OCandASN.MSPRT: Operating characteristics (OC) and Average Sample Number...
In MSPRT: A Modified Sequential Probability Ratio Test (MSPRT)
Description
Usage
Arguments
Details
Value
Author(s)
References
Examples
Description
This function obtains the operating characteristics, that is the probability of accepting H_0 and the sample size required on average for reaching a decision, for a designed MSPRT at the specified effect size(s).
Usage
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OCandASN.MSPRT(theta, design.MSPRT.object,
termination.threshold, test.type, side = "right",
theta0, Type1.target = 0.005, Type2.target = 0.2,
N.max, N1.max, N2.max,
sigma = 1, sigma1 = 1, sigma2 = 1,
batch.size, batch1.size, batch2.size,
nReplicate = 1e+06, nCore = max(1, detectCores() - 1),
verbose = T, seed = 1)
Arguments
theta
Numeric vector. Vector of effect size(s) where the operating characteristics of the MSPRT is desired.
design.MSPRT.object
List. The output returned from design.MSPRT corresponding to the MSPRT for which the operating characteristics are desired.
termination.threshold
Positive numeric. Termination threshold of the designed MSPRT.
test.type
Same as in design.MSPRT. Not required if design.MSPRT.object is provided.
side
Same as in design.MSPRT. Not required if design.MSPRT.object is provided.
theta0
Same as in design.MSPRT. Not required if design.MSPRT.object is provided.
Type1.target
Same as in design.MSPRT. Not required if design.MSPRT.object is provided.
Type2.target
Same as in design.MSPRT. Not required if design.MSPRT.object is provided.
N.max
Same as in design.MSPRT. Not required if design.MSPRT.object is provided.
N1.max
Same as in design.MSPRT. Not required if design.MSPRT.object is provided.
N2.max
Same as in design.MSPRT. Not required if design.MSPRT.object is provided.
sigma
Same as in design.MSPRT. Not required if design.MSPRT.object is provided.
sigma1
Same as in design.MSPRT. Not required if design.MSPRT.object is provided.
sigma2
Same as in design.MSPRT. Not required if design.MSPRT.object is provided.
batch.size
Same as in design.MSPRT. Not required if design.MSPRT.object is provided.
batch1.size
Same as in design.MSPRT. Not required if design.MSPRT.object is provided.
batch2.size
Same as in design.MSPRT. Not required if design.MSPRT.object is provided.
nReplicate
Positive integer. Total number of replications to be used in Monte Carlo simulation for calculating the termination threshold and the operating characteristics of the MSPRT.
Default: 1,000,000.
verbose
Logical. If TRUE (default), returns messages of the current proceedings. Otherwise it doesn't.
nCore
Positive integer. Total number of cores available for computation. Can be anything ≥ 1.
Default: detectCores() - 1. That is, 1 less than the total number of available cores.
seed
Integer. Random number generating seed.
Default: 1.
Details
If design.MSPRT.object is provided, one can only additionally provide nReplicate, nCore, verbose and seed (Easier option). Otherwise, just like in design.MSPRT, all the other arguments together with termination.threshold (obtained from design.MSPRT) needs to be provided adequately.
Value
Data frame.
One-sample tests: The data frame has 3 columns named theta, acceptH0.prob and EN, and the number of rows equals to the number of effect sizes (length of theta) where the operating characteristics are evaluated. Each row corresponds to a particular value of theta (effect size). The columns respectively contain the value of a particular theta (effect size), and the probability of accepting the $H_0$ and the average sample size required by the MSPRT for reaching a decision thereat.
Two-sample tests: The data frame has 4 columns named theta, acceptH0.prob, EN1 and EN2, and the number of rows equals to the number of effect sizes (length of theta) where the operating characteristics are evaluated. Each row corresponds to a particular value of theta (effect size). The columns respectively contain the value of a particular theta (effect size), and the probability of accepting the H_0 at that effect size, and the average sample size from Group-1 & 2 that is required by the MSPRT for reaching a decision thereat.
