Compute p-value boundaries of the parametric MTP method with overall alpha spending for all hypotheses

Usage

generate_bounds(
  type = 1,
  k = 2,
  w = w,
  m = m,
  corr = corr,
  alpha = 0.025,
  cum_alpha = NULL,
  maxpts = 50000,
  abseps = 1e-05,
  tol = 1e-10,
  sf = gsDesign::sfHSD,
  sfparm = -4,
  t = c(0.5, 1),
  ...
)

Arguments

type

Boundary type.

0 = Bonferroni. Separate alpha spending for each hypotheses.
1 = Fixed alpha spending for all hypotheses. Method 3a in the manuscript.
2 = Overall alpha spending for all hypotheses. Method 3b in the manuscript.
3 = Separate alpha spending for each hypotheses. Method 3c in the manuscript.

k

Number of analyses up to the current analysis.

w

Initial weights.

m

Transition matrix.

corr

Correlation matrix of all test statistics up to the current analysis. dim = k * length(w).

alpha

Overall alpha.

cum_alpha

Cumulative alpha spent at each analysis. Only required for type = 1.

maxpts

GenzBretz function maximum number of function values as integer.

abseps

GenzBretz function absolute error tolerance.

tol

Find root tolerance.

sf

A list of alpha spending functions to spend alpha for each hypotheses.

If type = 0 or 3 then length equals to number of hypotheses.
If type = 1 then sf is not needed.
If type = 2 then only the first component is used.

sfparm

A list of parameters to be supplied to sfs.

If type = 0 or 3 then length equals to number of hypotheses.
If type = 1 then sfparm is not needed.
If type = 2 then only the first component is used.

t

A list of information fraction used for alpha spending, may be different from the actual information fraction. Each component corresponds to a hypothesis.

If type = 0 or 3 then length equals to number of hypotheses.
If type = 1 then t is not needed.
If type = 2 then only the first component is used.

...

Additional arguments.

Value

A tibble with k * (2^(n_hypotheses - 1)) rows of p-value boundaries. Inflation factor is also provided if type = 3.

Examples

# Build the transition matrix
m <- matrix(c(
  0, 0.5, 0.5,
  0.5, 0, 0.5,
  0.5, 0.5, 0
), nrow = 3, byrow = TRUE)

# Initialize weights
w <- c(1 / 3, 1 / 3, 1 / 3)

# Input information fraction
IF_IA <- c(155 / 305, 160 / 320, 165 / 335)

# Input event count of intersection of paired hypotheses - Table 2
event <- tibble::tribble(
  ~H1, ~H2, ~Analysis, ~Event,
  1, 1, 1, 155,
  2, 2, 1, 160,
  3, 3, 1, 165,
  1, 2, 1, 85,
  1, 3, 1, 85,
  2, 3, 1, 85,
  1, 1, 2, 305,
  2, 2, 2, 320,
  3, 3, 2, 335,
  1, 2, 2, 170,
  1, 3, 2, 170,
  2, 3, 2, 170
)

# Generate correlation from events
gs_corr <- generate_corr(event)

# Generate bounds
generate_bounds(
  type = 3,
  k = 2,
  w = w,
  m = m,
  corr = gs_corr,
  alpha = 0.025,
  sf = list(gsDesign::sfLDOF, gsDesign::sfLDOF, gsDesign::sfLDOF),
  sfparm = list(0, 0, 0),
  t = list(c(IF_IA[1], 1), c(IF_IA[2], 1), c(IF_IA[3], 1))
)
#> # A tibble: 14 × 6
#>    Analysis Hypotheses        H1        H2        H3    xi
#>       <int> <chr>          <dbl>     <dbl>     <dbl> <dbl>
#>  1        1 H1          0.00167  NA        NA         1   
#>  2        1 H1, H2      0.000471  0.000423 NA         1.03
#>  3        1 H1, H2, H3  0.000223  0.000198  0.000177  1.04
#>  4        1 H1, H3      0.000470 NA         0.000382  1.02
#>  5        1 H2         NA         0.00153  NA         1   
#>  6        1 H2, H3     NA         0.000421  0.000381  1.02
#>  7        1 H3         NA        NA         0.00140   1   
#>  8        2 H1          0.0245   NA        NA         1   
#>  9        2 H1, H2      0.0135    0.0135   NA         1.09
#> 10        2 H1, H2, H3  0.00949   0.00950   0.00951   1.15
#> 11        2 H1, H3      0.0135   NA         0.0135    1.09
#> 12        2 H2         NA         0.0245   NA         1   
#> 13        2 H2, H3     NA         0.0134    0.0134    1.09
#> 14        2 H3         NA        NA         0.0245    1