Lesson 3.3: Measures of Association and Risk
Introduction
In this lesson, we will explore the concepts of measures of association and risk in the field of biostatistics and epidemiology. Understanding these measures is pivotal for interpreting study outcomes and applying statistical results to patient care decisions.
Learning Objectives
By the end of this lesson, students will be able to:
- Define and calculate relative risk, odds ratio, absolute and relative risk reduction, and number needed to treat or harm.
- Explain and interpret confidence intervals, p-values, and the distinction between statistical and clinical significance.
- Apply these measures to evaluate research findings effectively.
- Differentiate between statistical significance and clinical relevance in the context of patient care.
Hook
Consider a clinical trial evaluating a new medication that claims to reduce the risk of heart attacks. How do we determine the effectiveness of this drug quantitatively? This is where measures of association and risk come into play. By the end of this lesson, you'll be equipped to interpret study results like a pro, enabling you to make informed decisions in clinical practice.
Measures of Association
Measures of association are statistical tools that help us understand the relationship between exposures (such as medications or behaviors) and outcomes (such as diseases or health events). Key measures include relative risk (RR) and odds ratio (OR).
Relative Risk (RR)
Relative risk compares the risk of an event (such as developing a disease) in two groups. It is defined as:
$$
$RR = \frac{P_{exposed}}{P_{unexposed}}$
$$
Where:
- $P_{exposed}$ is the probability of the event occurring in the exposed group.
- $P_{unexposed}$ is the probability of the event occurring in the non-exposed group.
Example 1: Calculating Relative Risk
Suppose we conducted a study on the effect of smoking on lung cancer risk. In a sample of 1,000 smokers, 50 developed lung cancer, whereas in a sample of 1,000 non-smokers, only 10 developed lung cancer. We can calculate the probabilities:
- For smokers: $ P_{smokers} = \frac{50}{1000} = 0.05 $
- For non-smokers: $ P_{non-smokers} = \frac{10}{1000} = 0.01 $
Now substituting into the relative risk formula:
$$
$RR = \frac{0.05}{0.01} = 5$
$$
This means smokers are 5 times more likely to develop lung cancer compared to non-smokers.
Odds Ratio (OR)
The odds ratio compares the odds of an event occurring in the exposed group to the odds of it occurring in the unexposed group. It is calculated as:
$$
OR = \frac{Odds_{exposed}}{Odds_{unexposed}} = \frac{P_{exposed}/(1 - P_{exposed})}{P_{unexposed}/(1 - P_{unexposed})}
$$
Example 2: Calculating Odds Ratio
Continuing with our smoking study:
- The odds of lung cancer for smokers is $ Odds_{smokers} = \frac{50}{950} = 0.0526 $\ (since 950 is the total who did not develop lung cancer).
- The odds for non-smokers is $ Odds_{non-smokers} = \frac{10}{990} = 0.0101 $.
Thus, the odds ratio can be calculated as:
$$
$OR = \frac{0.0526}{0.0101} \approx 5.2$
$$
This indicates that smokers are about 5.2 times more likely to develop lung cancer compared to non-smokers.
Absolute Risk Reduction (ARR)
Absolute risk reduction is the difference in risk between the control and treatment groups. It is given by:
$$
ARR = P_{control} - P_{treatment}
$$
Example 3: Calculating Absolute Risk Reduction
If we find that in the clinical trial, the risk of heart attacks in the treatment group (who received the new medication) is 5% and in the control group it is 10%, we calculate:
$$
ARR = 0.10 - 0.05 = 0.05 \text{ or } 5\%
$$
This means there is a 5% absolute reduction in risk of heart attacks due to the new medication.
Relative Risk Reduction (RRR)
Relative risk reduction is a measure of the proportion by which the risk is reduced in the treatment group relative to the control group:
$$
RRR = \frac{ARR}{P_{control}} = \frac{P_{control} - P_{treatment}}{P_{control}}
$$
Example 4: Calculating Relative Risk Reduction
Using the previous example,
$$
RRR = $\frac{0.05}{0.10}$ = 0.5 \text{ or } 50\%
$$
This means the new medication reduces the risk of heart attacks by 50% compared to no treatment.
Number Needed to Treat (NNT)
The number needed to treat is the number of patients that need to be treated to prevent one additional bad outcome (like a heart attack). It is calculated as:
$$
$NNT = \frac{1}{ARR}$
$$
Example 5: Calculating Number Needed to Treat
From before, we calculated an ARR of 0.05, so:
$$
$NNT = \frac{1}{0.05} = 20$
$$
Therefore, 20 patients need to be treated with the medication to prevent one heart attack.
Statistical Significance vs. Clinical Significance
p-Values
The p-value indicates the likelihood that the observed results occurred by chance. A common cutoff is a p-value of 0.05, meaning there is a 5% chance the results occurred due to random variation.
Example 6: Interpreting p-Values
If a study reports a p-value of 0.03, this suggests strong evidence against the null hypothesis (no effect), leading researchers to say the result is statistically significant.
Confidence Intervals (CIs)
Confidence intervals provide a range of values that likely include the true effect size. For example, a 95% CI means that we are 95% confident that the true parameter lies within that range.
Example 7: Interpreting Confidence Intervals
If a study finds that the relative risk is 2.0 with a 95% CI of (1.5, 2.5), it suggests that the true relative risk likely falls between 1.5 and 2.5. If the CI includes 1, it is not statistically significant.
Distinguishing Statistical from Clinical Significance
It is essential to remember that statistical significance does not always imply clinical significance. A statistically significant result may not have a meaningful impact on patient care.
Example 8: Assessing Clinical Significance
Imagine a drug that reduces the risk of a disease by a statistically significant 1%. While the result may be statistically significant (p < 0.05), a 1% reduction may not change patient outcomes, making it clinically insignificant.
Conclusion
In this lesson, we explored the crucial concepts of measures of association and risk in epidemiology. Understanding relative risk, odds ratios, and the distinction between statistical and clinical significance enables students to make informed clinical decisions and interpret research findings effectively.
Study Notes
- Relative risk (RR): ratio of event probability in exposed vs. unexposed.
- Odds ratio (OR): odds of an event occurring in exposed vs. unexposed.
- Absolute risk reduction (ARR): difference in risk between groups.
- Relative risk reduction (RRR): proportionate reduction in risk.
- Number needed to treat (NNT): number of patients to treat to prevent one event.
- p-value: probability that observed results are due to chance.
- Confidence interval: range that likely contains the true effect size.
- Distinction between statistical significance and clinical significance is vital for patient care.