This document discusses the performance of diagnostic tests. It defines key terms used to evaluate diagnostic tests such as sensitivity, specificity, false positive rate, false negative rate, predictive value, accuracy, precision, validity, reliability and reproducibility. Sensitivity refers to the proportion of true positives detected, or individuals correctly identified as having the condition. Specificity refers to the proportion of true negatives detected, or individuals correctly identified as not having the condition. The document also provides examples of calculating these performance measures and compares the results of a survey test to a reference test using a 2x2 table.

1. 14
Describing the Performance
of a Diagnostic Test
[Q: Write shorts notes on: Performance of diagnostic test
(BSMMU, January, 2009)]
Types of diagnostic tests
1. Qualitative diagnostic tests classify patients as diseased
or disease-free according to the presence or absence of a
clinical sign or symptom. For example, an x-ray might
confirm or disprove the existence of a fracture.
2. Quantitative diagnostic tests classify patients as diseased
or disease-free on the basis of whether they fall above or

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below a reselected cutoff value known as the positivity
criterion. This cutoff value is also referred to as the critical
value or referent value.
Test performance characteristics
[Q:
 Define 'specify' and 'sensitivity' with example. (BSMMU,
Radiology, January, 2012)
 What do you mean by "sensitively" and "specificity". Give
example for each of them. (BSMMU, July, 2010)
 Discuss the statistical tools used to assess the performance of
a diagnosis test. (BSMMU, January, 2011)]
1. Sensitivity
Definition: Chance of having a positive test in patients with
the test condition
Calculating sensitivity: Sensitivity is calculated as the
proportion of diseased individuals with a positive test result,
using the formula
diseased with positive test
sensitivity = all diseased
Example: Of the 600 individuals with breast cancer as
determined by biopsy 570 had a positive result on the BCPF
test. Thus,
sensitivity = = 570/600 = .95
A high sensitivity implies few false negatives which is important
for very rare or lethal diseases, e.g. phenylketonuria.
2. Specificity

3. Biostatistics-140
Definition. Chance of having a negative test in patients
without the condition
Calculating specificity: Specificity is calculated as the
proportion of disease-free individuals with a negative test
result, using the formula
disease-free with negative test
specificity = all disease-free
Example: Of the 1000 individuals without breast cancer as
determined by biopsy 850 had a negative result on the BCPF
test. Thus,
specificity = 850/1000 = .85
A high specificity implies few false positives, which is important
for common diseases, e.g. diabetes.
3. False negative rate
a. Definition. The false negative rate (FNR) of a diagnostic test
is the probability that a diseased individual will have a negative
test result.
c. Calculation. FNR is calculated as the proportion of diseased
individuals with a negative test result, using the formula
diseased with negative test
all diseased
FNR=
4. False positive rate
a. Definition: The false positive rate(FPR) of a diagnostic test is
the probability that a diseases free individual will have a
positive result.

4. Biostatistics-141
Calculation: FPR is the calculated as the proportion of diseases
free individual with a positive result using the formula
diseases free with a positive test
all disease free
FPR=
Example: Of the 1000 individuals who did not have breast
cancer , 150 had positive result on the BCPF test, thus
FPR=150/1000=1.5
5. Predictive value
This is the proportion of positive test results that are truly
positive.
True positive (a) x 100
True positive (a) + false positive (b)
Accuracy
The proportion of all tests those are correct.
The accuracy of a laboratory test is its correspondence with the
true value. An inaccurate test is one that differs from the true
value even though the results may be reproducible. In the
clinical laboratory, accuracy of tests is maximized by calibrating
laboratory equipment with reference material and by
participation in external quality control programs.
Precision
Test precision is a measure of a test’s reproducibility when
repeated on the same sample. An imprecise test is one that
yields widely varying results on repeated measurements.
Validity
The extent to which a test measures what it is supposed to
measure. Sensitivity and specificity are two important
components of validity.

5. Biostatistics-142
Reliability
The extent to which a test yields consistent results and thus is
replicable
Comparison of a survey test with a reference test
Table: Comparison of a survey test with a reference test
Survey
test result
Reference test result Totals
Positive Negative
Positive True positives,
correctly
identified = (a)
False positives =
(b)
Total test
positives =
(a + b)
Negative False negatives
= (c)
True negatives
correctly
identified = (d)
Total test
negatives =
(c + d)
Totals Total true
positives =
(a + c)
Total true
negatives =
(b + d)
Grand total
=
(a + b + c +
Valid and reliable

6. Biostatistics-143
d)
From this table four important statistics can be derived:
Sensitivity = a/ (a + c).
Specificity = d/ (b + d).
Accuracy = (a+d)/(a+b+c+d)
Likelihood ratio
The likelihood ratio for a particular value of a diagnostic test is
defined as: the probability of that test result in the presence of a
disease, divided by the probability of the result in people without
the disease.
Likelihood ratios express how many times more (or less) likely a
test result is to be found in diseased as compared to non-
diseased people.
Reproducibility
It is the variability of repeated measurements under different
conditions.
[Q:
 Out of 1000 suspected lung cancer patients, 800 found to have
the disease diagnosed by CT scan. Among those, 320 patients
were found FNAC positive and the total FNAC positive were
322. Evaluate the performance of FNAC in the diagnosis of
lung cancer. (BSMMU, Radiology, January, 2012)
 USG negative cases respectively. Will you advocate USG for
diagnosis of hepatoma? (BSMMU, July, 2011)
 1000 suspected brain tumor patients were subjected to CT
scan & MRI. Based on MRI 200 diagnosed as brain tumor of
which 156 were CT positive out of total 420 CT Positive cases.
Evaluate the performance of CT scan of diagnosis of brain
tumor. (BSMMU, January, 2011)
 317 suspected cases of heptoma were subjected to FNAC and
CT scan. FNAC confirmed hepatoma in 113 and 08 cases out
of 128 CT positive & 189 CT negative cases respectively.
Evaluate the performance of CT scan in diagnosis of
hepatoma. (BSMMU, July, 2010)

7. Biostatistics-144
 370 suspected cases of prostate cancer were investigated by
CT scan and serum PSA. CT scan confirmed prostate cancer in
113 and 8 cases out of 8 cases out of 178 PSA positive and 192
PSA negative cases receptivity. Will you advocate PSA
measurement in diagnosis of prostate cancer? (BSMMU,
January, 2009)]