Introduction

The Risk Difference (RD), also known as the Absolute Risk Reduction (ARR) or Absolute Risk Difference, is a measure used in epidemiology and clinical research to quantify the absolute difference in the risk of an event occurring between two groups. It is a straightforward and intuitive way to express the impact of an intervention or exposure on the occurrence of a specific outcome.

The risk difference is calculated using the following formula:

RD = Risk in Group 1 − Risk in Group 2

In the context of a clinical trial or observational study, "Group 1" and "Group 2" could represent two different treatment groups, intervention groups, or exposure categories. The "risk" refers to the probability of a particular event or outcome occurring within each group.

Key components of the risk difference formula include:

  • Risk in Group 1: The proportion or percentage of individuals in Group 1 who experience the event of interest.
  • Risk in Group 2: The proportion or percentage of individuals in Group 2 who experience the same event.

A positive risk difference indicates that the event is more likely to occur in Group 1, while a negative risk difference suggests a higher likelihood in Group 2.

Interpretation:

  • Positive RD: Indicates that the intervention or exposure in Group 1 is associated with a higher absolute risk of the event compared to Group 2.
  • Negative RD: Suggests that the intervention or exposure in Group 2 is associated with a higher absolute risk reduction, meaning a lower risk of the event compared to Group 1.

Example:

Consider a clinical trial comparing a new medication (Group 1) to a placebo (Group 2) for preventing heart attacks. If the event is a heart attack, a positive risk difference might mean that the medication is associated with an increased absolute risk of heart attacks compared to the placebo. Conversely, a negative risk difference would suggest that the medication is associated with a reduction in the absolute risk of heart attacks.

This article introduces a web-based calculator designed to determine the unadjusted risk difference along with confidence interval bounds, a Z-score, and a p-value.

Variables Definitions

  1. Event 1: The number of events in Group 1.
  2. Total 1: The total number of participants in Group 1.
  3. Event 2: The number of events in Group 2.
  4. Total 2: The total number of participants in Group 2.
  5. Confidence Level: The desired confidence level for the calculation, often chosen as 90%, 95%, or 99%.

Calculation Formulas

The Unadjusted Risk Difference (RD) is calculated using the formula:

RD

Additionally, the calculator provides other statistical measures:

  1. Standard Error (SE):
    SE
  2. Z-score (Z):
    Z-score
  3. Confidence Interval (CI):
    CI
  4. P-value:
    P-value

Where erf is the error of function implementation

Formula Reference - Cochrane Handbook