Important EBM Concepts and Topics
When computing results for a clinical trial, researchers compare the number of people who experience the studied outcome against those who avoided it in both arms of the study. They often set up a table like the following to keep track of the results. For example, if the outcome is death at 12 months, the table would look like this:
# Dead at 12 months | # Alive at 12 months | |
Exposed to therapy | 300 | 700 |
Not exposed to therapy | 800 | 200 |
Risk
The risk of the studied outcome is the number of people who experienced the outcome as a percentage of all people in that group. For those exposed to the the therapy, the risk of death at 12 months is 300/(300+700) or 30%. The risk of death at 12 months of those not exposed to the therapy is 800/(800+200) or 80%.
Relative Risk Reduction
The Relative Risk Reduction (RRR) achieved by a particular therapy is the difference between the two risks as a percentage of the risk of those not exposed to the therapy. In the example above, the relative risk reduction would be (80%-30%)/80% or 62.5%.
Absolute Risk Reduction
The Absolute Risk Reduction (ARR) achieved by a particular therapy is simply the difference in the two risks. In the above example, the absolute risk reduction is 80%-30% or 50%.
Relative vs. Absolute Risk Reducation
Because it is presented as a percentage of the control group, Relative Risk Reduction does not take into account the size of the initial risk and the actual reduction. In the example below, while the actual reducations vary greatly, the Relative Risk Reduction remains the same.
Risk in Control. Group | Risk in Experimental Group | Relative Risk Reducation | Absolute Risk Reduction |
70% | 35% | 50% | 35% |
7% | 3.5% | 50% | 3.5% |
0.7% | 0.35% | 50% | 0.35% |
Although the Absolute Risk Reduction is a more accurate report of the effect of the intervention, it's harder for people to understand the distinction between the two. So EBM pratctitioners came up with another statistic to more clearly represent what the statistics mean.
Number Needed to Treat
The Number Needed to Treat (NNT) is the reciprocal of the Absolute Risk Reduction. If the ARR is expressed as a decimal, the Number Needed to Treat is 1/ARR; if the ARR is expressed as a percentage, the Number Needed to Treat is 100/ARR. In the above example, the Number Needed to Treat is 100%/50% or 2. The Number Needed to Treat tells how many people you need to treat in order to see the desired outcome in one additional patient . In this example, you would need to treat 2 patients to prevent one additional patient from dying at 12 months. The NNT gives you a clear number to use to balance benefits against risks. If you only need to treat 2 patients to see a benefit, you may feel comfortable ignoring extremely mild side effects. However, if you need to treat 2000 patients to see a benefit with a drug that has very severe side effects, you may not feel comfortable recommending this treatment.
Disease Present | Disease Not Present | |
Test Positive | 900 | 100 |
Test Negative | 200 | 800 |
Positive Predictive Value
The Positive Predictive Value of a test is the number of times the disease was present according to the gold standard as a percentage of the number of times the new test came back positive. In the above example, the Positive Predictive Value would be 900/(900 +100) or 90%.
Negative Predictive Value
The Negative Predictive Value of a test is the number of times the disease is absent according to the gold standard as a percentage of the number of times the new test comes back negative. In the above example, the Negative Predictive Value would be 800/(800+200)) or 80%.
Prevalance
The prevalance of a disease is the percentage of people with a particular disease within a given population. In the above example, the prevalance would be 900/(900+100+200+800) or 45%.
Positive and Negative Predictive Values are highly influenced by the prevalance of a disease. So researchers began to look for qualities that would not be so easily influenced.
Sensitivity
The Sensitivity of a test is the number of times a test came back positive as a percentage of the times the disease was present according to the gold standard. In the above example, the Sensitivity would be (900/900+200) or 81%.
Specificity
The Specificity of a test is the number of times a test comes back negative as a percentage of the times the disease was negative according to the gold standard. In the above example, the Specificity would be (800/800+100) or 88%.
While Sensitivity and Specificity are useful in that they are unaffected by prevalance, they are qualities of the test and not patient-related the way we would like evidence-based practice to be. So researchers came up with another quality that would satisfy both demands of being patient-centered and minimally affected by prevalance.
Pre- and Post-Test Probability
First, it is important to note that no test tells us absolutely whether a disease is present (This is not, strictly speaking. true. A pathologist performing an autopsy knows exactly what disease killed a patient, but by then it's too late). A diagnostic test simply tells us something about the probability that a disease is present. Evidence-based practice encourages the practitioner to assign a value to the probability that a disease is present, based on the practitioners's clinical judgment. This number is likely to be related to the prevalance of the disease in a particular population. As the prevalance of ectoptic pregnancies in men over 50 is 0%, that would be the pre-test probability. The results of a test raise or lower this number to a post-test probability that the condition is present. If the TVU for the 50-year old man comes back positive, the post-test probability is 100% that you need a new sonograph.
Likelihood Ratios
The positive and negative likelihood ratios of a test gauge the test's ability to bring the pre-test probability and post-test probability into allignment.
The likelihood ratio for the positive test measures the test's ability to raise the pre-test probability to a level high enough that a practioner feels comfortable choosing one therapy over another. It is computed with the following equation: Sensitivity/(1-Specificity) [where specificity and sensitivity are expressed as decimals rather than percentages].
The likelihood ratio for the negative test measures the test's ability to lower the pre-test probability to a level low enough that a practitioner feels comfortable in choosing not to apply the therapy for the suspected disease. It is computed with the following equation: (1-Sensitivity)/Specificity [where sensitivity and specificity are expressed as decimals rather than percentages].
