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Measuring Risk in Epidemiology — Complete Explanation
This PDF is a lecture on how scientists and doctors measure risk in public health research. Here's a full breakdown of every page:
📌 Page 1 — Title Slide
"Measuring Risk in Epidemiology"
Epidemiology is the study of how diseases spread and affect populations. This lecture teaches the tools used to measure how much risk a person faces based on certain exposures (like smoking, chemicals, diet, etc.).
📌 Page 2 — What is Risk?
Risk = the probability (chance) that something bad will happen to a person within a specific time period.
- Think of it like: "What are the chances a smoker gets lung cancer in the next 10 years?"
- Risk is expressed as a number (e.g., 0.20 = 20% chance)
- Measuring risk quantitatively gives us evidence to make public health decisions (e.g., should we ban a substance? Run a vaccination campaign?)
📌 Page 3 — Risk vs. Association
Association = when two things tend to happen together (they are correlated).
- Example: Ice cream sales and drowning rates both rise in summer — they are associated, but ice cream doesn't cause drowning. The real cause is hot weather.
- Correlation ≠ causation
- When an association is believed to actually cause the outcome, we call that factor a risk factor.
- Example: Smoking → lung disease. Smoking is a risk factor because it causes the disease.
The slide shows: Exposure → Outcome (e.g., cigarette → damaged lungs)
📌 Page 4 — Measures of Association
There are 5 main tools to measure how strong the relationship is between an exposure and a disease:
| Measure | Abbreviation |
|---|---|
| Relative Risk | RR |
| Odds Ratio | OR |
| Attributable Risk | AR |
| Population Attributable Risk | PAR |
| Population Attributable Risk Percent | PAR% |
Each one answers a slightly different question — explained in the slides that follow.
📌 Page 5 — Ratios, Proportions, and Rates
Before calculating risk, you need to understand these three basic concepts:
Ratio
- Simply compares two numbers
- Example: 5 women out of 12 people = 5:7 (women to men) or 5/12 = 0.42
Proportion
- A ratio where the top number (numerator) is included in the bottom number (denominator)
- Example: 5 women out of 12 total people = 42% are women
Rate
- A proportion that includes time
- Example: 8.1 deaths per 100,000 people per year
- Uses "person-years" as the denominator
- To make small numbers readable, multiply by a constant (like 100,000)
- 0.000081 × 100,000 = 8.1 deaths per 100,000
📌 Page 6 — The 2×2 Table (Contingency Table)
This is the most important tool in epidemiology. It's a simple grid that organizes data.
| Sick | Well | |
|---|---|---|
| Exposed | a | b |
| Non-exposed | c | d |
- Columns = outcome (did they get sick or not?)
- Rows = exposure (were they exposed or not?)
- Cells contain counts (number of people)
- a = exposed AND sick
- b = exposed AND well
- c = not exposed AND sick
- d = not exposed AND well
Almost every calculation in this lecture uses this table.
📌 Page 7 — Sources for Calculating Risk
Risk can come from:
- Published studies or statistics
Three key types of rates:
| Rate | Formula |
|---|---|
| Incidence rate | New cases in a year ÷ Total population at risk |
| Attack rate | Cases during an epidemic ÷ Population at risk (used during outbreaks) |
| Death rate | Deaths in a year ÷ Total population |
📌 Page 8 — Interpreting Risk (Be Careful!)
When you read a health statistic, you need to ask: Is this a true rate, or just a proportion?
The table shows stroke cases by age from a hospital:
- Ages 60–69 had 175 cases (35% of all cases)
- But does that mean people aged 60–69 are at highest risk? Not necessarily — there may just be more people in that age group overall.
Key warnings:
- You may not know the total population at risk
- Check whether the report used proportions or rates
- Proportions alone cannot define true risk — you need the denominator (total population)
📌 Page 9 — Relative Risk (RR)
Relative Risk answers: "How much more likely is the disease in exposed people compared to unexposed people?"
Formula:
RR = Incidence in exposed ÷ Incidence in unexposed
Interpretation:
| RR value | Meaning |
|---|---|
| RR = 1 | No association (same risk in both groups) |
| RR > 1 | Exposure is harmful (increases risk) |
| RR < 1 | Exposure is protective (decreases risk) |
- A larger RR = stronger evidence of a causal relationship
- But a large RR alone does not prove causation — other factors must be considered
📌 Page 10 — Calculating Relative Risk (Example)
Scenario: Factory workers exposed to toxic dust vs. non-exposed workers. Outcome: lung disease.
| Lung Disease | No Lung Disease | Total | |
|---|---|---|---|
| Exposed | 800 | 200 | 1000 |
| Non-exposed | 40 | 1960 | 2000 |
Step 1: Risk in exposed = 800/1000 = 0.80 = 80%
Step 2: Risk in non-exposed = 40/2000 = 0.02 = 2%
Step 3: RR = 80% ÷ 2% = 40
Conclusion: Exposed workers are 40 times more likely to develop lung disease than unexposed workers.
