pooledBinDiff: Confidence intervals for the difference of proportions

In bjbiggerstaff/PooledInfRate: Estimation for Pooled or Group Testing

Confidence intervals for the difference of proportions

Description

Calculates confidence intervals for the difference of two proportions based on pooled testing experiments allowing different pool sizes.

Usage

pooledBinDiff(x, ...)

pIRDiff(x, ...)

## S3 method for class 'formula'
pooledBinDiff(x, data,
 pt.method = c("firth", "gart", "bc-mle", "mle", "mir"),
 ci.method = c("skew-score", "bc-skew-score", "score", "lrt", "wald", "mir"),
 scale = 1, alpha = 0.05, tol = .Machine$double.eps^0.5, ...)

## S3 method for class 'formula'
pIRDiff(x, data,
 pt.method = c("firth", "gart", "bc-mle", "mle", "mir"),
 ci.method = c("skew-score", "bc-skew-score", "score", "lrt", "wald", "mir"),
 scale = 1, alpha = 0.05, tol = .Machine$double.eps^0.5, ...)

## Default S3 method:
pooledBinDiff(x, m, x2, m2, n = rep(1, length(x1)), n2 = rep(1, length(x2)),
 group.names = c("1","2"), pt.method = c("firth", "gart", "bc-mle", "mle", "mir"),
 ci.method = c("skew-score", "bc-skew-score", "score", "lrt", "wald", "mir"),
 scale = 1, alpha = 0.05, tol = .Machine$double.eps^0.5, ...)

## Default S3 method:
pIRDiff(x, m, x2, m2, n = rep(1, length(x1)), n2 = rep(1, length(x2)),
 group.names = c("1","2"), pt.method = c("firth", "gart", "bc-mle", "mle", "mir"),
 ci.method = c("skew-score", "bc-skew-score", "score", "lrt", "wald", "mir"),
 scale = 1, alpha = 0.05, tol = .Machine$double.eps^0.5, ...)

## S3 method for class 'pooledBinDiff'
print(x, ...)
## S3 method for class 'pooledBinDiff'
as.data.frame(x)
## S3 method for class 'pooledBinDiff'
x[i, j, drop = if (missing(i)) TRUE else length(cols) ==  1]

## S3 method for class 'pIRDiff'
print(x, ...)
## S3 method for class 'pIRDiff'
as.data.frame(x)
## S3 method for class 'pIRDiff'
x[i, j, drop = if (missing(i)) TRUE else length(cols) ==  1]

Arguments

x	If an object of class formula (or one that can be coerced to that class): a symbolic representation of the variables used to identify the number of positive pools, corresponding pool size, and number of pools of corresponding pool size, along with a required grouping variable. See the 'Details' section below. Otherwise a vector, specifying the observed number of positive pools, among the number of pools tested (n1) in population 1. For methods, objects of class pooledBinDiff/pIRDiff.
data	an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables specified in the formula. Records with mising data are omitted.
m	a vector of corresponding pool sizes in population 1, must have the same length as x1
x2	a vector, specifying the observed number of positive pools, among the number of pools tested (n2) in population 2
m2	a vector of corresponding pool sizes in population 2, must have the same length as x2
n	a vector of the corresponding number of pools with sizes m1
n2	a vector of the corresponding number of pools with sizes m2
group.names	a character vector of length 2 for the names of the groups when using the default only; the names are taken from the grouping variable for the formula implementation
pt.method	a character string, specifying the point estimator to compute, with the following options: "firth": recommended bias-corrected estimator (Hepworth & Biggerstaff, 2017), the default; "gart" bias-corrected MLE (Biggerstaff, 2008); "bc-mle": same as "gart", kept for backward compatibility ; "mle" MLE, and "mir" MIR.
ci.method	a character string, specifying the confidence interval to compute, with options: "skew-score" skewness-corrected, the default, "score" the score, "bc-skew-score" bias- and skewness-corrected "lrt" likelihood ratio test. See Biggerstaff (2008) for details. Further, the options "wald" wald and "mir" MIR are available but are not recommended.
scale	a single numeric, coefficient to scale the point estimates and intervals bounds in the print and summary method (print.pooledBinDiff, summary.pooledBinDiff)
alpha	a single numeric, specifying the type-I-error level
tol	accuracy required for iterations in internal functions
i,j	elements to extract or replace. For [ and [[, these are numeric or character or, for [ only, empty or logical. Numeric values are coerced to integer as if by as.integer.
drop	logical. If TRUE the result is coerced to the lowest possible dimension. The default is to drop if only one column is left, but not to drop if only one row is left.
...	future arguments

Details

formula specification is the same as in pooledBin/pIR. See the 'Details' there.

