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Approximate information from a random samples of a given size for ordinal outcomes

Source: R/asymptotic_information_mw.R
asymptotic_information_mann_whitney_fm.Rd

These functions provide an asymptotic approximation to the information (i.e. precision, inverse of the variance) provided by two samples under either an assumed value of the Mann-Whitney estimand or probability mass functions (PMFs) of an ordinal outcome in treatment and control populations.

Usage

asymptotic_information_mann_whitney_fm(
  n_0,
  n_1,
  mw = NULL,
  pmf_1 = NULL,
  pmf_0 = NULL,
  adjust = TRUE
)

Arguments

n_0

Numeric vector containing the sample size in the control arm

n_1

Numeric vector containing the sample size in the treatment arm

mw

Numeric vector containing the Mann-Whitney estimand

pmf_1

Numeric vector or matrix of row vectors, each containing the probability mass function of outcomes in the population of individuals receiving the active intervention

pmf_0

Numeric vector or matrix of row vectors, each containing the probability mass function of outcomes in the population of individuals receiving the control intervention

adjust

(Scalar: Logical) Should the estimand be adjusted for ties? NOTE: This can only be computed when pmf_0 and pmf_1 are supplied.

Value

When all parameters are scalars, the result is a scalar, indicating the approximate information. When multiple values are specified, a grid of unique parameters are constructed, and the approximate information is computed for each value of the parameters.

See also

asymptotic_information_difference_means and asymptotic_information_difference_proportions for continuous and binary outcomes, respectively.

Examples

# When a single value is supplied for each parameter, a scalar is returned:
asymptotic_information_mann_whitney_fm(
    n_0 = 100,
    n_1 = 100,
    mw = 0.75,
    adjust = FALSE
  )
#> [1] 0.001185536

# When multiple values are supplied for one or more parameters, the grid of
# parameters are created, and a data.frame is returned.
asymptotic_information_mann_whitney_fm(
  n_0 = c(100, 150),
  n_1 = c(100, 150),
  mw = 0.75,
  adjust = FALSE
)
#>   n_0 n_1   mw t information_asymptotic
#> 1 100 100 0.75 1           0.0011855357
#> 2 150 100 0.75 1           0.0009867857
#> 3 100 150 0.75 1           0.0009867857
#> 4 150 150 0.75 1           0.0007888095


# Specifying PMFs - With and Without Tie Adjustment
asymptotic_information_mann_whitney_fm(
  n_0 = 100,
  n_1 = 100,
  pmf_0 = c(0.2, 0.2, 0.6),
  pmf_1 = c(0.1, 0.1, 0.8),
  adjust = TRUE
)
#> [1] 0.001036432

# Specifying Multiple PMFs
asymptotic_information_mann_whitney_fm(
  n_0 = 100,
  n_1 = 100,
  pmf_0 =
    rbind(
      c(0.2, 0.2, 0.6),
      c(0.3, 0.1, 0.6)
    ),
  pmf_1 =
    rbind(
      c(0.1, 0.1, 0.8),
      c(0.05, 0.05, 0.9)
      ),
  adjust = TRUE
)
#>   n_0 n_1 pmf_0 pmf_1    mw         t pmf_0_1 pmf_0_2 pmf_0_3 pmf_1_1 pmf_1_2
#> 1 100 100     1     1 0.600 0.6502663     0.2     0.2     0.6    0.10    0.10
#> 2 100 100     2     1 0.610 0.6480162     0.3     0.1     0.6    0.10    0.10
#> 3 100 100     1     2 0.650 0.5742331     0.2     0.2     0.6    0.05    0.05
#> 4 100 100     2     2 0.655 0.5723581     0.3     0.1     0.6    0.05    0.05
#>   pmf_1_3 information_asymptotic
#> 1     0.8           0.0010364315
#> 2     0.8           0.0010218898
#> 3     0.9           0.0008578564
#> 4     0.9           0.0008481421