1. Bayesian Networks HAP 823 George Mason University
Tutor: Prof. Farook Alemi By
Akhil Anto

2. Teach One Assignment Question
Write an SQL code to calculate the probability of negative outcome in the situation where the patient is severely ill and has not signed a "Do Not Resuscitate" (DNR) order.  Note that probabilities for events that are mutually exclusive and exhaustive should add up to one. Data► 
Link

4. First, we need to eliminate the variables that we are not focusing on which are “Not Severe”
p(severity)
p(DNR)
p(Tx|DNR, Severity)
p(Outcome|Tx, Severity)
Severity p
DNR Tx
Outcome
Severe
0.4
Yes
0.1
Positive
0.2
Not Severe
0.6 No
0.9
Negative
0.0
0.3

5. Now we should join the first two tables using cross join as they don’t share features.
p(severity)
p(DNR)
Severity p
DNR
Severe
0.4
Yes
0.1
Not Severe
0.6 No
0.9
p(Sev DNR)
Severity
DNR p
Severe
Yes
0.04 No
0.36

6. Now that we have our variables of interest which reflects the severity and DNR. Next step is to combine the resulting table with treatment table given DNR and severity
We will do inner join using SQL coding for sever cases, with all the probabilities of DNR and the treatment. At the same time we will multiply the probabilities with its equivalent from each table.
p(Sev DNR)
Severity
DNR p
Severe
Yes
0.04 No
0.36
p(Tx|DNR, Severity)
DNR
Severity Tx p
Yes
Severe
0.1 No
0.2
0.3
Severity Tx
DNR p
Yes
Severe No
0.108
0.036
0.004
0.008

7. Here we select the treatment table above severity and treatment variables and the probabilities for each treatment and severity will be sum by combining each no and yes cases for treatment across different values of DNR and then we need to specify the grouping based on the treatment and severity only
p(Tx Sev) Tx
Severity
psum No
Severe
0.044
Yes
0.112

8. Join the previous table with the outcome table
p(Tx Sev) Tx
Severity
psum No
Severe
0.044
Yes
0.112
p(Outcome|Tx, Severity) Tx
Severity
Outcome p
Yes
Severe
Positive
0.2
Negative
0.1 No
0.3
p(Tx Sev Outcome) Tx
Severity
Outcome p
Yes
Severe
Positive
0.0224
Negative
0.0112 No
0.0044
0.0132

9. Because we are interested in the adverse outcome we will sum the probabilities of negative outcome over treatment values, and we can also add the probabilities of the positive values to compare
Severity
Outcome p
Severe
Negative
0.0244
Positive
0.0268

10. Finally we need to normalize the probabilities so they sum up to one
So we have 47.65% of our severe patients have adverse outcomes
Severity
Outcome p
pnormalized
Severe
Negative
0.0244
Positive
0.0268