The Role of Prevalence in Interpreting Laboratory Test Results
Dr Margaret S. Hamilton MD PhD,
Associate director of clinical laboratories, Children’s Mercy Hospital
It is not unusual for pathologists and medical laboratory technologists to be asked “What is the sensitivity of the test?” or “What is the specificity of the test?” This article will address the issues involved in answering those questions and the broader question of “What difference does this test result make in the diagnosis of the patient?”
Let’s start with a few definitions based on the simple two by two table below. A given patient either does or does not have the disease as established by some gold standard. For example, in strep throat, the gold standard is culture. The diagnostic test, for example the rapid strep test, is either positive or negative. An example which involves a numerical result is ferritin < 10 ng/ml, which could be considered positive for iron deficiency anemia. The gold standard for iron deficiency is bone marrow stain for iron. A patient who has the disease and a positive test is “true positive (TP)”. A patient who has the disease and a negative result is “false negative (FN)”. A patient without the disease and a positive result is “false positive (FP)”. And finally, a patient without the disease and a negative result is “true negative (TN)”. Based on these concepts the definitions of terms is given below.
|
Diagnostic Test Result |
Disease Present |
Disease Absent |
|
Positive |
TP |
FP |
|
Negative |
FN |
TN |
Prevalence: (TP+FN)/(TP+FN+FP+TN) – presence of disease in defined population
Sensitivity: TP/(TP+FN) – frequency of a positive test result in patients with disease x Likelihood Ratio
One of the most important concepts to grasp is the significance of prevalence of the disease in determining the usefulness of a particular test. It is necessary to define the population under consideration. Using the examples above, the prevalence of iron deficiency is quite different in pre – and post- menopausal women. The presence of a fever alters the prevalence of Group A Strep in patients with pharyngitis. In general, the prevalence in the population you test is derived from your own clinical experience, specific for type of practice you have and the patient population you see. The important role of prevalence is best illustrated by looking at the Positive Predictive Value of a test with 95% sensitivity and 95% specificity as shown in the table below. Only 16% of patients with a positive test result have the disease in question when the prevalence of the disease is 1% in the defined population. However, when the disease prevalence is 50%, 95% of the test positive patients will have the disease. It is convincing to do some arithmetic. If there are 10,000 patients and the disease prevalence is 1%, then 100 patients have the disease and 9900 do not. A test which is 95% sensitive will be positive in 95/100 patients with the disease. A test which is 95% specific (5% false positive rate) will be positive in 495/9900 patients who do NOT have the disease! There are more false positive then true positive results! With a prevalence of 5%, a test which is 95% sensitive and 95% specific will have a equal number of true positive and false positive results.
|
|
Predictive Value as a Function of Disease Prevalence |
|||||
|
Prevalence of Disease |
1% |
5% |
10% |
20% |
25% |
50% |
|
Positive Predictive Value |
16.1 |
50.0 |
67.9 |
82.6 |
86.4 |
95.0 |
The role of prevalence can also be discerned in this alternative expression for positive predictive value. As you can see Prevalence appears three times!
(Prevalence)(Sensitivity)
(Prevalence)(Sensitivity)+(1-Prevalence)(1-Specificity)
An alternative and more advanced method of analysis uses the patient’s odds for having a given disease and the likelihood ratio of the test being considered. Odds and probability are related but not the same. Probability is expressed as a decimal fraction from 0 to 1 or as a percent. Odds are defined as Probability (as a decimal fraction)/1-Probability. Probability equals Odds/ (1+Odds). For example, if a patient has a 20% chance of having a disease the Odds are 0.2/1-0.2 = 0.2/0.8 = 0.25/1.
|
|
Relationship of Probability to Odds |
|||||||
|
Probability |
.05 |
.10 |
.20 |
.33 |
.50 |
.66 |
.80 |
.90 |
|
Odds |
.05 |
.11 |
.25 |
.50 |
1.00 |
2.00 |
4.00 |
9.00 |
Odds are important because only odds, not probability, can be multiplied by the likelihood ratio of a test to obtain new post- test odds. To continue this example, if the test in question has a sensitivity of 90% and a specificity of 85% the positive likelihood ratio is .90/1-.85 or 6. The pre-test odds was 0.25 which times 6 gives a post-test odds of 1.5 which converts to a probability of 1.5/(1+1.5) or 60%. It is now possible to consider a second test. For the second test the pre-test probability is .6 which converts to pre-test odds of 1.5. If we assume a sensitivity of 80% and a specificity of 70% the positive likelihood ratio of the second test is .8/(1-.7) or 2.7. The pre-test odds of 1.5 is multiplied by 2.7 to give a post-test odds of 4.05 which gives a probability of 80%. This is the value of using multiple tests.
Galen, RS. Predictive Value Theory. Diag. Med., Feb 1979, 23-31
Sackett, DL et al. Evidenced Based Medicine, Churchill Livingston Press, 1997
Center for Evidence- Based Medicine: www.cebm.net