R/margins.R
get_margin_Bayesian.RdAs well as comparing against a threshold, the function
get_prevalence() can be used to estimate a Bayesian credible
interval (CrI) on the prevalence. This function returns the margin of error
(MOE) we can expect via this method, in terms of the expected lower and
upper limits of our credible interval (CrI).
get_margin_Bayesian(
N,
prevalence = 0.2,
ICC = 0.05,
alpha = 0.05,
prior_prev_shape1 = 1,
prior_prev_shape2 = 1,
prior_ICC_shape1 = 1,
prior_ICC_shape2 = 9,
CrI_type = "HDI",
n_intervals = 20,
round_digits = 2,
reps = 100,
use_cpp = TRUE,
return_full = FALSE,
silent = FALSE
)vector of the number of samples obtained from each cluster.
assumed true prevalence of pfhrp2/3 deletions as a proportion between 0 and 1.
assumed true intra-cluster correlation (ICC) as a value between 0 and 1.
the significance level of the credible interval - for example,
use alpha = 0.05 for a 95% interval. See also CrI_type
argument for how this is calculated.
parameters that dictate the shape of the Beta priors on prevalence and the ICC. See the Wikipedia page on the Beta distribution for more detail. The default values of these parameters were chosen based on an analysis of historical pfhrp2/3 studies, although this does not guarantee that they will be suitable in all settings.
which method to use when computing credible intervals.
Options are "ETI" (equal-tailed interval) or "HDI" (high-density interval).
The ETI searches a distance alpha/2 from either side of the [0,1]
interval. The HDI method returns the narrowest interval that subtends a
proportion 1-alpha of the distribution. The HDI method is used by
default as it guarantees that the MAP estimate is within the credible
interval, which is not always the case for the ETI.
the number of intervals used in the adaptive quadrature method. Increasing this value gives a more accurate representation of the true posterior, but comes at the cost of reduced speed.
the number of digits after the decimal point that are used when reporting estimates. This is to simplify results and to avoid giving the false impression of extreme precision.
number of times to repeat simulation per parameter combination.
if TRUE (the default) then use an Rcpp implementation
of the adaptive quadrature approach that is much faster than the base R
method.
if TRUE then return the complete distribution of
lower and upper CrI limits in a data.frame. If FALSE (the default)
return a summary including the mean and 95% CI of these limits.
if TRUE then suppress all console output.
If return_full = FALSE (the default) returns an estimate of
the lower and upper CrI limit in the form of a data.frame. The first row
gives the lower limit, the second row gives the upper limit, both as
percentages. The first column gives the point estimate, the subsequent
columns give the 95% CI on this estimate. If return_full = TRUE
then returns a complete data.frame of all lower and upper CI realisations over simulations.
Estimates MOE using the following approach:
Simulate data via the function rbbinom_reparam() using known
values, e.g. a known "true" prevalence and intra-cluster correlation.
Analyse data using get_prevalence(). Determine the upper and
lower limits of the credible interval.
Repeat steps 1-2 reps times to obtain the distribution of upper
and lower limits. Return the mean of this distribution along with upper and
lower 95% CIs. To be completely clear, we are producing a 95% CI on the
limits of a CrI, which can be confusing! See Value for a clear
explanation of how to interpret the output.
Note that we have not implemented a function to return the sample size
needed to achieve a given MOE under the Bayesian model, as this would
require repeated simulation over different values of N which is
computationally costly. The appropriate value can be established manually if
needed by running get_margin_Bayesian() for different sample sizes.
get_margin_Bayesian(N = c(120, 90, 150), prevalence = 0.15, ICC = 0.01 , reps = 1e2)
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#> estimate CI_2.5 CI_97.5
#> lower 7.8304 7.425267 8.235533
#> upper 29.0967 28.398922 29.794478