mirror of
https://github.com/msberends/AMR.git
synced 2025-07-10 19:41:55 +02:00
(v2.1.1.9133) update math formulae
This commit is contained in:
@ -232,48 +232,26 @@ You can also use functions from specific 'table reporting' packages to transform
|
||||
}
|
||||
\section{Why Use WISCA?}{
|
||||
|
||||
WISCA, as outlined by Barbieri \emph{et al.} (\doi{10.1186/s13756-021-00939-2}), stands for
|
||||
Weighted-Incidence Syndromic Combination Antibiogram, which estimates the probability
|
||||
of adequate empirical antimicrobial regimen coverage for specific infection syndromes.
|
||||
This method leverages a Bayesian hierarchical logistic regression framework with random
|
||||
effects for pathogens and regimens, enabling robust estimates in the presence of sparse
|
||||
data.
|
||||
|
||||
The Bayesian model assumes conjugate priors for parameter estimation. For example, the
|
||||
coverage probability \ifelse{latex}{\deqn{$theta$}}{$theta$} for a given antimicrobial regimen
|
||||
is modeled using a Beta distribution as a prior:
|
||||
WISCA, as outlined by Barbieri \emph{et al.} (\doi{10.1186/s13756-021-00939-2}), stands for Weighted-Incidence Syndromic Combination Antibiogram, which estimates the probability of adequate empirical antimicrobial regimen coverage for specific infection syndromes. This method leverages a Bayesian hierarchical logistic regression framework with random effects for pathogens and regimens, enabling robust estimates in the presence of sparse data.
|
||||
|
||||
\ifelse{latex}{\deqn{$theta$ \sim \text{Beta}($alpha$_0, $beta$_0)}}{
|
||||
\ifelse{html}{\figure{beta_prior.png}{options: width="300" alt="Beta prior"}}{$theta$ ~ Beta($alpha$_0, $beta$_0)}}
|
||||
The Bayesian model assumes conjugate priors for parameter estimation. For example, the coverage probability \eqn{\theta} for a given antimicrobial regimen is modelled using a Beta distribution as a prior:
|
||||
|
||||
where \eqn{$alpha$_0} and \eqn{$beta$_0} represent prior successes and failures, respectively,
|
||||
informed by expert knowledge or weakly informative priors (e.g., \eqn{$alpha$_0 = 1, $beta$_0 = 1}).
|
||||
\deqn{\theta \sim \text{Beta}(\alpha_0, \beta_0)}
|
||||
|
||||
The likelihood function is constructed based on observed data, where the number of covered
|
||||
cases for a regimen follows a binomial distribution:
|
||||
where \eqn{\alpha_0} and \eqn{\beta_0} represent prior successes and failures, respectively, informed by expert knowledge or weakly informative priors (e.g., \eqn{\alpha_0 = 1, \beta_0 = 1}). The likelihood function is constructed based on observed data, where the number of covered cases for a regimen follows a binomial distribution:
|
||||
|
||||
\ifelse{latex}{\deqn{y \sim \text{Binomial}(n, $theta$)}}{
|
||||
\ifelse{html}{\figure{binomial_likelihood.png}{options: width="300" alt="Binomial likelihood"}}{y ~ Binomial(n, $theta$)}}
|
||||
\deqn{y \sim \text{Binomial}(n, \theta)}
|
||||
|
||||
Posterior parameter estimates are obtained by combining the prior and likelihood using
|
||||
Bayes' theorem. The posterior distribution of \eqn{$theta$} is also a Beta distribution:
|
||||
Posterior parameter estimates are obtained by combining the prior and likelihood using Bayes' theorem. The posterior distribution of \eqn{\theta} is also a Beta distribution:
|
||||
|
||||
\ifelse{latex}{\deqn{$theta$ | y \sim \text{Beta}($alpha$_0 + y, $beta$_0 + n - y)}}{
|
||||
\ifelse{html}{\figure{posterior_beta.png}{options: width="300" alt="Beta posterior"}}{$theta$ | y ~ Beta($alpha$_0 + y, $beta$_0 + n - y)}}
|
||||
\deqn{\theta | y \sim \text{Beta}(\alpha_0 + y, \beta_0 + n - y)}
|
||||
|
||||
For hierarchical modeling, pathogen-level effects (e.g., differences in resistance
|
||||
patterns) and regimen-level effects are modelled using Gaussian priors on log-odds.
|
||||
This hierarchical structure ensures partial pooling of estimates across groups,
|
||||
improving stability in strata with small sample sizes. The model is implemented using
|
||||
Hamiltonian Monte Carlo (HMC) sampling.
|
||||
For hierarchical modelling, pathogen-level effects (e.g., differences in resistance patterns) and regimen-level effects are modelled using Gaussian priors on log-odds. This hierarchical structure ensures partial pooling of estimates across groups, improving stability in strata with small sample sizes. The model is implemented using Hamiltonian Monte Carlo (HMC) sampling.
|
||||
|
||||
Stratified results are provided based on covariates such as age, sex, and clinical
|
||||
complexity (e.g., prior antimicrobial treatments or renal/urological comorbidities).
|
||||
For example, posterior odds ratios (ORs) are derived to quantify the effect of these
|
||||
covariates on coverage probabilities:
|
||||
Stratified results can be provided based on covariates such as age, sex, and clinical complexity (e.g., prior antimicrobial treatments or renal/urological comorbidities) using \code{dplyr}'s \code{\link[=group_by]{group_by()}} as a pre-processing step before running \code{\link[=wisca]{wisca()}}. In this case, posterior odds ratios (ORs) are derived to quantify the effect of these covariates on coverage probabilities:
|
||||
|
||||
\ifelse{latex}{\deqn{\text{OR}_{\text{covariate}} = \frac{\exp($beta$_{\text{covariate}})}{\exp($beta$_0)}}}{
|
||||
\ifelse{html}{\figure{odds_ratio.png}{options: width="300" alt="Odds ratio formula"}}{OR_covariate = exp(beta_covariate) / exp(beta_0)}}
|
||||
\deqn{\text{OR}_{\text{covariate}} = \frac{\exp(\beta_{\text{covariate}})}{\exp(\beta_0)}}
|
||||
|
||||
By combining empirical data with prior knowledge, WISCA overcomes the limitations
|
||||
of traditional combination antibiograms, offering disease-specific, patient-stratified
|
||||
@ -360,7 +338,8 @@ antibiogram(example_isolates,
|
||||
|
||||
ureido <- antibiogram(example_isolates,
|
||||
antibiotics = ureidopenicillins(),
|
||||
ab_transform = "name"
|
||||
ab_transform = "name",
|
||||
wisca = TRUE
|
||||
)
|
||||
|
||||
# in an Rmd file, you would just need to return `ureido` in a chunk,
|
||||
@ -394,3 +373,6 @@ plot(ab1)
|
||||
plot(ab2)
|
||||
}
|
||||
}
|
||||
\author{
|
||||
Implementation: Dr. Larisse Bolton and Dr. Matthijs Berends
|
||||
}
|
||||
|
Reference in New Issue
Block a user