pooling_mc {mMPA}

Monte Carlo Simulation for Estimating the Number of Assays Required when Using Pooled Testing

Description

This function uses Monte Carlo (MC) to simulate different orders in which the samples would be collected to form pools. Unlike the function minipool, mpa, and mmpa that calculate the number of assays needed for pools that are formed following the exact order of the samples that are listed in the data, this function pooling_mc permutes the data many (perm_num) times so as to estimate the average number of assays required (ATR) per individual. Using MC avoids the dependence on any specific ordering of forming pools.

Usage

pooling_mc(v, s = NULL, K = 5, vf_cut = 1000, lod = 0,
  method = "mmpa", perm_num = 100, msg = F)

Arguments

v

A vector of non-negative numerical assay results.

s

A vector of risk scores; s must be provided if method = "mmpa" and have the same length as v. The risk score s needs to be positively associated with v; othewise an error message will be generated.

K

Pool size; default is K = 5.

vf_cut

Cutoff value for defining positive cases; default is vf_cut = 1000.

lod

A vector of lower limits of detection or a scalar if the limits are the same; default is lod = 0.

method

Method that is used for pooled testing; must be one of minipool, mpa, and mmpa. By default, method = "mmpa".

perm_num

The number of permutation to be used for the calculation; default is 100.

msg

Message generated during calculation; default is FALSE.

Value

The outcome is a matrix of dimension num_pool by perm_num. The row number is the number of pools (num_pool) from each permutation of the data, which is determined by the sample size N and pool size K; num_pool = N%/%K. The column number is the number of permutations (num_pool).

References

Liu T, Hogan JW, Daniels, MJ, Coetzer M, Xu Y, Bove G, et al. Improved HIV-1 Viral Load Monitoring Capacity Using Pooled Testing with Marker-Assisted Deconvolution. Journal of AIDS. 2017;75(5): 580-587.

Bilder CR, Tebbs JM, Chen P. Informative retesting. Journal of the American Statistical Association. 2010;105(491):942-955.

May S, Gamst A, Haubrich R, Benson C, Smith DM. Pooled nucleic acid testing to identify antiretroviral treatment failure during HIV infection. Journal of Acquired Immune Deficiency Syndromes. 2010;53(2):194-201.

Dorfman R. The detection of defective members of large populations. The Annals of Mathematical Statistics. 1943;14(4):436-440.

See Also

minipool, mpa, mmpa

Examples

### sample size = 300
n = 300;
set.seed(100)
pvl = rgamma(n, shape = 2.8, scale = 150)
summary(pvl)
#   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
#   53      225      392     424    564    1373
riskscore = (rank(pvl)/n) * 0.5 + runif(n) * 0.5
cor(pvl, riskscore, method = "spearman")
#   [1] 0.69
### Pool size K is set to 5
K=5;
### so, the number of pools = 60
n.pool  = n/K; n.pool
#   [1] 60
foo = pooling_mc(pvl, riskscore, perm_num = 100)
### Average number of assays needed per pool for each of the 100
### permutations of the data
apply(foo, 2, mean)
#   [1] 3.43 3.33 3.35 3.47 3.37 3.33 3.37 3.27 3.43 3.28 3.32 3.35 3.35 3.37
#   [15] 3.38 3.37 3.30 3.43 3.28 3.38 3.42 3.35 3.35 3.48 3.30 3.47 3.40 3.35
#  [29] 3.25 3.30 3.38 3.43 3.25 3.45 3.35 3.33 3.42 3.38 3.40 3.33 3.32 3.38
#   [43] 3.33 3.37 3.37 3.33 3.35 3.38 3.38 3.30 3.30 3.33 3.37 3.32 3.30 3.40
#   [57] 3.37 3.42 3.30 3.37 3.38 3.32 3.45 3.38 3.37 3.50 3.33 3.40 3.28 3.37
#   [71] 3.23 3.33 3.23 3.42 3.32 3.32 3.45 3.35 3.32 3.32 3.33 3.33 3.30 3.38
#   [85] 3.37 3.33 3.33 3.20 3.37 3.33 3.30 3.40 3.40 3.32 3.33 3.37 3.40 3.38
#   [99] 3.30 3.33
### Estimated average number of assays needed per pool
mean(foo)
#   3.35
### Estimated average number of assays needed per individual
mean(foo)/K
#   [1] 0.67