Calculates the boundaries at each interim analysis, i.e. the number of events in the experimental group that would lead to a stopping of the trial based on a binomial exact test, assuming that the events should be equally distributed amont both groups. The indicated scenario (and all more extreme) would lead to a rejection of H0 (equal distribution) and a stopping for safety.
getHarmBound(
nevents,
alpha_test,
pH0,
pH1 = NULL,
rrH1 = NULL,
orH1 = NULL,
rdH1 = NULL,
r0 = NULL,
n = NULL
)vector with number of events at which an interim analysis is done
the nominal alpha level to use for each test
proportion of events in the experimental arm under the null hypothesis, typically based on randomization ratio (e.g. 0.5 for a 1:1 randomization)
optional alternative, numeric vector, proportion of events in the experimental arm
alternative specification of alternative as risk ratio (experimental / control)
alternative specification of alternative as risk ratio (experimental / control). Requires the control proportion (r0).
alternative specification of alternative as risk difference (experimental - control). Requires the control proportion (r0) and the number of participants (n).
risk in the control group. Required if the alternative is given as risk difference or odds ratio.
total number of participants. Required if the alternative is given as risk difference.
a list with 2 data frames: bounds and cum_stop_prob. bounds has a row for each interim analysis and columns for number of events (n), number of events in control and experimental group that would lead to a stop (n_treat, n_control), risk ratio (rr) at that level, and the nominal alpha for each test (alpha_test) the null proportion (pH0), sopping probability (stop_prob_H0), and cumulative stopping probability (cum_stop_prob_H1), and if pH1!=NULL, the alternative proportion (pH1, first one if pH1 has length>1), sopping probability under the first H1 (stop_prob_H1), cumulative stopping probability under the first H1 (cum_stop_prob). cum_stop_prob includes the cumulative stopping probabilities for the null and each alternative.
getHarmBound(nevents=c(10,50,100), alpha_test=0.025, pH0=0.5)
#> $bounds
#> events events_exp events_control rr alpha_test pH0 stop_prob_H0
#> 1 10 9 1 9.000000 0.025 0.5 0.01074219
#> 2 50 33 17 1.941176 0.025 0.5 0.01490030
#> 3 100 61 39 1.564103 0.025 0.5 0.01194192
#> cum_stop_prob_H0
#> 1 0.01074219
#> 2 0.02564249
#> 3 0.03758441
#>
#> $cum_stop_prob
#> p cum_stop_prob hyp
#> 1 0.5 0.03758441 H0
#>
#> attr(,"class")
#> [1] "harmbound" "list"
#adding an alternative
getHarmBound(nevents=c(10,50,100), alpha_test=0.025, pH0=0.5, pH1=0.6)
#> $bounds
#> events events_exp events_control rr alpha_test pH0 stop_prob_H0
#> 1 10 9 1 9.000000 0.025 0.5 0.01074219
#> 2 50 33 17 1.941176 0.025 0.5 0.01490030
#> 3 100 61 39 1.564103 0.025 0.5 0.01194192
#> cum_stop_prob_H0 pH1 stop_prob_H1 cum_stop_prob_H1
#> 1 0.01074219 0.6 0.0463574 0.0463574
#> 2 0.02564249 0.6 0.2098108 0.2561682
#> 3 0.03758441 0.6 0.2505214 0.5066895
#>
#> $cum_stop_prob
#> hyp p cum_stop_prob
#> 1 H0 0.5 0.03758441
#> 2 H1 0.6 0.50668952
#>
#> attr(,"class")
#> [1] "harmbound" "list"
#or several alternatives
getHarmBound(nevents=c(10,50,100), alpha_test=0.025, pH0=0.5, pH1=seq(0,1,by=0.1))
#> $bounds
#> events events_exp events_control rr alpha_test pH0 stop_prob_H0
#> 1 10 9 1 9.000000 0.025 0.5 0.01074219
#> 2 50 33 17 1.941176 0.025 0.5 0.01490030
#> 3 100 61 39 1.564103 0.025 0.5 0.01194192
#> cum_stop_prob_H0 pH1 stop_prob_H1 cum_stop_prob_H1
#> 1 0.01074219 0 0 0
#> 2 0.02564249 0 0 0
#> 3 0.03758441 0 0 0
#>
#> $cum_stop_prob
#> hyp p cum_stop_prob
#> 1 H0 0.5 3.758441e-02
#> 2 H1 0.0 0.000000e+00
#> 3 H1 0.1 9.100000e-09
#> 4 H1 0.2 4.198402e-06
#> 5 H1 0.3 1.438344e-04
#> 6 H1 0.4 1.856785e-03
#> 7 H1 0.5 3.758441e-02
#> 8 H1 0.6 5.066895e-01
#> 9 H1 0.7 9.817810e-01
#> 10 H1 0.8 9.999970e-01
#> 11 H1 0.9 1.000000e+00
#> 12 H1 1.0 1.000000e+00
#>
#> attr(,"class")
#> [1] "harmbound" "list"
#or as risk ratio
getHarmBound(nevents=c(10,50,100), alpha_test=0.025, pH0=0.5, rrH1=1.5)
#> $bounds
#> events events_exp events_control rr alpha_test pH0 stop_prob_H0
#> 1 10 9 1 9.000000 0.025 0.5 0.01074219
#> 2 50 33 17 1.941176 0.025 0.5 0.01490030
#> 3 100 61 39 1.564103 0.025 0.5 0.01194192
#> cum_stop_prob_H0 pH1 stop_prob_H1 cum_stop_prob_H1
#> 1 0.01074219 0.6 0.0463574 0.0463574
#> 2 0.02564249 0.6 0.2098108 0.2561682
#> 3 0.03758441 0.6 0.2505214 0.5066895
#>
#> $cum_stop_prob
#> hyp p rr cum_stop_prob
#> 1 H0 0.5 1.0 0.03758441
#> 2 H1 0.6 1.5 0.50668952
#>
#> attr(,"class")
#> [1] "harmbound" "list"