admission and discharge time has been shifted to a specific value. DISCHTIME Discharge time ADMISSION TYPE Types of hospital admission (URGENT or EMERGENCY) DISCHARGE LOCATION Provides information about the location where the patient is discharged MARITAL STATUS Marital status of the patient GENDER Gender of the patient (M:Male, F:Female) LENGTH OF HOSPITAL STAY DAYS Number of days a patient stays in the hospital HOSPITAL EXPIRE FLAG Outcome of the hospital stay. Whether a patient is discharged as expired or non-expired. Expired and non-expired outcomes are encoded as 1 and 0, respectively AGE Patient's age HEART_RATE Heart rate RESPIRATORY RATE Respiratory rate GCS SCORE Glasgow Coma Scale score (it is related to nervous system) BLOOD PRESSURE Blood pressure CREATININE Creatinine 1.2 Objective The objective of this part of the project is that a student will advance his/her learning in developing statistical models using Excel. Specifically, students will enrich their course learnings in the following two areas: 1. Hypothesis testing 2. Linear regression (PROBLEMS TO SOLVE 1-9) 1.3 Problem Statements Your report should address the following problem statements, and must contain all the tables, graphs and numeric measures you derive from Excel. Your report must include all the results for the grading. And please do not forget to add correct labels in X and Y-axes of your plots. 1. (10 points) As a hospital quality manager, you are interested in investigating if patients with expired outcomes have the same average length of stay as patients with non- expired outcomes. For this, you decided to perform hypothesis testing using cuto_ (or critical) value approach. In your excel _le, show all four steps clearly in one sheet. In your report, write hypothesis formulation, t-statistic, rejection regions and your conclusion. DO NOT use the hypothesis testing feature of the Data Analysis tool. Perform all the calculations in Excel. 2. (5 points) Write a linear regression equation to derive the length of stay using the following measurements: • Age • Heart rate • Respiratory rate • Glasgow Coma Scale score • Blood pressure • Creatinine Use B1; B2; B3; B4; B5 and B6 as regression coefficients. We compute value of these coefficients later. 3. (5 points) Using Data Analysis tool, compute the coefficients associated with each explanatory variable. In your report, create a table and list coefficients of all the explanatory variables along with their p-values. 4. (4 points) Refer p-values to determine which of the explanatory variables are NOT significantly important? 5. (4 points) Write down the linear regression incorporating estimated coefficients. While writing the linear regression equation, use only significantly important explanatory variables and ignore others. 6. (4 points) Explain the interpretation of each coefficients that are significantly important. 7. (5 points) A 64-year patient gets admitted to the ICU in the hospital with Glasgow Coma Scale score of 6 and blood pressure of 63, what is the predicted length of the stay of the patient? 8. (6 points) There is a common belief among physicians that the length of stay increases by 0.5 days with every 1 mmHg increase in blood pressure. Investigate this claim using hypothesis testing. 9. (3 points) Report the Goodness of Fit measure. What do you think about the model? Is it a good model or poor? 10. (4 points) Clarity of your report.