The Likelihood Nomagram
The Likelihood Nomagram developed by T.J. Fagan (Fagan TJ. Letter: Nomogram for Bayes theorem. N Engl J Med 293. 257(1975)) is the tool used to make use of likelihood ratios. Find your pre-test probability on the left-hand column. Draw a line through the likelihood ratio of the test as reported in the study and find the post-test probability that the condition is present. As can be seen from the nomagram, a likelihood ratio of 1 is not at all effective. On the whole, a positive likelihood ratio (LR+) of greater than 10 and a negative likelihood ratio (LR-) of less than 0.1 provide the greatest results.
Patients with Renal Failure | Patients without Renal Failure | |
Patients with Diabetes | 150 | 850 |
Patients without Diabetes | 30 | 970 |
Risk
The Risk of an outcome is the number of times the outcome occurred as a percentage of all possible occurrences. In the case above, the risk of a patient with diabetes developing renal failure is 150/(150+850) or 15%. In other words, a patient with diabetes has a 15% chance of developing renal failure. Risk is often reported in descriptive articles where there is no control group.
Relative Risk
The Relative Risk of an outcome occurring is the risk of the outcome occurring in the group presenting the prognostic factor as a percentage of the risk of the outcome occurring in the group that did not present the prognostic factor. In the example above, the risk of a patient with diabetes developing renal failure is 15% (150/1000). The risk of a patient without diabetes developing renal failure is 3% (30/1000). The Relative Risk is 15%/3% or 5. In other words, patients with diabetes are 5 times more likely to have renal failure than patients without. Relative Risk is also reported as Relative Risk Ratio or Risk Ratio.
Odds
The odds of an outcome occurring is the number of times the outcome occurred in patients with the prognostic factor as a percentage of the times the outcome occurred in patients who did not present with the prognostic factor. In the example above, the odds of a patient with diabetes developing renal failure would be 150/30 or 5. In other words the odds are 5:1 that a patient with diabetes will develop renal failure
Odds Ratio
The Odds Ratio of an outcome occurring is the odds that the outcome occurs in the group presenting the prognostic factor as a percentage of the odds of the outcome not occurring in the group that presents the prognostic factor. In the example above the odds of a patient with diabetes developing renal failure was calculated as 5. The odds of a patient with diabetes not developing renal failure is .87 (850/970). The Odds Ratio would be 5/.87 or 5.7. In other words, a patient with diabetes, all other things being equal, is 5.7 times more likely to develop renal failure than not.
Relative Risk vs. Odds Ratio
Whether researchers report Relative Risk or Odds Ratio depends on whether they do a cohort study or a case control study. Because of the way subjects are chosen in a case control study, the percentages may be skewed. The Odds Ratio overcomes this problem by having both factors in the denominator.
Survival Curves
A survival curve is a graphic representation of risk over time. Rather than presenting the risk at one particular endpoint, risk of death is computed at given intervals and presented graphically.
Patients with Lung Cancer | Patients without Lung Cancer | |
Patients who Smoke | 150 | 850 |
Patients who Do Not Smoke | 30 | 970 |
Risk
The Risk of an outcome is the number of times the outcome occurred as a percentage of all possible occurrences. In the case above, the risk of a patient who smokes developing lung cancer is 150/(150+850) or 15%. In other words, a patient who smokes has a 15% chance of developing lung cancer. Risk is often reported in descriptive articles where there is no control group.
Relative Risk
The Relative Risk of an outcome occurring is the risk of the outcome occurring in the group exposed to the risk as a percentage of the risk of the outcome occurring in the group that was not exposed to the risk. In the example above, the risk of a patient who smokes developing lung cancer is 15% (150/1000). The risk of a patient who does not smoke developing lung cancer is 3% (30/1000). The Relative Risk is 15%/3% or 5. In other words, patients who smoke are 5 times more likely to have lung cancer than patients who do not. Relative Risk is also reported as Relative Risk Ratio or Risk Ratio.
Odds
The odds of an outcome occurring is the number of times the outcome occurred in patients exposed to the risk as a percentage of the times the outcome occurred in patients who were not exposed to the risk. In the example above, the odds of a patient who smokes developing lung cancer would be 150/30 or 5. In other words the odds are 5:1 that a patient who snokes will develop lung cancer.
Odds Ratio
The Odds Ratio of an outcome occurring is the odds that the outcome occurs in the group exposed to the risk as a percentage of the odds of the outcome not occurring in the group that is exposed to the risk. In the example above the odds of a patient who smokes developing lung cancer was calculated as 5. The odds of a patient who smokes not developing lung cancer is .87 (850/970). The Odds Ratio would be 5/.87 or 5.7. In other words, a smoker is 5.7 times more likely to develop lung cancer than not.
Relative Risk vs. Odds Ratio
Whether researchers report Relative Risk or Odds Ratio depends on whether they do a cohort study or a case control study. Because of the way subjects are chosen in a case control study, the percentages may be skewed. The Odds Ratio overcomes this problem by having both factors in the denominator.
Until now, the discussion of a harm study has been similar to the discussion of a prognosis study. However, it happens occassionally that researchers come upon a risk accidentally, most often when they are studying a therapy. In those cases they have been able to do a randomized double-blinded placebo-controlled clinical trial to (accidentally) assess harm and the results are presented in a similar way as with a therapy study.
Absolute Risk Increase
The Absolute Risk Increase (ARI) is the difference in risk between the two arms of the study. If the risk of breast cancer in a patient receiving hormone replacement therapy is 1.25% and the risk of breast cancer in a patient receiving a placebo is 1.1%, then the Absolute Risk Increase is 0.15%.
Number Needed to Harm
The Number Needed to Harm is the reciprocal of the Absolute Risk Increase. NNT=1/ARI (where the ARI is reported as a decimal) or 100/ARI (where the ARI is reported as a percentage. In the above example, the Number Needed to Harm would be 667. You would have to treat 667 patients with hormone replacement therapy to increase the risk of breast cancer in one additional patient.