C.I. Calculator: Diagnostic Statistics

Data Input: (Help) (Formula) (Example)

	Disease	No Disease	Totals
Test Outcome Positive
Test Outcome Negative
Totals
1-α

Result	Point Estimate	Lower C.I.	Upper C.I.
Sensitivity
Specificity
Positive Predictive Value
Negative Predictive Value

Diagnostic Test	Point Estimate	Lower C.I.	Upper C.I.
Pre-test probability
Likelihood Ratio Positive
Positive Post-test probability
Likelihood Ratio Negative
Negative Post-test probability

---

Help Aids Top

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.

Pre-test and Post-test 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 post-test probability and for negative test, we find the negative post-test probability.

Procedure:

1. Enter

a)    Value of Disease and No Disease in the Positive and Negative Test Outcome group

b)    Value of 1-α, the two-sided confidence level

2. Click the button “Calculate” to obtain

a)    The Sensitivity and the corresponding 100(1-α)% confidence interval

b)    The Specificity and the corresponding 100(1-α)% confidence interval

c)    The Positive Predictive Value and the corresponding 100(1-α)% confidence interval

d)    The Negative Predictive Value and the corresponding 100(1-α)% confidence interval

e)    The Pre-test probability, Positive Post-test probability, Negative Post-test probability

f)     The Likelihood Ratio Positive, Likelihood Ratio Negative and their corresponding 100(1-α)% confidence interval

3. Click the button “Reset” for another new calculation

Formula:

Variables:

	Disease	No disease	Totals
Test Outcome Positive	a (True Positive)	b (False Positive)	n1=a+b
Test Outcome Negative	c (False Negative)	d (True Negative)	n2=c+d
Totals	m1=a+c	m2=b+d	N=n1+n2

Top

For Sensitivity,

Define:

The 100(1-α)% confidence interval is defined as:

For Specificity,

Define:

The 100(1-α)% confidence interval is defined as:

For Positive Predictive Value (PPV),

Define:

The 100(1-α)% confidence interval is defined as:

For Negative Predictive Value (NPV),

Define:

The 100(1-α)% confidence interval is defined as:

Top

For Pre-test probability,

For Likelihood Ratio Positive (LR+),

Define:

The 100(1-α)% confidence interval is defined as:

For Positive Post-test probability,

Define

For Likelihood Ratio Negative (LR-),

Define:

The 100(1-α)% confidence interval is defined as:

For Negative Post-test probability,

Define

Notation:

100(1-α)% confidence interval: We are 100(1-α)% sure the true value of the parameter is included in the confidence interval

: The z-value for standard normal distribution with left-tail probability

---

Example

Suppose

	Disease	No disease	Totals
Test Outcome Positive	a=20	b=180	n1=200
Test Outcome Negative	c=10	d=1820	n2=1830
Totals	m1=30	m2=2000	N=2030

Then the Sensitivity is 0.66667 and the corresponding 95% C.I. ((1-α) =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 Pre-Test Probability is 0.01478.

The Likelihood Ratio Positive (LR+) is 7.40741 and the 95% C.I. is (5.54896, 9.88828).

The Positive Post-Test Probability is 0.1.

The Likelihood Ratio Negative (LR-) is 0.3663 and the 95% C.I. is (0.22079, 0.60771).

The Negative Post-Test Probability is 0.00546.

Top