Constructing a Multi-Morbidity Index from Simulated Data Farrokh Alemi, Ph.D.

Cases Controls Averages Just taking the average effects of each diagnosis will not do. A condition that is rare but requires long stays will have misleading results. A more careful analysis will need to match Cases with diagnosis against Controls without. Averages

Combination Length of stay Number of Patients 1 MI CHF DM 5.56 10 3 AA 5.54 4 3.56 20 5 7.03 30 6 5.02 7 5.04 8 7.62 40 3.03 2 4.10 9 2.03 11 2.60 50 12 2.57 13 0.61 60 14 2.12 70 15 0.01 80 16 4.57 120 MI = Myocardial Infarction; CHF = Congestive Heart Failure; DM=Diabetes Mellitus; AA=Alcohol abuse Here are the data we will work with. The first group of patients have three diagnosis, MI, CHF and DM. They stay on average 5.56 days. There were 10 such patients in our medical record.

Combination Length of stay Number of Patients 1 MI CHF DM 5.56 10 3 AA 5.54 4 3.56 20 5 7.03 30 6 5.02 7 5.04 8 7.62 40 3.03 2 4.10 9 2.03 11 2.60 50 12 2.57 13 0.61 60 14 2.12 70 15 0.01 80 16 4.57 120 MI = Myocardial Infarction; CHF = Congestive Heart Failure; DM=Diabetes Mellitus; AA=Alcohol abuse Note that the number of patients with different sets of diagnosis are quite different. Some combination of diagnoses occur many more times than others.

If cell c7 is CHF then assign a 1 otherwise a 0 Use the if statement to create a series of binary columns where the presence of a disease is shown as 1 and the absence as 0

Sum product of column H and F divided by sum of column H Calculate the length of stay for the cases. Do this as the product of the two columns divided by number of combinations that have MI. Since number of cases and controls are going to be matched we do not need to include the number of patients in the analysis, it will always be the same within the same combination of diagnosis.

Same as before, except now 1 minus column H Calculate the number of control but this time use 1 minus the column.

Calculate difference of cases and controls Estimate the score for each diagnosis as the difference of the length of stay of cases and controls. These scores can now be used to score the patient’s prognosis.

Sum of product of diagnoses indicators and score for the diagnoses The severity score is the sum of the diagnosis that are present. Note the $ sign so that the cell address does not change when you copy and paste it. This way you can make the score in one cell and copy to other cells.

3 Days is Shorter than length of stay specified by the patient’s severity The severity score of a patient with MI, CHF and DM predicts that they will stay longer than 3 days