Relative Risk Reduction versus Absolute Risk Reduction

Link to YouTube Video

I just watched a video in which Dr. Suneel Dhand explained the differences between Relative Risk Reduction (RRR) and Absolute Risk Reduction (ARR). I asked Google's Gemini the following question:

Can you explain the differences between "relative risk reduction" and "absolute risk reduction" and include some numerical examples to illustrate these differences?

Here is its response:

Both RRR and ARR are important statistics used in medicine to understand the effectiveness of a treatment or intervention in reducing the risk of a particular outcome. They might seem similar, but they convey information in slightly different ways. Here's a breakdown:

Relative Risk Reduction (RRR):

• Concept: RRR tells you by what percentage the risk of an outcome is reduced in the treatment group compared to the control group.
• Calculation: It's expressed as a percentage and is calculated using the following formula:

RRR = (1 - Relative Risk) x 100%

Where Relative Risk (RR) is the risk of the outcome in the treatment group divided by the risk of the outcome in the control group.

Absolute Risk Reduction (ARR):

• Concept: ARR tells you the absolute difference in the risk of an outcome between the treatment group and the control group.
• Calculation: It's expressed as a percentage or a decimal and is calculated as:

ARR = Risk in Control Group - Risk in Treatment Group

Example:

Let's say a study investigates a new medication for preventing heart disease. Here's some hypothetical data:

• Control Group: 10% of participants experience a heart attack within 5 years.
• Treatment Group: 5% of participants experience a heart attack within 5 years.

Calculating RRR:

• Relative Risk (RR): 5% (risk in treatment group) / 10% (risk in control group) = 0.5
• RRR = (1 - 0.5) x 100% = 50%

This means the medication appears to reduce the relative risk of a heart attack by 50%.

Calculating ARR:

• ARR = 10% (control group risk) - 5% (treatment group risk) = 5%

This means the medication is associated with a 5% absolute reduction in the risk of a heart attack within 5 years.

Interpretation:

While the RRR seems very impressive (a 50% reduction in risk!), the ARR clarifies the real-world impact. In this case, only 5% fewer people experienced heart attacks in the treatment group compared to the control group.

Why Both Are Important:

• RRR: Useful for understanding the proportional benefit of a treatment, especially when the baseline risk is high.
• ARR: Provides a clearer picture of the actual reduction in risk, which might be smaller than the RRR suggests, particularly for uncommon conditions.

In conclusion:

Both RRR and ARR offer valuable insights. Considering both statistics gives a more complete understanding of a treatment's effectiveness in reducing the risk of a specific outcome.

 I also asked Gemini about the relative sizes of control and treatment groups:

Do the control group and the treatment group need to be of the same size?

The response was:

No, the control group and the treatment group in a study don't necessarily need to be exactly the same size. There are advantages and disadvantages to consider when deciding on the sample size for each group.

Here's a breakdown of why the size might differ:

• Power Analysis: Researchers often conduct a power analysis before a study to determine the ideal sample size for each group. This analysis considers factors like the desired effect size (how big of a difference they expect to see between the groups) and the acceptable level of error. The analysis might indicate that a slightly larger or smaller control group compared to the treatment group is optimal for achieving statistically significant results.

• Logistical Constraints: Sometimes, recruiting participants for a study can be challenging. Researchers might need to adjust the group sizes based on feasibility and resource limitations.

What matters most is achieving sufficient statistical power. This means having a high enough chance of detecting a true effect (difference between groups) if it actually exists, and avoiding getting misleading results due to chance alone.

Here's what to consider regarding group size:

• Larger Samples are Generally Better: Larger samples in both groups generally lead to more statistically powerful studies. This means a higher chance of getting reliable results.

• Unequal Groups Can Be Efficient: In some cases, having a slightly larger control group compared to the treatment group can be statistically efficient. This is because the control group provides a clearer baseline for comparison and helps account for random variation that might not be due to the treatment itself.

• Focus on Statistical Power: Aim for a sample size in each group that ensures sufficient power to detect the effect size of interest. A statistician can help determine the optimal sample sizes based on your specific research question and desired level of precision.

Here are some additional points:

• Balance is Desirable: While some imbalance might be acceptable, having extremely unequal group sizes can be problematic. A very small treatment group might make it difficult to detect a true effect, even if it exists.

• Transparency is Key: Regardless of the chosen sample sizes, it's important to clearly report the group sizes and any justifications for unequal sizes in the research report.

In conclusion, the ideal size for the control and treatment group depends on the specific study design and the need for statistical power. While larger samples are generally better, some variation might be acceptable as long as the study can still achieve reliable and generalizable results.

Let's consider an example of our own making. Suppose we have total of 100 participants in a clinical trial involving exposure to an external irritant. There are 60 people in the control group who receive no treatment and a treatment group of 40 people who receive an injection of a Substance B. In the control group, 36 persons display symptoms while in the control group 19 display symptoms. Let's work at RRR and ARR for this scenario.$$ \begin{align} \text{RR } &= \frac{19/40} {36/60} \\ &= 0.7917 \\ \text{RRR } &= (1 - \text{ RR }) \times 100 \% \\ &= (1 - 0.7917) \times 100 \% \\ &= 20.83 \% \\ \text{ARR } &= \text{ Risk in Control Group - Risk in Treatment Group } \\ &= \Big (\frac{36}{60} - \frac{19}{40} \Big ) \times 100 \% \\ &= 12.50 \% \end{align}$$