Obtains the adjusted p-values for the standard gatekeeping procedures for multiplicity problems involving serial and parallel logical restrictions.
fstdmix(
p,
family = NULL,
serial,
parallel = NULL,
gamma,
test = "hommel",
exhaust = TRUE
)The raw p-values for elementary hypotheses.
The matrix of family indicators for the hypotheses.
The matrix of serial rejection set for the hypotheses.
The matrix of parallel rejection set for the hypotheses.
The truncation parameters for each family. The truncation parameter for the last family is automatically set to 1.
The component multiple testing procedure. Options include "holm", "hochberg", or "hommel". Defaults to "hommel".
Whether to use alpha-exhausting component testing procedure
for the last family with active hypotheses. It defaults to TRUE.
A list with the following components:
inthyp: The indicator matrix for the intersection hypotheses.
pinter: The local p-values for the intersection hypotheses.
padj: The adjusted p-values for the elementary hypotheses.
Alex Dmitrienko and Ajit C Tamhane. Mixtures of multiple testing procedures for gatekeeping applications in clinical trials. Statistics in Medicine. 2011; 30(13):1473–1488.
p <- c(0.0194, 0.0068, 0.0271, 0.0088, 0.0370, 0.0018, 0.0814, 0.0066)
family <- matrix(c(1, 1, 0, 0, 0, 0, 0, 0,
0, 0, 1, 1, 0, 0, 0, 0,
0, 0, 0, 0, 1, 1, 0, 0,
0, 0, 0, 0, 0, 0, 1, 1),
nrow=4, byrow=TRUE)
serial <- matrix(c(0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0,
0, 1, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 0, 1, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 0, 0,
0, 0, 0, 0, 0, 1, 0, 0),
nrow=8, byrow=TRUE)
parallel <- matrix(0, 8, 8)
gamma <- c(0.6, 0.6, 0.6, 1)
fstdmix(p, family, serial, parallel, gamma, test = "hommel",
exhaust = FALSE)
#> $inthyp
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
#> [1,] 1 1 1 1 1 1 1 1
#> [2,] 1 1 1 1 1 1 1 0
#> [3,] 1 1 1 1 1 1 0 1
#> [4,] 1 1 1 1 1 1 0 0
#> [5,] 1 1 1 1 1 0 1 1
#> [6,] 1 1 1 1 1 0 1 0
#> [7,] 1 1 1 1 1 0 0 1
#> [8,] 1 1 1 1 1 0 0 0
#> [9,] 1 1 1 1 0 1 1 1
#> [10,] 1 1 1 1 0 1 1 0
#> [11,] 1 1 1 1 0 1 0 1
#> [12,] 1 1 1 1 0 1 0 0
#> [13,] 1 1 1 1 0 0 1 1
#> [14,] 1 1 1 1 0 0 1 0
#> [15,] 1 1 1 1 0 0 0 1
