Test-wise alpha necessary to control either the family-wise type I error or the power at a specified level

Exactly one of alpha_total or power have to be specified. The power requires the specification of an alternative via one of pH1, rrH1, orH1 or rdH1.

Usage

getAlphaPerTest(
  nevents,
  alpha_total = NULL,
  power = NULL,
  pH0 = 0.5,
  alpha.interval = c(10^(-10), 1),
  maxevents = NULL,
  icc = NULL,
  pH1 = NULL,
  rrH1 = NULL,
  orH1 = NULL,
  rdH1 = NULL,
  r0 = NULL,
  ...
)

Arguments

nevents: vector with number of events at which an interim analysis is done
alpha_total: target family-wise type I error
power: target power at the specified alternative
pH0: proportion of events in the treatment arm under the null hypothesis, typically based on randomization ratio (e.g. 0.5 for a 1:1 randomization)
alpha.interval: Range for test-wise alpha, c(10^(-10),0.05) by default
maxevents: optional maximum number of events expected for the trial (over both arms), used to calculate the expected number of events
icc: intraclass correlation if there is more than one event per patient
pH1: optional alternative, numeric vector, proportion of events in the treatment arm
rrH1: alternative specification of alternative as risk ratio (treatment / control)
orH1: alternative specification of alternative as odds ratio (treatment / control). Requires the control proportion (r0).
rdH1: alternative specification of alternative as risk difference (treatment - control). Requires the control proportion (r0).
r0: risk in the control arm. Required if the alternative is given as risk difference or odds ratio.
...: input for backward compatibility

Value

Test-wide alpha

Details

If there are several events per patient, the intraclass correlation coefficient has to be given and a beta-binomial framework is used.

Examples

#Control overall family-wise type I error:
apt<-getAlphaPerTest(nevents = c(10,50,100), alpha_total = 0.05, pH0 = 0.5)
apt
#> [1] 0.03245429
getHarmBound(nevents = c(10,50,100),alpha_test = apt, pH0 = 0.5)
#> $bounds
#>   events events_treatment events_control alpha_test
#> 1     10                9              1 0.03245429
#> 2     50               33             17 0.03245429
#> 3    100               60             40 0.03245429
#> 
#> $stopprob
#> $stopprob$`0.5`
#>   events  pH hyp  stop_prob cum_stop_prob
#> 1     10 0.5  H0 0.01074219    0.01074219
#> 2     50 0.5  H0 0.01490030    0.02564249
#> 3    100 0.5  H0 0.02085634    0.04649882
#> 
#> 
#> $opchar
#>     p cum_stop_prob expected_events hyp
#> 1 0.5    0.04649882        98.28819  H0
#> 
#> attr(,"class")
#> [1] "harmbound" "list"     

#Control power assuming 80% of events in expermintal arm
apt<-getAlphaPerTest(nevents = c(10,50,100), power = 0.8, pH0 = 0.5, pH1 = 0.6)
apt
#> [1] 0.1013193
getHarmBound(nevents = c(10,50,100),alpha_test = apt, pH0 = 0.5, pH1 = 0.6)
#> $bounds
#>   events events_treatment events_control alpha_test
#> 1     10                8              2  0.1013193
#> 2     50               31             19  0.1013193
#> 3    100               57             43  0.1013193
#> 
#> $stopprob
#> $stopprob$`0.5`
#>   events  pH hyp  stop_prob cum_stop_prob
#> 1     10 0.5  H0 0.05468750     0.0546875
#> 2     50 0.5  H0 0.04648929     0.1011768
#> 3    100 0.5  H0 0.05797765     0.1591544
#> 
#> $stopprob$`0.6`
#>   events  pH hyp stop_prob cum_stop_prob
#> 1     10 0.6  H1 0.1672898     0.1672898
#> 2     50 0.6  H1 0.3260615     0.4933512
#> 3    100 0.6  H1 0.3043610     0.7977123
#> 
#> 
#> $opchar
#>     p cum_stop_prob expected_events hyp
#> 1 0.5     0.1591544        92.75366  H0
#> 2 0.6     0.7977123        68.64085  H1
#> 
#> attr(,"class")
#> [1] "harmbound" "list"