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Obsidian | Level 7

I am hoping someone can point out the error of my ways.  I am trying to understand why greater power is achieved by increasing the assumed standard deviation of the predictor variable as in the example below:


proc power;


      hazardratio = 1.4

      rsquare = 0.15

      stddev = 1.2 2.4

      ntotal = 80

      eventprob = 0.8

      power = .




(This code was taken from the example provided in SAS documentation.)

Why would power be greater for a predictor that has greater variability?  It seems like it should have the opposite effect...that the power should decrease.



                               The POWER Procedure

                Cox Score Test in Proportional Hazards Regression


                             Fixed Scenario Elements


           Method                    Hsieh-Lavori normal approximation

           Probability of Event                                    0.8

           R-square of Predictors                                 0.15

           Test Hazard Ratio                                       1.4

           Total Sample Size                                        80

           Number of Sides                                           2

           Alpha                                                  0.05



                                  Computed Power



                               Index     Dev    Power


                                   1     1.2    0.846

                                   2     2.4    >.999


Obsidian | Level 7


Obsidian | Level 7

Please see the following paper:
Hsieh, F. Y., and Lavori, P. W. (2000). “Sample-Size Calculations for the Cox Proportional Hazards Regression Model with Nonbinary Covariates.” Controlled Clinical Trials 21:552–560.


In this paper, the authors state the following:
"In a regression model, the variance of the estimate b1 of the parameter θ1 is inversely related to the variance of the corresponding covariate X1."


Therefore, the variance of the parameter estimate would get smaller as the variance of the covariate increases.

I have not yet worked through the reasoning behind this argument though.


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