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:
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The logistic regression model is
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The hypothesis test of the first predictor variable is
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Assuming independence among all predictor variables, is defined as follows:
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where is calculated according to the following algorithm:
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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:
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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,
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The primary noncentrality for the power computation is
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where
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where
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The power is
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Alternative input parameterizations are handled by the following transformations:
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