1. A key performance for hospitals is the 30-day unplanned readmission rate—the proportion of patients discharged from the hospital who had an unplanned readmission within 30 days. Programs like the Hospital Readmissions Reduction Program (HRRP) apply penalties (up to a 3% reduction in payments) to underperforming U.S. hospitals—resulting in withheld payments in excess of $500 million in 2018.
Hospitals can employ some low-cost strategies to reduce unplanned readmissions, such as confirming patient follow-up plans prior to discharge and asking patients to verbally repeat their treatment directions. However, other approaches are more involved and costly. One example is to arrange “telehealth” interventions, in which health care providers contact patients routinely after discharge. Given the cost of these interventions, they are only appropriate for patients at elevated risk of readmission.
You are working for a mid-sized hospital in the northeast United States and are tasked to assess the impact of telehealth interventions on diabetic patients—with the ultimate goal of reducing the 30-day read- mission rate. The intervention will cost approximately $1,200 per patient. Clearly, it must be limited in scope, and a key component of your strategy will be targeting the “right” patients.
Unfortunately, your hospital does not document 30-day readmissions, as this requires significant follow-up with discharged patients. You will thus use a publicly available dataset to study readmission risk. The dataset includes over 100,000 hospital discharges of over 70,000 diabetic patients from 130 hospitals across the United States during the period 1999–2008. All patients were hospital inpatients for 1–14 days, and received both lab tests and medications while in the hospital. The 130 hospitals represented in the dataset vary in size and location: 58 are in the northeast United States and 78 are mid-sized (100–499 beds).
The dataset is provided in the “readmission.csv” file. It contains the following variables:
· readmission: 1 if the patient had an unplanned readmission within 30 days, 0 otherwise
· Patient characteristics: race, gender, and age capture demographic information.
· Recent medical system use: The variables numberOutpatient, numberEmergency, and numberInpatient capture the number of times the patient used the medical system in the last year.
· Diabetic treatments: A number of variables capture the patient’s diabetic treatments: acarbose, chlorpropamide, glimepiride, glipizide, glyburide, glyburide.metformin, insulin, metformin, nateglinide, pioglitazone, repaglinide, and rosiglitazone.
· Admission information: The variables admissionType and admissionSource contain information about how the patient was admitted to the hospital. The variable numberDiagnoses captures the number of diagnoses the patient had recorded for their admission. There are also a number of variables that indicate whether a patient was diagnosed with various conditions when admitted: diagAcuteKidneyFailure, diagAnemia, diagAsthma, diagAthlerosclerosis, diagBronchitis, diagCardiacDysrhythmia, diagCardiomyopathy, diagCellulitis, diagCKD, diagCOPD, diagDyspnea, diagHeartFailure, diagHypertension, diagHypertensiveCKD,diagIschemicHeartDisease, diagMyocardialInfarction, diagOsteoarthritis, diagPneumonia, and diagSkinUlcer.
· Treatment information: timeInHospital is the number of days the patient was in the hospital, and numLabProcedures, numNonLabProcedures, and numMedications capture the amount of care the patient received in the hospital.
a) Open the data file “readmission.csv” in R. Perform some exploratory data analysis on the full data set and report two interesting insights you gained from your analysis.
b) Based on conversations with the hospital’s management, you estimate the cost of a 30-day unplanned readmission at $35,000. From published information at a similar institution, you estimate that tele- health interventions will reduce the incidence of 30-day unplanned readmissions in the treated popuation by 25%. Given the cost of $1,200 per intervention, what are:
– the “loss” of a false positive, as compared to a true negative; and
– the “loss” of a false negative, as compared to a true positive?
Define the loss matrix for your CART model.
c) Fit a CART model using a cp parameter of 0.001 and the loss matrix defined in Question b. Include an image of your tree.
d) Assess the model’s predictive performance using the test set. What is the accuracy, true positive rate and false positive rate? Contrast the decisions resulting from your model and those resulting from current practice (under which no patient is subject to a telehealth intervention). Provide summary statistics to explain how the decisions differ, and discuss the costs and benefits of each approach. Make sure to compare the total monetary costs of patient readmission. [7 pts]
e) Can cross validation improve your model or is a cp of .001 optimal? [3 pts]
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