Author(s)
Sandipan Pramanik, Valen E. Johnson and Anirban Bhattacharya
References
Pramanik S., Johnson V. E. and Bhattacharya A. (2020+). A Modified Sequential Probability Ratio Test. [Arxiv]
Examples
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#################### one-sample proportion test ####################
#### right sided ####
### design
#design.oneprop.right <- design.MSPRT(test.type = 'oneProp', side = 'right',
# N.max = 20)
### OC and ASN
#OC.oneprop.right <- OCandASN.MSPRT(theta = seq(design.oneprop.right$theta0, 1,
# length.out = 3),
# design.MSPRT.object = design.oneprop.right)
#### left sided ####
### design
#design.oneprop.left = design.MSPRT(test.type = 'oneProp', side = 'left',
# N.max = 20)
### OC and ASN
#OC.oneprop.left = OCandASN.MSPRT(theta = seq(0, design.oneprop.right$theta0,
# length.out = 3),
# design.MSPRT.object = design.oneprop.left)
#### both sided ####
### design
#design.oneprop.both = design.MSPRT(test.type = 'oneProp', side = 'both',
# N.max = 20)
### OC and ASN
#OC.oneprop.both = OCandASN.MSPRT(theta = seq(0, 1, length.out = 3),
# design.MSPRT.object = design.oneprop.both)
#################### one-sample z test ####################
#### right sided ####
### design
#design.onez.right = design.MSPRT(test.type = 'oneZ', side = 'right',
# N.max = 20)
### OC and ASN
#OC.onez.right = OCandASN.MSPRT(theta = seq(design.onez.right$theta0,
# design.onez.right$theta0 + 3*design.onez.right$sigma,
# length.out = 3),
# design.MSPRT.object = design.onez.right)
#### left sided ####
### design
#design.onez.left = design.MSPRT(test.type = 'oneZ', side = 'left',
# N.max = 20)
### OC and ASN
#OC.onez.left = OCandASN.MSPRT(theta = seq(design.onez.left$theta0 - 3*design.onez.left$sigma,
# design.onez.left$theta0,
# length.out = 3),
# design.MSPRT.object = design.onez.left)
#### both sided ####
### design
#design.onez.both = design.MSPRT(test.type = 'oneZ', side = 'both',
# N.max = 20)
### OC and ASN
#OC.onez.both = OCandASN.MSPRT(theta = seq(design.onez.both$theta0 - 3*design.onez.both$sigma,
# design.onez.both$theta0 + 3*design.onez.both$sigma,
# length.out = 3),
# design.MSPRT.object = design.onez.both)
#################### one-sample t test ####################
#### right sided ####
### design
#design.onet.right = design.MSPRT(test.type = 'oneT', side = 'right',
# N.max = 20)
### OC and ASN
#OC.onet.right = OCandASN.MSPRT(theta = seq(design.onet.right$theta0, 1,
# length.out = 3),
# design.MSPRT.object = design.onet.right)
#### left sided ####
### design
#design.onet.left = design.MSPRT(test.type = 'oneT', side = 'left',
# N.max = 20)
### OC and ASN
#OC.onet.left = OCandASN.MSPRT(theta = seq(-1, design.onet.left$theta0,
# length.out = 3),
# design.MSPRT.object = design.onet.left)
#### both sided ####
### design
#design.onet.both = design.MSPRT(test.type = 'oneT', side = 'both',
# N.max = 20)
### OC and ASN
#OC.onet.both = OCandASN.MSPRT(theta = seq(-1, 1, length.out = 3),
# design.MSPRT.object = design.onet.both)
#################### two-sample z test ####################
#### right sided ####
### design
#design.twoz.right = design.MSPRT(test.type = 'twoZ', side = 'right',
# N1.max = 20, N2.max = 20)
### OC and ASN
#OC.twoz.right = OCandASN.MSPRT(theta = seq(design.twoz.right$theta0,
# design.twoz.right$theta0 + 2,
# length.out = 3),
# design.MSPRT.object = design.twoz.right)
#### left sided ####
### design
#design.twoz.left = design.MSPRT(test.type = 'twoZ', side = 'left',
# N1.max = 20, N2.max = 20)
### OC and ASN
#OC.twoz.left = OCandASN.MSPRT(theta = seq(design.twoz.left$theta0 - 2,
# design.twoz.left$theta0,
# length.out = 3),
# design.MSPRT.object = design.twoz.left)
#### both sided ####
### design
#design.twoz.both = design.MSPRT(test.type = 'twoZ', side = 'both',
# N1.max = 20, N2.max = 20)
### OC and ASN
#OC.twoz.both = OCandASN.MSPRT(theta = seq(design.twoz.both$theta0 - 2,
# design.twoz.both$theta0 + 2,
# length.out = 3),
# design.MSPRT.object = design.twoz.both)
#################### two-sample t test ####################
#### right sided ####
### design
#design.twot.right = design.MSPRT(test.type = 'twoT', side = 'right',
# N1.max = 20, N2.max = 20)
### OC and ASN
#OC.twot.right = OCandASN.MSPRT(theta = seq(design.twot.right$theta0,
# design.twot.right$theta0 + 2,
# length.out = 3),
# design.MSPRT.object = design.twot.right)
#### left sided ####
### design
#design.twot.left = design.MSPRT(test.type = 'twoT', side = 'left',
# N1.max = 20, N2.max = 20)
### OC and ASN
#OC.twot.left = OCandASN.MSPRT(theta = seq(design.twot.left$theta0 - 2,
# design.twot.left$theta0,
# length.out = 3),
# design.MSPRT.object = design.twot.left)
#### both sided ####
### design
#design.twot.both = design.MSPRT(test.type = 'twoT', side = 'both',
# N1.max = 20, N2.max = 20)
### OC and ASN
#OC.twot.both = OCandASN.MSPRT(theta = seq(design.twot.both$theta0 - 2,
# design.twot.both$theta0 + 2,
# length.out = 3),
# design.MSPRT.object = design.twot.both)
MSPRT documentation built on Nov. 13, 2020, 5:07 p.m.
