What is the value of the stddev option in the PROC POWER coxreg procedure?

[TomHsiung]

Hi, everyone

I met a trouble when doing with the power and sample size stuff with PROC POWER coxreg procedure. I am not sure about the values of the option stddev. I compute its value from the study's HR confidence interval via (logHRupper - logHRlower)/(2 x 1.96). I know this is a standard error but I don't know how to derive the standard deviation of it.

I also have used Stata to compare my results. Same problem. The values of stddev I configured must have been wrong. How could a 80% power require so much events number?

[FreelanceReinh · Accepted solution]

Hello @TomHsiung,

The PROC POWER documentation says

STDDEV=number-list
STD=number-list

  specifies the standard deviation of the predictor of interest. 

So my understanding is: If x₁ is the predictor of interest and b₁ its regression coefficient (exp(b₁) being the hazard ratio specified in the HAZARDRATIO= option of the COXREG statement), you specify the standard deviation s of x₁ (or a list of reasonably possible values of s) in the STDDEV= option, not the standard deviation of b₁.

The formula in https://documentation.sas.com/doc/en/pgmsascdc/9.4_3.5/statug/statug_power_details22.htm implies that increasing s will increase the power, which seems plausible: With smaller values of s it tends to be less likely to obtain a significant (score) test result about b₁.

Similarly, the RSQUARE= option is about an aspect of the joint distribution of the predictors x_i.

[TomHsiung]

Hello, Freelance

I think you're right. The default value of stddev is 0.5, which is the standard deviation of a binary 1:1 match grouping variable, i.e., square root of 0.5(1 - 0.5). Thank you.