The power computing formula is based on Shieh and O’Brien (1998), Shieh (2000), and Self, Mauritsen, and Ohara (1992).
Define the following notation for a logistic regression analysis:
The logistic regression model is
The hypothesis test of the first predictor variable is
Assuming independence among all predictor variables, is defined as follows:
where is calculated according to the following algorithm:
This algorithm causes the elements of the transposed vector to vary fastest to slowest from right to left as increases, as shown in the following table of values:
The values are determined in a completely analogous manner.
The discretization is handled as follows (unless the distribution is ordinal, or binomial with sample size parameter at least as large as requested number of bins): for , generate quantiles at evenly spaced probability values such that each such quantile is at the midpoint of a bin with probability . In other words,
The primary noncentrality for the power computation is
The power is
Alternative input parameterizations are handled by the following transformations: