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MSPRT (version 3.0)

OCandASN.MSPRT: Operating characteristics (OC) and Average Sample Number (ASN) of a designed MSPRT

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

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 \(\ge 1\).

Default: detectCores() - 1. That is, 1 less than the total number of available cores.

seed

Integer. Random number generating seed.

Default: 1.

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.

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.

References

Pramanik S., Johnson V. E. and Bhattacharya A. (2020+). A Modified Sequential Probability Ratio Test. [Arxiv]

Examples

Run this code
# NOT RUN {
#################### 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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