openEBGM: quantBisect – R documentation

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quantBisect

Find quantiles of the posterior distribution

Description

quantBisect finds the desired quantile of the posterior distribution using the bisection method. Used to create credibility limits.

Usage

quantBisect(
  percent,
  theta_hat,
  N,
  E,
  qn,
  digits = 2,
  limits = c(-1e+05, 1e+05),
  max_iter = 2000
)

Arguments

`percent`	A numeric scalar between 1 and 99 for the desired percentile (e.g., 5 for 5th percentile).
`theta_hat`	A numeric vector of hyperparameter estimates (likely from `autoHyper` or from directly minimizing `negLLsquash`) ordered as: α_1, β_1, α_2, β_2, P.
`N`	A whole number vector of actual counts from `processRaw`.
`E`	A numeric vector of expected counts from `processRaw`.
`qn`	A numeric vector of posterior probabilities that λ came from the first component of the mixture, given N = n (i.e., the mixture fraction). See function `Qn`.
`digits`	A scalar whole number that determines the number of decimal places used when rounding the results.
`limits`	A whole number vector of length 2 for the upper and lower bounds of the search space.
`max_iter`	A whole number scalar for the maximum number of iterations. Used to prevent infinite loops.

Details

The hyperparameter estimates (theta_hat) are:

α_1, β_1: Parameter estimates of the first component of the prior distribution
α_2, β_2: Parameter estimates of the second component
P: Mixture fraction estimate of the prior distribution

Although this function can find any quantile of the posterior distribution, it will often be used to calculate the 5th and 95th percentiles to create a 90% credibility interval.

The quantile is calculated by solving for x in the general equation F(x) = cutoff, or equivalently, F(x) - cutoff = 0, where F(x) is the cumulative distribution function of the posterior distribution and cutoff is the appropriate cutoff level (e.g., 0.05 for the 5th percentile).

Value

A numeric vector of quantile estimates.

Warning

The digits argument determines the tolerance for the bisection algorithm. The more decimal places you want returned, the longer the run time.

Examples

theta_init <- data.frame(
  alpha1 = c(0.2, 0.1),
  beta1  = c(0.1, 0.1),
  alpha2 = c(2,   10),
  beta2  = c(4,   10),
  p      = c(1/3, 0.2)
)
data(caers)
proc <- processRaw(caers)
squashed <- squashData(proc, bin_size = 100, keep_pts = 100)
squashed <- squashData(squashed, count = 2, bin_size = 10, keep_pts = 20)
suppressWarnings(
  theta_hat <- autoHyper(data = squashed, theta_init = theta_init)$estimates
)
qn <- Qn(theta_hat, N = proc$N, E = proc$E)
proc$QUANT_05 <- quantBisect(percent = 5, theta = theta_hat, N = proc$N,
                             E = proc$E, qn = qn)
proc$QUANT_95 <- quantBisect(percent = 95, theta = theta_hat, N = proc$N,
                             E = proc$E, qn = qn)
head(proc)

openEBGM

EBGM Disproportionality Scores for Adverse Event Data Mining

v0.8.3

GPL-2 | GPL-3

Authors

John Ihrie [cre, aut], Travis Canida [aut], Ismaïl Ahmed [ctb] (author of 'PhViD' package (derived code)), Antoine Poncet [ctb] (author of 'PhViD'), Sergio Venturini [ctb] (author of 'mederrRank' package (derived code)), Jessica Myers [ctb] (author of 'mederrRank')

Initial release