test_pe {pooling}

Test for Underestimated Processing Error Variance in Pooling Studies

Description

In studies where a biomarker is measured in combined samples from multiple subjects rather than for each individual, design parameters (e.g. optimal pool size, sample size for 80% power) are very sensitive to the magnitude of processing errors. This function provides a test that can be used midway through data collection to test whether the processing error variance is larger than initially assumed, in which case the pool size may need to be adjusted.

Usage

test_pe(xtilde, g, sigsq, sigsq_m = 0, multiplicative = FALSE,
  mu = NULL, alpha = 0.05, boots = 1000, seed = NULL)

Arguments

xtilde

Numeric vector of pooled measurements.

g

Numeric value specifying the pool size.

sigsq

Numeric value specifying the variance of observations.

sigsq_m

Numeric value specifying the variance of measurement errors.

multiplicative

Logical value for whether to assume multiplicative rather than additive errors.

mu

Numeric value specifying the mean of observations. Only used if multiplicative = TRUE.

alpha

Numeric value specifying significance level for bootstrap confidence interval.

boots

Numeric value specifying the number of bootstrap samples to take.

seed

Numeric value specifying the random number seed, in case it is important to be able to reproduce the lower bound.

Details

The method is fully described in a manuscript currently under review. Briefly, the test of interest is H0: sigsq_p <= c, where sigsq_p is the processing error variance and c is the value assumed during study design. Under additive errors, a point estimate for sigsq_p is given by:

sigsq_p.hat = s2 - sigsq / g - sigsq_m

where s2 is the sample variance of poolwise measurements, g is the pool size, and sigsq_m is the measurement error variance which may be 0 if the assay is known to be precise.

Under multiplicative errors, the estimator is:

sigsq_p.hat = [(s2 - sigsq / g) / (mu^2 + sigsq / g) - sigsq_m] / (1 + sigsq_m).

In either case, bootstrapping can be used to obtain a lower bound for a one-sided confidence interval. If the lower bound is greater than c, H0 is rejected.

Value

List containing point estimate and lower bound of confidence interval.

Examples

# Generate data for hypothetical study designed assuming sigsq_p = 0.1, but
# truly sigsq_p = 0.25. Have data collected for 40 pools of size 5, and wish
# to test H0: sigsq_p <= 0.1. In this instance, a false negative occurs.
set.seed(123)
xtilde <- replicate(n = 40, expr = mean(rnorm(5)) + rnorm(n = 1, sd = sqrt(0.25)))
(fit <- test_pe(xtilde = xtilde, g = 5, sigsq = 1, sigsq_m = 0))