Differences in proportions are computed as detailed in Biggerstaff (2008). All pairwise differences for groups specified using the grouping variable (formula method) or with the separate specifications (x1,x2, etc.) are computed. Note that no adjustment for multiple comparisons is made, so it is recommended to adjust alpha if such is needed.

As with estimation for groups indivdiually, point estimation: bias preventative ("firth") and bias corrected ("gart") estimators are recommended, with details described in Hepworth G, Biggerstaff BJ (2017). Use of MLE ("mle"), and MIR ("mir") estimators is not recommended.

Confidence intervals: Note, that the methods "mir" and "wald" can not be recommended, because they return too narrow intervals in relevant situations, "mir" because it ignores the pooling, and "wald" because it relies on simple large sample methods. For computational details and simulation results of the remaining methods, see Biggerstaff (2008).

The subsetting or extractor functions [.pooledBin and [.pIR mimic the same [ behavior as with data frames.

Value

A list with elements

d	the estimated difference of proportions
lcl	the lower confidence limit
ucl	the upper confidence limit
pt.method	the method used for point estimation
ci.method	the method used for interval estimation
alpha	the type-I-error level
scale	Scaling coefficient for the output
x1	the numbers of postive pools in population 1
m1	the size of the pools in population 1
n1	the numbers of pools with corresponding pool sizes m1 in population 1
x2	the numbers of postive pools in population 2
m2	the size of the pools in population 2
n2	the numbers of pools with corresponding pool sizes m1 in population 2

along with attributes class, pt.method, ci.method, alpha, nComparisons, comparisonNames, grp.pooledBin, group.var, group.names, scale, and call.

Author(s)

Brad Biggerstaff

References

Walter SD, Hildreth SW, Beaty BJ: Estimation of infection rates in population of organisms using pools of variable size. Am J Epidemiol 1980, 112(1):124-128

Hepworth G: Estimation of proportions by group testing. PhD Dissertation. Melbourne, Australia: The University of Melbourne; 1999.

Biggerstaff BJ (2008): Confidence interval for the difference of proportions estmimated from pooled samples. Journal of Agricultural Biological and Environmental Statistics 2008, 13(4):478-496.

Hepworth G, Biggerstaff BJ: Bias correction in estimating Proportions by pooled testing. JABES 2017, to appear.

Examples

# Consider an imaginary example, where pools of size
# 1, 5, 10 and 50 are tested, 5 pools of each size. The same
# design is applied to estimate the prevalence in
# two populations:
# In population 1, among the 5 pools with size 1 and 5,
# no positive pool is observed,
# while among the 5 pools of size 10 and 50, 1 and 2 positive
# pools are identified, respectively.

# In population 2, 1 positive result is observed
# among the 5 pools each pooling 5 elements,
# no positive result among the pools pooling 10 elements,
# 4 positive results among the pools pooling 50 elements,

x1 <- c(0,0,1,2)
m1 <- c(1,5,10,50)
n1 <- c(5,5,5,5)

x2<- c(0,1,0,4)
m2 <- m1
n2 <- n1

pooledBinDiff(x1, m1, x2, m2, n1, n2)

summary(pooledBinDiff(x1, m1, x2, m2, n1, n2), scale=1000)

# The formula interface

ex.dat <- data.frame(NumPos = c(x1,x2),
                      NumPos2 = c(1,0,0,1,1,0,0,0),
                      PoolSize = c(m1,m2),
                      NumPools = c(n1,n2),
                      Population = rep(1:2, each=4))

pooledBinDiff(NumPos ~ PoolSize + n(NumPools) | Population, data = ex.dat)

pIRDiff(NumPos2 ~ PoolSize | Population, data = ex.dat)

bjbiggerstaff/PooledInfRate documentation built on Jan. 19, 2024, 6:54 p.m.