📌 Page 11 — Key Points on Relative Risk
- RR measures the likelihood of disease in exposed vs. unexposed people
- It is a ratio (division of two incidence rates)
- Also called "risk ratio"
- Formula: Incidence in exposed ÷ Incidence in non-exposed
- Used primarily in cohort studies (where you follow people forward in time)
📌 Page 12 — Odds Ratio (OR)
In case-control studies, you cannot calculate RR directly (because you start with sick people, not a whole population). Instead, you use the Odds Ratio.
OR can approximate RR when:
- Cases and controls are similar (matched)
- The disease is rare in the population
📌 Page 13 — Calculating the Odds Ratio (Example)
Scenario: Suicide deaths in Washington State (2003–2005). Question: Does living alone increase suicide risk in men?
| Suicide: Yes | Suicide: No | Total | |
|---|---|---|---|
| Lived alone | 48 (a) | 12 (b) | 60 |
| Not alone | 52 (c) | 88 (d) | 140 |
| Total | 100 | 100 | 200 |
Formula: OR = (a × d) ÷ (b × c)
OR = (48 × 88) ÷ (12 × 52) = 4224 ÷ 624 = 6.8
Conclusion: Living alone increases the odds of suicide in men by a factor of 6.8.
📌 Page 14 — Summary (Part 1)
| Measure | Study Type | What It Does |
|---|---|---|
| Relative Risk | Cohort studies | Measures strength of association |
| Odds Ratio | Case-control studies | Approximates relative risk |
Key reminder: A larger risk does not prove causation.
📌 Page 15 — Key Points on Odds Ratio
OR formula using the 2×2 table:
OR = (a × d) ÷ (b × c) = ad/bc
Assumptions for OR to approximate RR:
- Cases and controls come from the same population
- Disease is rare
Example table setup for a food poisoning investigation: "Ate suspect food" vs. "Didn't eat suspect food" in cases vs. controls.
📌 Page 16 — Attributable Risk (AR)
Attributable Risk answers: "How many extra cases of disease are caused by the exposure?"
- Unlike RR (which is a ratio), AR is expressed as an actual rate (number of cases)
- It tells you the absolute burden of disease due to the exposure
- Used to estimate how much disease could be eliminated if we removed the exposure
Formula:
AR = Incidence in exposed − Incidence in unexposed
📌 Page 17 — Calculating Attributable Risk (Example)
Using the same factory worker data:
- Incidence in exposed = 800/1000 = 800 per 1000
- Incidence in non-exposed = 40/2000 = 20/1000 (converted to same denominator)
AR = 800/1000 − 20/1000 = 780 per 1000 (i.e., 780 extra cases per 1000 workers are due to the exposure)
This means: if the toxic dust were removed, 780 out of every 1000 exposed workers would not have gotten sick.
📌 Page 18 — Utility of Attributable Risk (Smoking Example)
This table compares smoking's effect on lung cancer vs. heart disease:
| Lung Cancer | Heart Disease | |
|---|---|---|
| Heavy smokers | 166 per 100,000 | 599 per 100,000 |
| Non-smokers | 7 per 100,000 | 422 per 100,000 |
| Relative Risk | 166/7 = 23.7 | 599/422 = 1.4 |
| Attributable Risk | 166−7 = 159 | 599−422 = 177 |
Key insight: Smoking has a higher relative risk for lung cancer (23.7×), but it causes more absolute deaths from heart disease (177 vs. 159 per 100,000). This is because heart disease is already common even in non-smokers.
This shows why you need both RR and AR to get the full picture.
📌 Page 19 — Attributable Risk Percent (AR%)
Sometimes it's more useful to express AR as a percentage.
Formula:
AR% = (Risk in exposed − Risk in unexposed) ÷ Risk in exposed × 100
Using the smoking data:
- Lung cancer AR% = (166 − 7) ÷ 166 × 100 = 96%
- 96% of lung cancer in smokers is due to smoking
- Heart disease AR% = (599 − 422) ÷ 599 × 100 = 30%
- Only 30% of heart disease in smokers is due to smoking
📌 Page 20 — Population Attributable Risk (PAR) and PAR%
These measures zoom out to the entire population (not just the exposed group).
PAR = Incidence in general population − Incidence in unexposed population
Answers: How much disease would disappear from the whole population if we eliminated the exposure?
