Measures of Association and Effect Size

Therapeutic Efficacy Measures

The measures of association and effect size are used to quantify the strength of the relationship between an exposure (such as a treatment or intervention) and an outcome (such as a disease or adverse event). The following are commonly used measures:

Absolute Risk Reduction (ARR) / Risk Difference (RD): The ARR is the absolute difference in the risk of an event occurring between the control group and the treatment group. It is calculated as:

ARR / RD = CIe - CIu

where CIe is the cumulative incidence (risk) in the exposed group and CIu is the cumulative incidence (risk) in the unexposed group. If the exposure is harmful, a positive risk difference indicates an excess risk in the exposed group. If the exposure is preventive, a negative risk difference indicates a reduction in risk in the exposed group.

Relative Risk Reduction (RRR): is a measure of the proportion by which the risk of an outcome is reduced in an experimental group compared to a control group. It is calculated by subtracting the relative risk (RR) from 1.

RRR = 1 - RR

where RR is relative risk. The formula for calculating relative risk reduction does not differ if the exposure is harmful or preventive. However, the interpretation of the result changes. If the exposure is harmful, a positive relative risk reduction indicates a reduction in risk in the experimental group. If the exposure is preventive, a negative relative risk reduction indicates an increase in risk in the experimental group.

Number Needed to Treat (NNT): The NNT is the number of patients who need to be treated to prevent one adverse event. It is calculated as:

NNT = 1 / ARR

The NNT represents the inverse of the ARR and provides a measure of the effectiveness of a treatment in terms of the number of patients who need to be treated to prevent one adverse event.

Attributable Risk (AR) / Attributable Risk Percent (ARP): also known as etiologic fraction, is a measure of the proportion of disease in the exposed group that can be attributed to the exposure. It is calculated by dividing the risk difference by the incidence in the exposed group. Attributable risk can also be expressed as a percent, i.e., the percentage of disease in the exposed group that can be attributed to the exposure (sometimes called the attributable risk %).

AR = RD / CIe

where RD is the risk difference and CIe is the cumulative incidence (risk) in the exposed group. The formula for calculating attributable risk does not differ if the exposure is harmful or preventive. However, when dealing with an exposure that reduces the risk of disease, it makes more sense to think about the preventive fraction (PF). This is similar to attributable risk, except that the risk difference (i.e., the risk reduction) is divided by the cumulative incidence in the unexposed group.

PF = (CIu - CIe) / CIu

An easier way to calculate the ARP is to derive it from the relative risk (RR):

AR = (RR - 1) / RR

PF = 1 - RR

Overall, these measures provide different perspectives on the efficacy of a therapeutic intervention and are useful for comparing the effectiveness of different treatments or interventions. It is important to consider the context of the study and the specific outcome of interest when choosing which measure to use.

The 2 x 2 table (A, B, C, D) in the Google Sheet provided above can be used to generate measures of association. By analyzing the calculated measures, you can gain a better understanding of their characteristics and how they are influenced by different 2 x 2 tables. To obtain an editable version, click on the top right corner of the sheet above to open it in Google sheets. You can then download the file and enable editing on your device.

You can also visit our interactive web app, Measures of Association Calculator, where you can input you 2x2 table data and get an interactive figure and key measure below.

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