Power Calculations: Quantitative Traits

Calculating power for simple study designs is one of the most common tasks faced by a Biostatistician. However, for most of them, it barely makes the list of the top 1000 things they might enjoy doing. So, make your neighborhood biostatistician marginally happier by calculating your own power tables before you next meet with them (yes, even if you can calculate power, you will probably still need professional advice on study design!).

A Simple Genetic Association Study

In this example, we will use R to carry a simple power calculation for a genetic association study. We will assume that you are interested in a quantitative trait and that you have phenotyped and genptyped **N** randomly sampled individuals. Further, we will assume that you are using signficance level $alpha$ for your analyses (typically, $alpha=0.05/M$ where **M** is the number of independent markers examined) and **H2** is the variance explained by additive effects at the marker of interest.

In this setting, a simple power calculation might look like:

  N = 1000
  alpha = 0.05
  H2 = 0.01

  threshold = qchisq(alpha, df = 1, lower.tail = FALSE)
  power = pchisq(threshold, df = 1, lower.tail = FALSE, ncp = N * H2)