PAR% = PAR ÷ Incidence in general population × 100
Example (lung cancer deaths):
- General population: 62 per 100,000
- Non-smokers: 7 per 100,000
PAR = 62 − 7 = 55 deaths per 100,000 attributable to smoking in the whole population
PAR% = (62 − 7) ÷ 62 × 100 = 89%
Meaning: 89% of all lung cancer deaths in the population could be prevented if nobody smoked.
📌 Page 21 — Uses of RR and PAR in Public Health
| Measure | Who uses it | Why |
|---|---|---|
| Relative Risk | Researchers | Important for inferring causation; identifying risk factors |
| Population Attributable Risk | Public health practitioners | Guides resource allocation and policy decisions |
Using the factory lung disease data (RR = 40), if you also calculate PAR, you can tell policymakers how many cases in the whole community would be prevented by cleaning up the factory.
📌 Page 22 — Uses of RR and PAR (Continued, with Numbers)
For the factory town (population = 100,000):
- Community incidence: 28 per 1,000/year
- Non-exposed incidence: 20 per 1,000/year
AR% = (800 − 20) ÷ 800 × 100 = 98% of risk in exposed workers is due to the exposure
PAR = 28 − 20 = 8 cases per 1,000
PAR% = (28 − 20) ÷ 28 = 28.5%
Conclusion: Eliminating toxic substances in the factory could reduce lung disease in the whole town by 28%.
📌 Page 23 — Key Points on AR, ARP, PAR, PAR%
| Measure | What it means | How to calculate |
|---|---|---|
| AR | Absolute extra risk in exposed people due to the exposure | Incidence(exposed) − Incidence(unexposed) |
| AR% (ARP) | What % of disease in exposed people is due to the exposure | AR ÷ Incidence(exposed) |
| PAR | Disease that would disappear from whole population if exposure eliminated | Incidence(population) − Incidence(unexposed) |
| PAR% | What % of all disease in population is due to the exposure | PAR ÷ Incidence(population) |
📌 Page 24 — Final Summary
| Measure | Key feature |
|---|---|
| Risk | Probability of an outcome |
| Relative Risk (RR) | Measures strength of association; larger ≠ causation |
| Attributable Risk (AR) | Absolute amount of disease attributable to exposure in exposed |
| AR% | AR as a percentage |
| Population Attributable Risk (PAR) | Same idea but for the whole population |
| PAR% | PAR as a percentage |
| Odds Ratio (OR) | Approximates RR in case-control studies |
📌 Pages 25–32 — Deep Dive into Odds Ratio
Page 25 — Design of Case-Control Study
- Step 1: Identify Cases (people who have the disease)
- Step 2: Identify Controls (people without the disease)
- Step 3: Look backwards — were the cases more often exposed than the controls?
Page 26 — Why You Can't Use RR in Case-Control Studies
In case-control studies, you select people based on disease status, so you don't have a true "population at risk" to calculate incidence. Therefore: you cannot calculate Relative Risk. Instead, use the Odds Ratio.
The OR asks: How much higher are the odds of having been exposed in cases compared to controls?
Pages 27–29 — OR Formula Derivation
From the 2×2 table:
- Odds of exposure in CASES = a/c (exposed cases ÷ unexposed cases)
- Odds of exposure in CONTROLS = b/d (exposed controls ÷ unexposed controls)
OR = (a/c) ÷ (b/d) = ad/bc
This is the classic "cross-product" formula — multiply diagonals.
Page 30 — Uses of OR
- Determines whether an exposure is related to a disease outcome
- Compares the strength of different risk factors against each other
Page 31 — Interpreting OR (mirrors RR interpretation)
| OR value | Meaning |
|---|---|
| OR = 1 | Exposure has no effect on disease odds |
| OR > 1 | Exposure increases odds → Risk factor |
| OR < 1 | Exposure decreases odds → Protective factor |
Page 32 — OR vs. RR
- When a disease is rare, OR is a good approximation of RR
- As disease becomes more common/prevalent, OR overestimates RR (the OR will be larger than the true RR)
🧠 Big Picture Summary
Epidemiology measures RISK using:
COHORT studies (follow people forward)
→ Calculate RELATIVE RISK (RR)
→ Calculate ATTRIBUTABLE RISK (AR, AR%)
→ Calculate POPULATION ATTRIBUTABLE RISK (PAR, PAR%)
CASE-CONTROL studies (start from disease, look backward)
→ Cannot calculate RR
→ Calculate ODDS RATIO (OR) ≈ approximates RR when disease is rare
The goal of all these measures is to answer: "How dangerous is this exposure, and how much disease could we prevent by eliminating it?"
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