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Description Usage Arguments Details Value Author(s) References Examples
Description
This function obtains the operating characteristics, that is the probability of accepting H_0 and the sample size required on average for reaching a decision, for a designed MSPRT at the specified effect size(s).
Usage
1 2 3 4 5 6 7 8 | OCandASN.MSPRT(theta, design.MSPRT.object,
termination.threshold, test.type, side = "right",
theta0, Type1.target = 0.005, Type2.target = 0.2,
N.max, N1.max, N2.max,
sigma = 1, sigma1 = 1, sigma2 = 1,
batch.size, batch1.size, batch2.size,
nReplicate = 1e+06, nCore = max(1, detectCores() - 1),
verbose = T, seed = 1)
|
Arguments
theta |
Numeric vector. Vector of effect size(s) where the operating characteristics of the MSPRT is desired. |
design.MSPRT.object |
List. The output returned from |
termination.threshold |
Positive numeric. Termination threshold of the designed MSPRT. |
test.type |
Same as in |
side |
Same as in |
theta0 |
Same as in |
Type1.target |
Same as in |
Type2.target |
Same as in |
N.max |
Same as in |
N1.max |
Same as in |
N2.max |
Same as in |
sigma |
Same as in |
sigma1 |
Same as in |
sigma2 |
Same as in |
batch.size |
Same as in |
batch1.size |
Same as in |
batch2.size |
Same as in |
nReplicate |
Positive integer. Total number of replications to be used in Monte Carlo simulation for calculating the termination threshold and the operating characteristics of the MSPRT. Default: 1,000,000. |
verbose |
Logical. If |
nCore |
Positive integer. Total number of cores available for computation. Can be anything ≥ 1. Default: |
seed |
Integer. Random number generating seed. Default: 1. |
Details
If design.MSPRT.object is provided, one can only additionally provide nReplicate, nCore, verbose and seed (Easier option). Otherwise, just like in design.MSPRT, all the other arguments together with termination.threshold (obtained from design.MSPRT) needs to be provided adequately.
Value
Data frame.
One-sample tests: The data frame has 3 columns named
theta,acceptH0.probandEN, and the number of rows equals to the number of effect sizes (length oftheta) where the operating characteristics are evaluated. Each row corresponds to a particular value of theta (effect size). The columns respectively contain the value of a particular theta (effect size), and the probability of accepting the $H_0$ and the average sample size required by the MSPRT for reaching a decision thereat.Two-sample tests: The data frame has 4 columns named
theta,acceptH0.prob,EN1andEN2, and the number of rows equals to the number of effect sizes (length oftheta) where the operating characteristics are evaluated. Each row corresponds to a particular value of theta (effect size). The columns respectively contain the value of a particular theta (effect size), and the probability of accepting the H_0 at that effect size, and the average sample size from Group-1 & 2 that is required by the MSPRT for reaching a decision thereat.
