R: Operating characteristics (OC) and Average Sample Number...

OCandASN.MSPRT {MSPRT}

R Documentation

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.

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


#################### 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)

[Package MSPRT version 3.0 Index]