The power-computing formula is based on Hsieh and Lavori (2000, equation (2) and the section "Variance Inflation Factor" on page 556).
Define the following notation for a Cox proportional hazards regression analysis:
The Cox proportional hazards regression model is
You can convert a regression coefficient to a hazard ratio by using the equation .
The hypothesis test of the first predictor variable is
The upper and lower one-sided cases are expressed differently than in other analyses. This is because corresponds to a negative correlation between the tested predictor and survival and thus, by the convention used in PROC POWER for regression analyses, the lower side.
The approximate power is
For the one-sided cases, a closed-form inversion of the power equation yields an approximate total sample size
For the two-sided case, the solution for N is obtained by numerically inverting the power equation.