Custom optimization method for calibrate_thresholds objects

Determines the optimal designs based on a variety of criteria. The optimal efficiency design is the one with the shortest Euclidean distance to the upper left point on a plot of the average sample size under the null by the average sample size under the alternative. The optimal accuracy design is the one with the shortest Euclidean distance to the upper left point on a plot of the type I error by the power.

Usage

# S3 method for calibrate_thresholds
optimize_design(
  x,
  type1_range = c(0, 1),
  minimum_power = 0,
  w_type1 = 1,
  w_power = 1,
  w_Nnull = 1,
  w_Nalt = 1,
  ...
)

Arguments

x

an object of class 'calibrate_thresholds', usually returned by the calibrate_thresholds function

type1_range

a vector specifying the minimum and maximum acceptable type I error. Specify NULL to return the full range of resulting type I error. Defaults to c(0, 1) to return all results.

minimum_power

a numeric between 0 and 1 specifying the minimum acceptable power. Specify NULL to return the full range of resulting power. Defaults to 0 to return all results.

w_type1

a user-specified weight on the type 1 error. Defaults to 1 for no weighting.

w_power

a user-specified weight on the power. Defaults to 1 for no weighting.

w_Nnull

a user-specified weight on the average sample size under the null. Defaults to 1 for no weighting.

w_Nalt

a user-specified weight on the average sample size under the alternative. Defaults to 1 for no weighting.

...

ignored

Value

A list of length two containing details of the optimal efficiency and optimal accuracy designs

Examples

# Setting S = 50 and nsim = 50 for speed
# In practice you would want a much larger sample and more simulations

# One-sample case
set.seed(123)

cal_tbl1 <- calibrate_thresholds(
  p_null = 0.1, 
  p_alt = 0.4,
  n = seq(5, 15, 5), 
  N = 15,
  pp_threshold = c(0.85, 0.9),
  ppp_threshold = c(0.1, 0.2),
  S = 10, 
  nsim = 10
  )

optimize_design(cal_tbl1)
#> $`Optimal accuracy design:`
#> # A tibble: 1 × 6
#>   pp_threshold ppp_threshold `Type I error` Power `Average N under the null`
#>          <dbl>         <dbl>          <dbl> <dbl>                      <dbl>
#> 1         0.85           0.1            0.1     1                       13.5
#>   `Average N under the alternative`
#>                               <dbl>
#> 1                                15
#> 
#> $`Optimal efficiency design:`
#> # A tibble: 1 × 6
#>   pp_threshold ppp_threshold `Type I error` Power `Average N under the null`
#>          <dbl>         <dbl>          <dbl> <dbl>                      <dbl>
#> 1         0.85           0.2            0.1   0.9                       10.5
#>   `Average N under the alternative`
#>                               <dbl>
#> 1                                15
#> 


# Two-sample case
set.seed(456)

cal_tbl2 <- calibrate_thresholds(
  p_null = c(0.1, 0.1), 
  p_alt = c(0.1, 0.5),
  n = cbind(seq(5, 15, 5), seq(5, 15, 5)), 
  N = c(15, 15),
  pp_threshold = c(0.8, 0.85),
  ppp_threshold = c(0.2, 0.3),
  delta = 0,
  S = 10, 
  nsim = 10
  )

optimize_design(cal_tbl2)
#> $`Optimal accuracy design:`
#> # A tibble: 1 × 6
#>   pp_threshold ppp_threshold `Type I error` Power `Average N under the null`
#>          <dbl>         <dbl>          <dbl> <dbl>                      <dbl>
#> 1         0.85           0.3              0     1                          8
#>   `Average N under the alternative`
#>                               <dbl>
#> 1                                15
#> 
#> $`Optimal efficiency design:`
#> # A tibble: 1 × 6
#>   pp_threshold ppp_threshold `Type I error` Power `Average N under the null`
#>          <dbl>         <dbl>          <dbl> <dbl>                      <dbl>
#> 1          0.8           0.3              0     1                        7.5
#>   `Average N under the alternative`
#>                               <dbl>
#> 1                                15
#>