truePrevPools {prevalence}

Estimate true prevalence from pooled samples

Description

Bayesian estimation of true prevalence from apparent prevalence obtained by testing pooled samples.

Usage

truePrevPools(x, n, SE = 1, SP = 1, prior = c(1, 1),
              nchains = 2, burnin = 10000, update = 10000,
              verbose = FALSE)

Arguments

x

The vector of indicator variables, indicating whether a pool was positive ("1") or negative ("0")

n

The vector of pool sizes

SE, SP

The prior distribution for sensitivity (SE) and specificity (SP); see 'Details' below for specification of these distributions

prior

The parameters of the prior Beta distribution for true prevalence; defaults to c(1, 1)

nchains

The number of chains used in the estimation process; nchains must be \ge 2

burnin

The number of discarded model iterations; defaults to 10,000

update

The number of withheld model iterations; defaults to 10,000

verbose

Logical flag, indicating if JAGS process output should be printed to the R console; defaults to FALSE

Details

truePrevPools calls on JAGS/rjags to estimate the true prevalence from the apparent prevalence in a Bayesian framework. The default model, in BUGS language, is given below. To see the actual fitted model, see the model slot of the prev-object.

  model {
    for (i in 1:N) {
      x[i] ~ dbern(AP[i])
      AP[i] <- SEpool[i] * (1 - pow(1 - TP, n[i])) + (1 - SPpool[i]) * pow(1 - TP, n[i])
      SEpool[i] <- 1 - (pow(1 - SE, n[i] * TP) * pow(SP, n[i] * (1 - TP)))
      SPpool[i] <- pow(SP, n[i])
    }
  # SE ~ user-defined (see below)
  # SP ~ user-defined (see below)
  TP ~ dbeta(prior[1], prior[2])
  }
  

The test sensitivity (SE) and specificity (SP) can be specified by the user, independently, as one of "fixed", "uniform", "beta", "pert", or "beta-expert", with "fixed" as the default. Note that SE and SP must correspond to the test characteristics for testing individual samples; truePrevPools will calculate SEpool and SPpool, the sensitivity and specificitiy for testing pooled samples, based on Boelaert et al. (2000).

Distribution parameters can be specified in a named list() as follows:

• Fixed: list(dist = "fixed", par)

• Uniform: list(dist = "uniform", min, max)

• Beta: list(dist = "beta", alpha, beta)

• PERT: list(dist = "pert", method, a, m, b, k)
'method' must be "classic" or "vose";
  'a' denotes the pessimistic (minimum) estimate, 'm' the most likely estimate, and 'b' the optimistic (maximum) estimate;
  'k' denotes the scale parameter.
  See betaPERT for more information on Beta-PERT parametrization.

• Beta-Expert: list(dist = "beta-expert", mode, mean, lower, upper, p)
'mode' denotes the most likely estimate, 'mean' the mean estimate;
  'lower' denotes the lower bound, 'upper' the upper bound;
  'p' denotes the confidence level of the expert.
  Only mode or mean should be specified; lower and upper can be specified together or alone.
  See betaExpert for more information on Beta-Expert parameterization.

For Uniform, Beta and Beta-PERT distributions, BUGS-style short-hand notation is also allowed:

• Uniform: ~dunif(min, max)

• Beta: ~dbeta(alpha, beta)

• Beta-PERT: ~dpert(min, mode, max)

Value

An object of class prev.

Note

Markov chain Monte Carlo sampling in truePrevPools is performed by JAGS (Just Another Gibbs Sampler) through the rjags package. JAGS can be downloaded from https://mcmc-jags.sourceforge.io/.

Author(s)

Brecht Devleesschauwer <[e-mail]>

References

• Speybroeck N, Williams CJ, Lafia KB, Devleesschauwer B, Berkvens D (2012) Estimating the prevalence of infections in vector populations using pools of samples. Med Vet Entomol 26:361-371

• Boelaert F, Walravens K, Biront P, Vermeersch JP, Berkvens D, Godfroid J (2000) Prevalence of paratuberculosis (Johne's disease) in the Belgian cattle population. Vet Microbiol 77:269-281

See Also

coda for various functions that can be applied to the prev@mcmc object
truePrev: estimate true prevalence from apparent prevalence obtained by testing individual samples with a single test
truePrevMulti: estimate true prevalence from apparent prevalence obtained by testing individual samples with multiple tests, using a conditional probability scheme
truePrevMulti2: estimate true prevalence from apparent prevalence obtained by testing individual samples with multiple tests, using a covariance scheme
betaPERT: calculate the parameters of a Beta-PERT distribution
betaExpert: calculate the parameters of a Beta distribution based on expert opinion

Examples

## Sandflies in Aurabani, Nepal, 2007
pool_results <- c(0, 0, 0, 0, 0, 0, 0, 0, 1, 0)
pool_sizes <- c(2, 1, 6, 10, 1, 7, 1, 4, 1, 3)

## Sensitivity ranges uniformly between 60% and 95%
## Specificity is considered to be 100%

#> BUGS-style:
truePrevPools(x = pool_results, n = pool_sizes,
              SE = ~dunif(0.60, 0.95), SP = 1)
			  
#> list-style:
SE <- list(dist = "uniform", min = 0.60, max = 0.95)
truePrevPools(x = pool_results, n = pool_sizes,
              SE = SE, SP = 1)