THE PRECISION PROTOCOL
The Definitive Guide to USMLE Biostatistics.
Chapter 3: Measures of Risk and Association
To reach a HIGH score, you must understand how to quantify "danger" and "benefit." In Chapter 1, we learned how to build the study; now, in Chapter 3, we calculate the Surgical Outcome.
1. Relative Risk (RR) vs. Odds Ratio (RR)
This is the most frequent calculation on the USMLE. Use the same 2x2 table from Chapter 2, but the "logic" of the denominator changes.
You must always build the table the same way. Disease goes on top; Test goes on the side.
A. Relative Risk (RR)
- The Study: Used in Cohort Studies (following people forward).
- The Question: "How much more likely is the exposed group to get sick compared to the unexposed group?"
- Formula: c/(c+d)a/(a+b)​
Interpretation: RR = 1: No association.
- RR > 1: Exposure increases risk (harmful).
- RR < 1: Exposure decreases risk (protective).
B. Odds Ratio (OR)
- The Study: Used in Case-Control Studies (looking backward).
- The Question: "What are the odds that the sick group was exposed compared to the odds that the healthy group was exposed?"
- Formula: axd/bxc (The "Cross-Product" ratio).
- The Rule: Remember the Rare Disease Assumption—if the disease is rare, OR≈RR.
2. Attributable Risk (AR)
- The Logic: "How much of the disease is actually caused by the exposure?"
- Formula: Incidence in Exposed−Incidence in Unexposed
- Example: If 10% of smokers get lung cancer and 1% of non-smokers get it, the AR is 9%. This means 9% of the cancer is directly "attributed" to smoking.
3. Clinical Impact: NNT and NNH
The USMLE loves these because they translate math into Clinical Decisions.
A. Number Needed to Treat (NNT)
- The Logic: How many patients do I need to treat to prevent one bad outcome?
- The Formula: 1/Absolute Risk Reduction (ARR)
- The Goal: You want this number to be LOW (e.g., treating 5 people to save 1 life is great).
B. Number Needed to Harm (NNH)
- The Logic: How many patients must be exposed to a drug before one person has a side effect?
- The Formula: 1/Attributable Risk (AR)
- The Goal: You want this number to be HIGH (e.g., you want to treat 1,000 people before seeing 1 side effect).
4. Training Question
A 50-year-old physician is reviewing an RCT for a new statin. The incidence of myocardial infarction (MI) was 2% in the statin group and 4% in the placebo group.
What is the Number Needed to Treat (NNT) to prevent one MI?
A. 2
B. 25
C. 50
D. 100
1. First, find the Absolute Risk Reduction (ARR): (4%−2%) = 2%.
2. Then, NNT= 1/ARR= 1/0.02= 50.
You need to treat 50 patients to prevent one MI. This is a high-yield calculation.
Correct Answer C
5. The Hazard Ratio (HR)
- The Logic: This is basically a "Relative Risk" but for Time. It is used in survival analysis (like cancer studies).
- The Question: "At any given moment, what is the risk of an event in the treatment group compared to the control group?"
Interpretation:
- HR = 1: No difference in survival.
- HR < 1: The treatment group is surviving longer (The "Hazard" is lower).
- HR > 1: The treatment group is dying/failing faster (The "Hazard" is higher).
6. Attributable Risk Percent (ARP)
- The Logic: "Of all the sick people who were exposed, what percentage of their sickness was only due to that exposure?"
- The Formula: RR-1/RR
- Clinical Pearl: This is high-yield for public health questions. If the RR of lung cancer in smokers is 10, then (10−1)/10 = 90%. This means 90% of lung cancer in smokers would disappear if they never picked up a cigarette.
7. Population Attributable Risk (PAR)
- The Logic: This looks at the entire population, not just the exposed group.
- The Question: "If we eliminate this risk factor from the whole city, how many cases would we prevent total?"
- The Driver: This depends on how common the risk factor is. A small risk that affects everyone (like air pollution) might have a higher PAR than a huge risk that only affects three people.
8. Training Question
A 50-year-old physician is reviewing a 5-year study on a new chemotherapy drug. The study uses a Kaplan-Meier curve and reports a Hazard Ratio (HR) of 0.70.
Which of the following is the most accurate interpretation of this result?
A. 70% of the patients died during the study.
B. The treatment group had a 30% lower risk of death at any specific point in time compared to the control group.
C. The treatment group lived exactly 70% longer than the control group.
D. The drug is 70% more toxic than the placebo.
A Hazard Ratio of 0.70 means the "Hazard" (risk of the event) is 70% of the control, which is a 30% reduction in risk. This is a high-yield concept for reading survival data.
Correct Answer B.
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