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DECISION TREE

 

St. Vol Hospital needs reliable cardiology coverage on Saturdays to maintain their reputation as a first rate healthcare facility. The coverage is now considered required for emergent care, primarily responding to Code STEMI’s.  The local cardiologist group has offered several “fee for coverage” options that need to be evaluated.  Note that these fees are for the “coverage” only, i.e. the cardiologist would still separately bill the patient for any procedures performed.  As CMO for the hospital, you need to recommend a strategy that minimizes the expected cost to the hospital. 

 

The cardiology group has offered the following three options.  One option is for the hospital to simply pay a fixed fee of $1200 each week for emergent cardiology coverage on Saturdays irrespective of whether or not there are any Code STEMI’s that occur.  A second option is that the hospital pays a base fee ($700) for coverage, but then also pays a per-call-in fee of $400 for each Code STEMI.  A third option is that there is no base fee, but there is a higher per-call-in fee of $1300 for each Code STEMI. 

 

Data was pulled for the prior 12 months (52 weeks) and the number of Code STEMI’s for the 52 Saturdays in the data set was observed to be as follows:

 

Number of Code STEMI’s	Number of Saturdays
0	13
1	31
2	8
Total	52

 

Part A) Construct and evaluate a decision tree for this decision situation (use the values in the table to compute probabilities).  Clearly identify and explain the most cost-effective option and its cost implications.

 

 

 

Part B) After further discussions, a variation of the first option was put forth by the cardiology group.  On Saturday mornings, the hospital often finds itself with several patients who were admitted the day before and only need stress testing.  Under the current system, these patients will stay in the hospital until Monday, at which time they will undergo their stress tests and be discharged.  If some or all of these patients could have their stress tests performed on Saturday, the hospital costs would be reduced by having lower weekend census.   In fact, the hospital estimates a cost savings of $800 for each patient that needs stress testing and gets it done on Saturday rather than waiting till Monday.  The cardiology group (which has traditionally resisted doing any stress testing on Saturdays) has now offered a fourth option as follows.  The group will provide emergent cardiology coverage on Saturdays for a fee of $2000, but will also do stress testing if there are patients who need it and if the hospital is willing to call in and pay for the necessary support staff.  If needed, the support staff can be called in on Saturday morning at a total cost of $900 for a 4-hour period (note, a call-in is guaranteed 4 hours). The prior 52 weeks were analyzed and the number of waiting stress-test patients on Saturday mornings was given as follows:

 

Number of patients awaiting stress testing	Number of Saturdays
0	3
1	10
2	17
3	13
4	9
Total	52

 

Each stress test takes less than one hour so it would never be necessary for the support staff to work more than 4 hours. 

 

Clearly, on any given Saturday, it wouldn’t make sense to call in support staff and do testing if there were no admitted patients waiting for stress testing.   On the other hand, if there were 4 patients waiting, it is easy to show that it makes sense to bring in the support staff and do the testing.  Somewhere in-between, is there an optimal policy for whether or not to call in support staff and doing stress testing on waiting patients that minimizes overall costs?

 

The above question can be answered by constructing and evaluating a decision tree for this fourth option.  What is the most cost effective strategy and what are the expected financial implications?  Compared with the first three options, what would you recommend?

 

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