#> [16,] 1 1 1 1 0 0 0 0
#> [17,] 1 1 1 0 1 1 1 1
#> [18,] 1 1 1 0 1 1 1 0
#> [19,] 1 1 1 0 1 1 0 1
#> [20,] 1 1 1 0 1 1 0 0
#> [21,] 1 1 1 0 1 0 1 1
#> [22,] 1 1 1 0 1 0 1 0
#> [23,] 1 1 1 0 1 0 0 1
#> [24,] 1 1 1 0 1 0 0 0
#> [25,] 1 1 1 0 0 1 1 1
#> [26,] 1 1 1 0 0 1 1 0
#> [27,] 1 1 1 0 0 1 0 1
#> [28,] 1 1 1 0 0 1 0 0
#> [29,] 1 1 1 0 0 0 1 1
#> [30,] 1 1 1 0 0 0 1 0
#> [31,] 1 1 1 0 0 0 0 1
#> [32,] 1 1 1 0 0 0 0 0
#> [33,] 1 1 0 1 1 1 1 1
#> [34,] 1 1 0 1 1 1 1 0
#> [35,] 1 1 0 1 1 1 0 1
#> [36,] 1 1 0 1 1 1 0 0
#> [37,] 1 1 0 1 1 0 1 1
#> [38,] 1 1 0 1 1 0 1 0
#> [39,] 1 1 0 1 1 0 0 1
#> [40,] 1 1 0 1 1 0 0 0
#> [41,] 1 1 0 1 0 1 1 1
#> [42,] 1 1 0 1 0 1 1 0
#> [43,] 1 1 0 1 0 1 0 1
#> [44,] 1 1 0 1 0 1 0 0
#> [45,] 1 1 0 1 0 0 1 1
#> [46,] 1 1 0 1 0 0 1 0
#> [47,] 1 1 0 1 0 0 0 1
#> [48,] 1 1 0 1 0 0 0 0
#> [49,] 1 1 0 0 1 1 1 1
#> [50,] 1 1 0 0 1 1 1 0
#> [51,] 1 1 0 0 1 1 0 1
#> [52,] 1 1 0 0 1 1 0 0
#> [53,] 1 1 0 0 1 0 1 1
#> [54,] 1 1 0 0 1 0 1 0
#> [55,] 1 1 0 0 1 0 0 1
#> [56,] 1 1 0 0 1 0 0 0
#> [57,] 1 1 0 0 0 1 1 1
#> [58,] 1 1 0 0 0 1 1 0
#> [59,] 1 1 0 0 0 1 0 1
#> [60,] 1 1 0 0 0 1 0 0
#> [61,] 1 1 0 0 0 0 1 1
#> [62,] 1 1 0 0 0 0 1 0
#> [63,] 1 1 0 0 0 0 0 1
#> [64,] 1 1 0 0 0 0 0 0
#> [65,] 1 0 1 1 1 1 1 1
#> [66,] 1 0 1 1 1 1 1 0
#> [67,] 1 0 1 1 1 1 0 1
#> [68,] 1 0 1 1 1 1 0 0
#> [69,] 1 0 1 1 1 0 1 1
#> [70,] 1 0 1 1 1 0 1 0
#> [71,] 1 0 1 1 1 0 0 1
#> [72,] 1 0 1 1 1 0 0 0
#> [73,] 1 0 1 1 0 1 1 1
#> [74,] 1 0 1 1 0 1 1 0
#> [75,] 1 0 1 1 0 1 0 1
#> [76,] 1 0 1 1 0 1 0 0
#> [77,] 1 0 1 1 0 0 1 1
#> [78,] 1 0 1 1 0 0 1 0
#> [79,] 1 0 1 1 0 0 0 1
#> [80,] 1 0 1 1 0 0 0 0
#> [81,] 1 0 1 0 1 1 1 1
#> [82,] 1 0 1 0 1 1 1 0
#> [83,] 1 0 1 0 1 1 0 1
#> [84,] 1 0 1 0 1 1 0 0
#> [85,] 1 0 1 0 1 0 1 1
#> [86,] 1 0 1 0 1 0 1 0
#> [87,] 1 0 1 0 1 0 0 1
#> [88,] 1 0 1 0 1 0 0 0
#> [89,] 1 0 1 0 0 1 1 1
#> [90,] 1 0 1 0 0 1 1 0
#> [91,] 1 0 1 0 0 1 0 1
#> [92,] 1 0 1 0 0 1 0 0
#> [93,] 1 0 1 0 0 0 1 1
#> [94,] 1 0 1 0 0 0 1 0
#> [95,] 1 0 1 0 0 0 0 1
#> [96,] 1 0 1 0 0 0 0 0
#> [97,] 1 0 0 1 1 1 1 1
#> [98,] 1 0 0 1 1 1 1 0
#> [99,] 1 0 0 1 1 1 0 1
#> [100,] 1 0 0 1 1 1 0 0
#> [101,] 1 0 0 1 1 0 1 1
#> [102,] 1 0 0 1 1 0 1 0
#> [103,] 1 0 0 1 1 0 0 1
