Obtains the adjusted p-values for the modified gatekeeping procedures for multiplicity problems involving serial and parallel logical restrictions.
fmodmix(
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, George Kordzakhia, and Thomas Brechenmacher. Mixture-based gatekeeping procedures for multiplicity problems with multiple sequences of hypotheses. Journal of Biopharmaceutical Statistics. 2016; 26(4):758–780.
George Kordzakhia, Thomas Brechenmacher, Eiji Ishida, Alex Dmitrienko, Winston Wenxiang Zheng, and David Fuyuan Li. An enhanced mixture method for constructing gatekeeping procedures in clinical trials. Journal of Biopharmaceutical Statistics. 2018; 28(1):113–128.
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)
fmodmix(p, family, serial, parallel, gamma, test = "hommel", exhaust = TRUE)
#> $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] 0.01360 0.01360 0.01360 0.01360 0.01360 0.01360 0.01360 0.01360 0.01360
#> [10] 0.01360 0.01360 0.01360 0.01360 0.01360 0.01360 0.01360 0.01360 0.01360
#> [19] 0.01360 0.01360 0.01360 0.01360 0.01360 0.01360 0.01360 0.01360 0.01360
#> [28] 0.01360 0.01360 0.01360 0.01360 0.01360 0.01360 0.01360 0.01360 0.01360
#> [37] 0.01360 0.01360 0.01360 0.01360 0.01360 0.01360 0.01360 0.01360 0.01360
#> [46] 0.01360 0.01360 0.01360 0.01360 0.01360 0.01360 0.01360 0.01360 0.01360
#> [55] 0.01360 0.01360 0.01360 0.01360 0.01360 0.01360 0.01360 0.01360 0.01360
#> [64] 0.01360 0.02425 0.02425 0.02425 0.02425 0.02425 0.02425 0.02425 0.02425
#> [73] 0.02425 0.02425 0.02425 0.02425 0.02425 0.02425 0.02425 0.02425 0.00900
#> [82] 0.00900 0.00900 0.00900 0.02425 0.01940 0.02425 0.01940 0.00900 0.00900
#> [91] 0.00900 0.00900 0.02425 0.01940 0.02425 0.01940 0.02425 0.02425 0.02425
#> [100] 0.02425 0.02425 0.02425 0.02425 0.02425 0.02425 0.02425 0.02425 0.02425
#> [109] 0.02425 0.02425 0.02425 0.02425 0.00900 0.00900 0.00900 0.00900 0.02425
#> [118] 0.01940 0.02425 0.01940 0.00900 0.00900 0.00900 0.00900 0.02425 0.01940
#> [127] 0.02425 0.01940 0.00850 0.00850 0.00850 0.00850 0.00850 0.00850 0.00850
#> [136] 0.00850 0.00850 0.00850 0.00850 0.00850 0.00850 0.00850 0.00850 0.00850
#> [145] 0.00850 0.00850 0.00850 0.00850 0.00850 0.00850 0.00850 0.00850 0.00850
#> [154] 0.00850 0.00850 0.00850 0.00850 0.00850 0.00850 0.00850 0.00850 0.00850
#> [163] 0.00850 0.00850 0.00850 0.00850 0.00850 0.00850 0.00850 0.00850 0.00680
#> [172] 0.00680 0.00850 0.00850 0.00680 0.00680 0.00850 0.00850 0.00850 0.00850
#> [181] 0.00850 0.00850 0.00850 0.00850 0.00850 0.00850 0.00680 0.00680 0.00850
#> [190] 0.00850 0.00680 0.00680 0.01760 0.01760 0.01760 0.01760 0.01760 0.01760
#> [199] 0.01760 0.01760 0.01760 0.01760 0.01760 0.01760 0.01760 0.01760 0.01760
#> [208] 0.01760 0.00900 0.00900 0.00900 0.00900 0.03300 0.02710 0.03300 0.02710
#> [217] 0.00900 0.00900 0.00900 0.00900 0.03300 0.02710 0.03300 0.02710 0.01100
#> [226] 0.01100 0.01100 0.01100 0.01100 0.01100 0.01100 0.01100 0.01100 0.01100
#> [235] 0.00880 0.00880 0.01100 0.01100 0.00880 0.00880 0.00360 0.00360 0.00360
#> [244] 0.00360 0.03300 0.03700 0.03300 0.03700 0.00225 0.00225 0.00180 0.00180
#> [253] 0.01320 0.08140 0.00660
#>
#> $padj
#> [1] 0.02425 0.01360 0.03300 0.02425 0.03700 0.02425 0.08140 0.03300
#>