Probability that vector x is element-wise greater than y by bootstrap.

To estimate the confidence intervals for the posterior probability that the event rate in the active treatment group is higher than in the placebo group (Prob(Event rate in arm 2 > Event rate in arm 1)), the function employs a bootstrap-like method. This involves generating samples through circular shifts and comparing elements between the shifted versions of x and y. Let I be the length of vectors x and y. For i varying from 1 to I, the elements of the vector x are shifted to the left by i elements to build the i-th sample. For each bootstrap sample, the proportion of elements of x that are greater than the corresponding elements of y is computed. These proportions are then used to estimate the mean, median, and standard deviation for the calculated sample statistics. Highest density interval (HDI) is also computed, which provides the lower and upper bounds of the proportions for given confidence level alpha.

Usage

p_xgty_bootstrap(x, y, offset = 0, alpha = 0.05)

Arguments

x: numerical vector.
y: numerical vector.
offset: We calculate Pr(x > y + offset). Default offset is 0.
alpha: if not null, 1 - alpha confidence interval is calculated.

Value

tibble with columns mean and sd, and also .lower and .upper, if alpha is not null, from the highest density posterior interval.

Examples

set.seed(2023)
x <- rbeta(n = 1000, shape1 = 0.2, shape2 = 0.8)
y <- rbeta(n = 1000, shape1 = 0.1, shape2 = 0.9)
p_xgty_bootstrap(x, y)
#> # A tibble: 1 × 5
#>    mean median      sd .lower .upper
#>   <dbl>  <dbl>   <dbl>  <dbl>  <dbl>
#> 1 0.684  0.684 0.00896  0.666    0.7
p_xgty_bootstrap(x, y, offset = 0.05)
#> # A tibble: 1 × 5
#>    mean median      sd .lower .upper
#>   <dbl>  <dbl>   <dbl>  <dbl>  <dbl>
#> 1 0.413  0.413 0.00635    0.4  0.424
p_xgty_bootstrap(x, y, offset = 0.1)
#> # A tibble: 1 × 5
#>    mean median      sd .lower .upper
#>   <dbl>  <dbl>   <dbl>  <dbl>  <dbl>
#> 1 0.348  0.348 0.00551  0.337  0.358
p_xgty_bootstrap(x, y, offset = 0.2)
#> # A tibble: 1 × 5
#>    mean median      sd .lower .upper
#>   <dbl>  <dbl>   <dbl>  <dbl>  <dbl>
#> 1 0.275  0.275 0.00519  0.264  0.284
p_xgty_bootstrap(x, y, offset = 0.3)
#> # A tibble: 1 × 5
#>    mean median      sd .lower .upper
#>   <dbl>  <dbl>   <dbl>  <dbl>  <dbl>
#> 1 0.226  0.226 0.00505  0.217  0.236