Author(s)
Sandipan Pramanik, Valen E. Johnson and Anirban Bhattacharya
References
Pramanik S., Johnson V. E. and Bhattacharya A. (2020+). A Modified Sequential Probability Ratio Test. [Arxiv]
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 | #################### one-sample proportion test ####################
#### right sided ####
### design
#design.oneprop.right <- design.MSPRT(test.type = 'oneProp', side = 'right',
# N.max = 20)
### OC and ASN
#OC.oneprop.right <- OCandASN.MSPRT(theta = seq(design.oneprop.right$theta0, 1,
# length.out = 3),
# design.MSPRT.object = design.oneprop.right)
#### left sided ####
### design
#design.oneprop.left = design.MSPRT(test.type = 'oneProp', side = 'left',
# N.max = 20)
### OC and ASN
#OC.oneprop.left = OCandASN.MSPRT(theta = seq(0, design.oneprop.right$theta0,
# length.out = 3),
# design.MSPRT.object = design.oneprop.left)
#### both sided ####
### design
#design.oneprop.both = design.MSPRT(test.type = 'oneProp', side = 'both',
# N.max = 20)
### OC and ASN
#OC.oneprop.both = OCandASN.MSPRT(theta = seq(0, 1, length.out = 3),
# design.MSPRT.object = design.oneprop.both)
#################### one-sample z test ####################
#### right sided ####
### design
#design.onez.right = design.MSPRT(test.type = 'oneZ', side = 'right',
# N.max = 20)
### OC and ASN
#OC.onez.right = OCandASN.MSPRT(theta = seq(design.onez.right$theta0,
# design.onez.right$theta0 + 3*design.onez.right$sigma,
# length.out = 3),
# design.MSPRT.object = design.onez.right)
#### left sided ####
### design
#design.onez.left = design.MSPRT(test.type = 'oneZ', side = 'left',
# N.max = 20)
### OC and ASN
#OC.onez.left = OCandASN.MSPRT(theta = seq(design.onez.left$theta0 - 3*design.onez.left$sigma,
# design.onez.left$theta0,
# length.out = 3),
# design.MSPRT.object = design.onez.left)
#### both sided ####
### design
#design.onez.both = design.MSPRT(test.type = 'oneZ', side = 'both',
# N.max = 20)
### OC and ASN
#OC.onez.both = OCandASN.MSPRT(theta = seq(design.onez.both$theta0 - 3*design.onez.both$sigma,
# design.onez.both$theta0 + 3*design.onez.both$sigma,
# length.out = 3),
# design.MSPRT.object = design.onez.both)
#################### one-sample t test ####################
#### right sided ####
### design
#design.onet.right = design.MSPRT(test.type = 'oneT', side = 'right',
# N.max = 20)
### OC and ASN
#OC.onet.right = OCandASN.MSPRT(theta = seq(design.onet.right$theta0, 1,
# length.out = 3),
# design.MSPRT.object = design.onet.right)
#### left sided ####
### design
#design.onet.left = design.MSPRT(test.type = 'oneT', side = 'left',
# N.max = 20)
### OC and ASN
#OC.onet.left = OCandASN.MSPRT(theta = seq(-1, design.onet.left$theta0,
# length.out = 3),
# design.MSPRT.object = design.onet.left)
#### both sided ####
### design
#design.onet.both = design.MSPRT(test.type = 'oneT', side = 'both',
# N.max = 20)
### OC and ASN
#OC.onet.both = OCandASN.MSPRT(theta = seq(-1, 1, length.out = 3),
# design.MSPRT.object = design.onet.both)
#################### two-sample z test ####################
#### right sided ####
### design
#design.twoz.right = design.MSPRT(test.type = 'twoZ', side = 'right',
# N1.max = 20, N2.max = 20)
### OC and ASN
#OC.twoz.right = OCandASN.MSPRT(theta = seq(design.twoz.right$theta0,
# design.twoz.right$theta0 + 2,
# length.out = 3),
# design.MSPRT.object = design.twoz.right)
#### left sided ####
### design
#design.twoz.left = design.MSPRT(test.type = 'twoZ', side = 'left',
# N1.max = 20, N2.max = 20)
### OC and ASN
#OC.twoz.left = OCandASN.MSPRT(theta = seq(design.twoz.left$theta0 - 2,
# design.twoz.left$theta0,
# length.out = 3),
# design.MSPRT.object = design.twoz.left)
#### both sided ####
### design
#design.twoz.both = design.MSPRT(test.type = 'twoZ', side = 'both',
# N1.max = 20, N2.max = 20)
### OC and ASN
#OC.twoz.both = OCandASN.MSPRT(theta = seq(design.twoz.both$theta0 - 2,
# design.twoz.both$theta0 + 2,
# length.out = 3),
# design.MSPRT.object = design.twoz.both)
#################### two-sample t test ####################
#### right sided ####
### design
#design.twot.right = design.MSPRT(test.type = 'twoT', side = 'right',
# N1.max = 20, N2.max = 20)
### OC and ASN
#OC.twot.right = OCandASN.MSPRT(theta = seq(design.twot.right$theta0,
# design.twot.right$theta0 + 2,
# length.out = 3),
# design.MSPRT.object = design.twot.right)
#### left sided ####
### design
#design.twot.left = design.MSPRT(test.type = 'twoT', side = 'left',
# N1.max = 20, N2.max = 20)
### OC and ASN
#OC.twot.left = OCandASN.MSPRT(theta = seq(design.twot.left$theta0 - 2,
# design.twot.left$theta0,
# length.out = 3),
# design.MSPRT.object = design.twot.left)
#### both sided ####
### design
#design.twot.both = design.MSPRT(test.type = 'twoT', side = 'both',
# N1.max = 20, N2.max = 20)
### OC and ASN
#OC.twot.both = OCandASN.MSPRT(theta = seq(design.twot.both$theta0 - 2,
# design.twot.both$theta0 + 2,
# length.out = 3),
# design.MSPRT.object = design.twot.both)
|
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