Power of Interaction Test for Exponential Survival

Uses the method of Peterson and George to compute the power of an interaction test in a 2 x 2 setup in which all 4 distributions are exponential. This will be the same as the power of the Cox model test if assumptions hold. The test is 2-tailed. The duration of accrual is specified (constant accrual is assumed), as is the minimum follow-up time. The maximum follow-up time is then accrual + tmin. Treatment allocation is assumed to be 1:1.

ciapower(tref, n1, n2, m1c, m2c, r1, r2, accrual, tmin, 
         alpha=0.05, pr=TRUE)

Arguments

tref: time at which mortalities estimated
n1: total sample size, stratum 1
n2: total sample size, stratum 2
m1c: tref-year mortality, stratum 1 control
m2c: tref-year mortality, stratum 2 control
r1: % reduction in m1c by intervention, stratum 1
r2: % reduction in m2c by intervention, stratum 2
accrual: duration of accrual period
tmin: minimum follow-up time
alpha: type I error probability
pr: set to FALSE to suppress printing of details

Value

power

Side Effects

prints

AUTHOR

Frank Harrell

Department of Biostatistics

Vanderbilt University

fh@fharrell.com

References

Peterson B, George SL: Controlled Clinical Trials 14:511–522; 1993.

Examples

# Find the power of a race x treatment test.  25% of patients will
# be non-white and the total sample size is 14000.  
# Accrual is for 1.5 years and minimum follow-up is 5y.
# Reduction in 5-year mortality is 15% for whites, 0% or -5% for
# non-whites.  5-year mortality for control subjects if assumed to
# be 0.18 for whites, 0.23 for non-whites.
n <- 14000
for(nonwhite.reduction in c(0,-5)) {
  cat("\n\n\n% Reduction in 5-year mortality for non-whites:",
      nonwhite.reduction, "\n\n")
  pow <- ciapower(5,  .75*n, .25*n,  .18, .23,  15, nonwhite.reduction,  
                  1.5, 5)
  cat("\n\nPower:",format(pow),"\n")
}
#> 
#> 
#> 
#> % Reduction in 5-year mortality for non-whites: 0 
#> 
#> 
#> Accrual duration: 1.5 y  Minimum follow-up: 5 y
#> 
#> Sample size Stratum 1: 10500   Stratum 2: 3500 
#> 
#> Alpha= 0.05 
#> 
#> 5-year Mortalities
#>           Control Intervention
#> Stratum 1    0.18        0.153
#> Stratum 2    0.23        0.230
#> 
#> Hazard Rates
#>              Control Intervention
#> Stratum 1 0.03969019   0.03321092
#> Stratum 2 0.05227295   0.05227295
#> 
#> Probabilities of an Event During Study
#>             Control Intervention
#> Stratum 1 0.2039322    0.1737512
#> Stratum 2 0.2594139    0.2594139
#> 
#> Expected Number of Events
#>           Control Intervention
#> Stratum 1  1070.6        912.2
#> Stratum 2   454.0        454.0
#> 
#> Ratio of hazard ratios: 0.8367538 
#> Standard deviation of log ratio of ratios: 0.08022351 
#> 
#> 
#> Power: 0.6032173 
#> 
#> 
#> 
#> % Reduction in 5-year mortality for non-whites: -5 
#> 
#> 
#> Accrual duration: 1.5 y  Minimum follow-up: 5 y
#> 
#> Sample size Stratum 1: 10500   Stratum 2: 3500 
#> 
#> Alpha= 0.05 
#> 
#> 5-year Mortalities
#>           Control Intervention
#> Stratum 1    0.18       0.1530
#> Stratum 2    0.23       0.2415
#> 
#> Hazard Rates
#>              Control Intervention
#> Stratum 1 0.03969019   0.03321092
#> Stratum 2 0.05227295   0.05528250
#> 
#> Probabilities of an Event During Study
#>             Control Intervention
#> Stratum 1 0.2039322    0.1737512
#> Stratum 2 0.2594139    0.2720973
#> 
#> Expected Number of Events
#>           Control Intervention
#> Stratum 1  1070.6        912.2
#> Stratum 2   454.0        476.2
#> 
#> Ratio of hazard ratios: 0.7912015 
#> Standard deviation of log ratio of ratios: 0.07958098 
#> 
#> 
#> Power: 0.8371925