#> [104,] 1 0 0 1 1 0 0 0
#> [105,] 1 0 0 1 0 1 1 1
#> [106,] 1 0 0 1 0 1 1 0
#> [107,] 1 0 0 1 0 1 0 1
#> [108,] 1 0 0 1 0 1 0 0
#> [109,] 1 0 0 1 0 0 1 1
#> [110,] 1 0 0 1 0 0 1 0
#> [111,] 1 0 0 1 0 0 0 1
#> [112,] 1 0 0 1 0 0 0 0
#> [113,] 1 0 0 0 1 1 1 1
#> [114,] 1 0 0 0 1 1 1 0
#> [115,] 1 0 0 0 1 1 0 1
#> [116,] 1 0 0 0 1 1 0 0
#> [117,] 1 0 0 0 1 0 1 1
#> [118,] 1 0 0 0 1 0 1 0
#> [119,] 1 0 0 0 1 0 0 1
#> [120,] 1 0 0 0 1 0 0 0
#> [121,] 1 0 0 0 0 1 1 1
#> [122,] 1 0 0 0 0 1 1 0
#> [123,] 1 0 0 0 0 1 0 1
#> [124,] 1 0 0 0 0 1 0 0
#> [125,] 1 0 0 0 0 0 1 1
#> [126,] 1 0 0 0 0 0 1 0
#> [127,] 1 0 0 0 0 0 0 1
#> [128,] 1 0 0 0 0 0 0 0
#> [129,] 0 1 1 1 1 1 1 1
#> [130,] 0 1 1 1 1 1 1 0
#> [131,] 0 1 1 1 1 1 0 1
#> [132,] 0 1 1 1 1 1 0 0
#> [133,] 0 1 1 1 1 0 1 1
#> [134,] 0 1 1 1 1 0 1 0
#> [135,] 0 1 1 1 1 0 0 1
#> [136,] 0 1 1 1 1 0 0 0
#> [137,] 0 1 1 1 0 1 1 1
#> [138,] 0 1 1 1 0 1 1 0
#> [139,] 0 1 1 1 0 1 0 1
#> [140,] 0 1 1 1 0 1 0 0
#> [141,] 0 1 1 1 0 0 1 1
#> [142,] 0 1 1 1 0 0 1 0
#> [143,] 0 1 1 1 0 0 0 1
#> [144,] 0 1 1 1 0 0 0 0
#> [145,] 0 1 1 0 1 1 1 1
#> [146,] 0 1 1 0 1 1 1 0
#> [147,] 0 1 1 0 1 1 0 1
#> [148,] 0 1 1 0 1 1 0 0
#> [149,] 0 1 1 0 1 0 1 1
#> [150,] 0 1 1 0 1 0 1 0
#> [151,] 0 1 1 0 1 0 0 1
#> [152,] 0 1 1 0 1 0 0 0
#> [153,] 0 1 1 0 0 1 1 1
#> [154,] 0 1 1 0 0 1 1 0
#> [155,] 0 1 1 0 0 1 0 1
#> [156,] 0 1 1 0 0 1 0 0
#> [157,] 0 1 1 0 0 0 1 1
#> [158,] 0 1 1 0 0 0 1 0
#> [159,] 0 1 1 0 0 0 0 1
#> [160,] 0 1 1 0 0 0 0 0
#> [161,] 0 1 0 1 1 1 1 1
#> [162,] 0 1 0 1 1 1 1 0
#> [163,] 0 1 0 1 1 1 0 1
#> [164,] 0 1 0 1 1 1 0 0
#> [165,] 0 1 0 1 1 0 1 1
#> [166,] 0 1 0 1 1 0 1 0
#> [167,] 0 1 0 1 1 0 0 1
#> [168,] 0 1 0 1 1 0 0 0
#> [169,] 0 1 0 1 0 1 1 1
#> [170,] 0 1 0 1 0 1 1 0
#> [171,] 0 1 0 1 0 1 0 1
#> [172,] 0 1 0 1 0 1 0 0
#> [173,] 0 1 0 1 0 0 1 1
#> [174,] 0 1 0 1 0 0 1 0
#> [175,] 0 1 0 1 0 0 0 1
#> [176,] 0 1 0 1 0 0 0 0
#> [177,] 0 1 0 0 1 1 1 1
#> [178,] 0 1 0 0 1 1 1 0
#> [179,] 0 1 0 0 1 1 0 1
#> [180,] 0 1 0 0 1 1 0 0
#> [181,] 0 1 0 0 1 0 1 1
#> [182,] 0 1 0 0 1 0 1 0
#> [183,] 0 1 0 0 1 0 0 1
#> [184,] 0 1 0 0 1 0 0 0
#> [185,] 0 1 0 0 0 1 1 1
#> [186,] 0 1 0 0 0 1 1 0
#> [187,] 0 1 0 0 0 1 0 1
#> [188,] 0 1 0 0 0 1 0 0
