August 1, 2016

## Power Curves

By UNM CCC

A common issue in designing a clinical or animal study is to determine the number of subjects required. Power calculations provide an estimate of the number of study subjects that will be necessary to be able detect a difference between experimental and control subjects. The numbers required will depend on the magnitude of the difference between the two groups. For some experiments the primary measurement is the proportion of individuals with a certain outcome (e.g. yes/no or live vs. dead). The following graph depicts the results of power calculations using Fisher's exact method which is better for small numbers than a chi-square test. The data was generated with G*Power3 software. A different type of power calculation should be done if a numerical outcome is being measured for each individual (e.g. survival time) not simply a proportion.

The variables mentioned in the graphs are:

• N1 + N2 (the number of subjects in the experimental and control groups, combined)
• P1 (the proportion of experimental subjects which are positive for the endpoint)
• P2 (the proportion of control subjects which are positive for the endpoint)
• alpha ≤ 0.05 (the p-value of the study, the probability that such results might occur by chance)
• power = 0.8 (1- ß) (80% chance of being able to detect a difference between the groups)

Example: Suppose that you have strain of lab mice in which 10% develop tumors by 1 year of age (P2 = 0.1, see curve with red triangles). If your experimental group develops a higher frequency of tumors, say 40% (P1 = 0.4) then the total number of animals needed in the study (N1 + N2, on the Y-axis) is 60, or about 30 in each group. Notice how the curves rise sharply as the proportion of positive animals in the experimental group (P1) decreases. 