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Description:
Sensitivity is the ability of the test to pick up what it is testing for and Specificity is ability to reject what it is not testing for.
Likelihood ratios determine how the test result changes the probability of certain outcomes and events.
Pretest and Posttest probabilities are the subjective probabilities of the presence of a clinical event or status before and after the diagnostic test.
For positive test, we find the positive posttest probability and for negative test, we find the negative posttest probability.
Procedure:
a) Value of Disease and No Disease in the Positive and Negative Test Outcome group
b) Value of 1£\, the twosided confidence level
a) The Sensitivity and the corresponding 100(1£\)% confidence interval
b) The Specificity and the corresponding 100(1£\)% confidence interval
c) The Positive Predictive Value and the corresponding 100(1£\)% confidence interval
d) The Negative Predictive Value and the corresponding 100(1£\)% confidence interval
e) The Pretest probability, Positive Posttest probability, Negative Posttest probability
f) The Likelihood Ratio Positive, Likelihood Ratio Negative and their corresponding 100(1£\)% confidence interval
Variables:
Disease 
No disease 
Totals 

Test Outcome Positive 
a (True Positive) 
b (False Positive) 
n_{1}=a+b 
Test Outcome Negative 
c (False Negative) 
d (True Negative) 
n_{2}=c+d 
Totals 
m_{1}=a+c 
m_{2}=b+d 
N=n_{1}+n_{2} 
For Sensitivity,
Define:
The 100(1£\)% confidence interval is defined as:
For Specificity,
Define:
The 100(1£\)% confidence interval is defined as:
For Positive Predictive Value (PPV),
Define:
The 100(1£\)% confidence interval is defined as:
For Negative Predictive Value (NPV),
Define:
The 100(1£\)% confidence interval is defined as:
For Pretest probability,
For Likelihood Ratio Positive (LR+),
Define:
The 100(1£\)% confidence interval is defined as:
For Positive Posttest probability,
Define
For Likelihood Ratio Negative (LR),
Define:
The 100(1£\)% confidence interval is defined as:
For Negative Posttest probability,
Define
Notation:
100(1£\)% confidence interval: We are 100(1£\)% sure the true value of the parameter is included in the confidence interval
: The zvalue for standard normal distribution with lefttail probability
Suppose

Disease 
No disease 
Totals 
Test Outcome Positive 
a=20 
b=180 
n_{1}=200 
Test Outcome Negative 
c=10 
d=1820 
n_{2}=1830 
Totals 
m_{1}=30 
m_{2}=2000 
N=2030 
Then the Sensitivity is 0.66667 and the corresponding 95% C.I. ((1£\) =0.95) is (0.49798, 0.83535).
The Specificity is 0.91 and the 95% C.I. is (0.89746, 0.92254).
The Positive Predictive Value (PPV) is 0.1 and the 95% C.I. is (0.05842, 0.14158).
The Negative Predictive Value (NPV) is 0.99454 and the 95% C.I. is (0.99116, 0.99791).
The PreTest Probability is 0.01478.
The Likelihood Ratio Positive (LR+) is 7.40741 and the 95% C.I. is (5.54896, 9.88828).
The Positive PostTest Probability is 0.1.
The Likelihood Ratio Negative (LR) is 0.3663 and the 95% C.I. is (0.22079, 0.60771).
The Negative PostTest Probability is 0.00546.