Complete HW 2 questions 1-4 and Excel Sheet.
ISE 505: Modeling for Health Policy and Medical Decision Making Homework 2 1. Use the data in overnightStay.xlsx to estimate the following logistic regression in Excel: We are using Excel for this problem because it is so unsuited to logistic regression – you must do everything yourself -- unlike in many other software platforms, there is no “logistic regression” command. Doing it once “manually” will help you understand what’s going on under the hood. Note that you will need to use Excel solver. Instructions on loading the Solver add-in can be found by google-searching “Load the Solver Add-in Excel” and using the Office Support website. Either submit your Excel sheet as a .xlsx file on blackboard or write the equations you’re using in the cells if you submit it as a printout. a. Explain, in words and equations, what you are doing to find the regression coefficients. b. What are the coefficients and ? c. What is the increase in odds ratio of staying overnight if the patient is a year older? d. Plot the true overnight stay outcome by age, and on the same graph, plot your predicted probabilities for staying overnight by age. e. The hospital wishes to predict how many beds to prepare for this group of patients. If they will prepare beds for everyone with over 50% probability of staying the night, how many beds should they prepare? What if their threshold is 25% or 75%? f. Now we can use the predicted probabilities from your logistic regression to see if we can accurately forecast if someone will stay overnight or not. Treat “staying overnight” as a “positive” event and plot the ROC (Receiver Operating Characteristic) curve using different thresholds for mapping your probabilities to 0/1 outcomes. 2. Suppose we wish to create a compartmental model of chicken pox in a healthy adult population – let’s assume that for this population, the disease is non-fatal, and once an individual recovers, he or she is immune from the disease for the rest of his or her life. a. Draw a schematic of the compartmental model appropriate to this disease. b. Suppose the rate of infection is β and the rate of recovery is υ. Draw the compartment diagram for your disease, with health states labeled. Label all arrows with the appropriate rates. c. What are the equations that govern this system? (i.e., write out di/dt, etc.) d. What are equilibrium states of this system? 3. Suppose we wish to create a compartmental model of the flu in a healthy adult population – let’s assume that for this population, the disease is non-fatal, but once an individual recovers, he or she is can get the disease again. a. Draw a schematic of the compartmental model appropriate to this disease. b. Suppose the rate of infection is β and the rate of recovery is υ. Draw the compartment diagram for your disease, with health states labeled. Label all arrows with the appropriate rates. c. What are the equations that govern this system? (i.e., write out di/dt, etc.) d. If the system started with half the population infected, and β = 0.5 and υ = 0.2, what is the system steady state? 4. Pick one of the following articles to read: · Mangasarian OL, Street WN, Wolberg WH, Breast cancer diagnosis and prognosis via linear programming,” Operations Research, 1995, Vol. 43, pp. 570-577. · Stefan Klöppel, et. Al. Automatic classification of MR scans in Alzheimer's disease, Brain, 2008, 131 (3): 681-689. a. Summarize the main goals, methods, and findings of the paper in three paragraphs or less (please type this up, for readability). b. What are the biggest assumptions the authors make?