#> [189,] 0 1 0 0 0 0 1 1
#> [190,] 0 1 0 0 0 0 1 0
#> [191,] 0 1 0 0 0 0 0 1
#> [192,] 0 1 0 0 0 0 0 0
#> [193,] 0 0 1 1 1 1 1 1
#> [194,] 0 0 1 1 1 1 1 0
#> [195,] 0 0 1 1 1 1 0 1
#> [196,] 0 0 1 1 1 1 0 0
#> [197,] 0 0 1 1 1 0 1 1
#> [198,] 0 0 1 1 1 0 1 0
#> [199,] 0 0 1 1 1 0 0 1
#> [200,] 0 0 1 1 1 0 0 0
#> [201,] 0 0 1 1 0 1 1 1
#> [202,] 0 0 1 1 0 1 1 0
#> [203,] 0 0 1 1 0 1 0 1
#> [204,] 0 0 1 1 0 1 0 0
#> [205,] 0 0 1 1 0 0 1 1
#> [206,] 0 0 1 1 0 0 1 0
#> [207,] 0 0 1 1 0 0 0 1
#> [208,] 0 0 1 1 0 0 0 0
#> [209,] 0 0 1 0 1 1 1 1
#> [210,] 0 0 1 0 1 1 1 0
#> [211,] 0 0 1 0 1 1 0 1
#> [212,] 0 0 1 0 1 1 0 0
#> [213,] 0 0 1 0 1 0 1 1
#> [214,] 0 0 1 0 1 0 1 0
#> [215,] 0 0 1 0 1 0 0 1
#> [216,] 0 0 1 0 1 0 0 0
#> [217,] 0 0 1 0 0 1 1 1
#> [218,] 0 0 1 0 0 1 1 0
#> [219,] 0 0 1 0 0 1 0 1
#> [220,] 0 0 1 0 0 1 0 0
#> [221,] 0 0 1 0 0 0 1 1
#> [222,] 0 0 1 0 0 0 1 0
#> [223,] 0 0 1 0 0 0 0 1
#> [224,] 0 0 1 0 0 0 0 0
#> [225,] 0 0 0 1 1 1 1 1
#> [226,] 0 0 0 1 1 1 1 0
#> [227,] 0 0 0 1 1 1 0 1
#> [228,] 0 0 0 1 1 1 0 0
#> [229,] 0 0 0 1 1 0 1 1
#> [230,] 0 0 0 1 1 0 1 0
#> [231,] 0 0 0 1 1 0 0 1
#> [232,] 0 0 0 1 1 0 0 0
#> [233,] 0 0 0 1 0 1 1 1
#> [234,] 0 0 0 1 0 1 1 0
#> [235,] 0 0 0 1 0 1 0 1
#> [236,] 0 0 0 1 0 1 0 0
#> [237,] 0 0 0 1 0 0 1 1
#> [238,] 0 0 0 1 0 0 1 0
#> [239,] 0 0 0 1 0 0 0 1
#> [240,] 0 0 0 1 0 0 0 0
#> [241,] 0 0 0 0 1 1 1 1
#> [242,] 0 0 0 0 1 1 1 0
#> [243,] 0 0 0 0 1 1 0 1
#> [244,] 0 0 0 0 1 1 0 0
#> [245,] 0 0 0 0 1 0 1 1
#> [246,] 0 0 0 0 1 0 1 0
#> [247,] 0 0 0 0 1 0 0 1
#> [248,] 0 0 0 0 1 0 0 0
#> [249,] 0 0 0 0 0 1 1 1
#> [250,] 0 0 0 0 0 1 1 0
#> [251,] 0 0 0 0 0 1 0 1
#> [252,] 0 0 0 0 0 1 0 0
#> [253,] 0 0 0 0 0 0 1 1
#> [254,] 0 0 0 0 0 0 1 0
#> [255,] 0 0 0 0 0 0 0 1
#>
#> $pinter
#> [1] 0.013600 0.013600 0.013600 0.013600 0.013600 0.013600 0.013600 0.013600
#> [9] 0.013600 0.013600 0.013600 0.013600 0.013600 0.013600 0.013600 0.013600
#> [17] 0.013600 0.013600 0.013600 0.013600 0.013600 0.013600 0.013600 0.013600
#> [25] 0.013600 0.013600 0.013600 0.013600 0.013600 0.013600 0.013600 0.013600
#> [33] 0.013600 0.013600 0.013600 0.013600 0.013600 0.013600 0.013600 0.013600
#> [41] 0.013600 0.013600 0.013600 0.013600 0.013600 0.013600 0.013600 0.013600
