Description:
Suppose that a long-used diagnostic test has a sensitivity of 0.74 and a specificity 0.81. A new diagnostic test is considered for adoption, but it must be shown to have greater sensitivity and specificity than these two values.
The researchers wish to know the sample sizes needed to obtain 90% power, if the assumed sensitivity of the new diagnostic test is between 0.05 and 0.1 greater than 0.74, and the assumed specificity is 0.86.
For the population of interest, somewhere between 10% and 25% of subjects are expected to have the condition.
When solving for sample size, one must choose whether to base the sample size on the Sensitivity power or the Specificity power. Often, when the power is high enough for the Sensitivity, it is also high enough for the Specificity, but that is not always the case. We will first run the sample size analysis based on the Sensitivity Power.
For all scenarios, except the last one, the power condition is met for both Sensitivity and Specificity.
In a moment, we can re-run the sample size analysis based on the Specificity power.
For each scenario, the total sample size is given (as N), and the sample size of the positive condition group, which is derived using the prevalence, is given (as N1).
The sample size chart gives a visual comparison of each sensitivity-prevalence combination.
The sample size analysis can be re-run, based on Specificity power, to determine the needed sample size for the last scenario.
For the last line, the power requirement is now met for both sensitivity and specificity.
Notably, the sensitivity powers for all other scenarios are below the needed 90%.