#> [49] 0.013600 0.013600 0.013600 0.013600 0.013600 0.013600 0.013600 0.013600
#> [57] 0.013600 0.013600 0.013600 0.013600 0.013600 0.013600 0.013600 0.013600
#> [65] 0.024250 0.024250 0.024250 0.024250 0.024250 0.024250 0.024250 0.024250
#> [73] 0.024250 0.024250 0.024250 0.024250 0.024250 0.024250 0.024250 0.024250
#> [81] 0.024250 0.024250 0.024250 0.024250 0.024250 0.024250 0.024250 0.024250
#> [89] 0.024250 0.024250 0.024250 0.024250 0.024250 0.024250 0.024250 0.024250
#> [97] 0.024250 0.024250 0.024250 0.024250 0.024250 0.024250 0.024250 0.024250
#> [105] 0.024250 0.024250 0.024250 0.024250 0.024250 0.024250 0.024250 0.024250
#> [113] 0.011250 0.011250 0.011250 0.011250 0.024250 0.024250 0.024250 0.024250
#> [121] 0.011250 0.011250 0.011250 0.011250 0.024250 0.024250 0.024250 0.024250
#> [129] 0.008500 0.008500 0.008500 0.008500 0.008500 0.008500 0.008500 0.008500
#> [137] 0.008500 0.008500 0.008500 0.008500 0.008500 0.008500 0.008500 0.008500
#> [145] 0.008500 0.008500 0.008500 0.008500 0.008500 0.008500 0.008500 0.008500
#> [153] 0.008500 0.008500 0.008500 0.008500 0.008500 0.008500 0.008500 0.008500
#> [161] 0.008500 0.008500 0.008500 0.008500 0.008500 0.008500 0.008500 0.008500
#> [169] 0.008500 0.008500 0.008500 0.008500 0.008500 0.008500 0.008500 0.008500
#> [177] 0.008500 0.008500 0.008500 0.008500 0.008500 0.008500 0.008500 0.008500
#> [185] 0.008500 0.008500 0.008500 0.008500 0.008500 0.008500 0.008500 0.008500
#> [193] 0.017600 0.017600 0.017600 0.017600 0.017600 0.017600 0.017600 0.017600
#> [201] 0.017600 0.017600 0.017600 0.017600 0.017600 0.017600 0.017600 0.017600
#> [209] 0.011250 0.011250 0.011250 0.011250 0.033875 0.033875 0.033875 0.033875
#> [217] 0.011250 0.011250 0.011250 0.011250 0.033000 0.033875 0.033000 0.033875
#> [225] 0.011000 0.011000 0.011000 0.011000 0.011000 0.011000 0.011000 0.011000
#> [233] 0.011000 0.011000 0.011000 0.011000 0.011000 0.011000 0.011000 0.011000
#> [241] 0.003600 0.003600 0.003600 0.003600 0.033000 0.046250 0.033000 0.046250
#> [249] 0.002250 0.002250 0.002250 0.002250 0.013200 0.081400 0.006600
#>
#> $padj
#> [1] 0.024250 0.013600 0.033875 0.024250 0.046250 0.024250 0.081400 0.033875
#>