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Estimating Empirical Coverage with WISCA

Source: vignettes/WISCA.Rmd
WISCA.Rmd

This explainer was largely written by our AMR for R Assistant, a ChatGPT manually-trained model able to answer any question about the AMR package.

Introduction

Clinical guidelines for empirical antimicrobial therapy require probabilistic reasoning: what is the chance that a regimen will cover the likely infecting organisms, before culture results are available?

This is the purpose of WISCA, or Weighted-Incidence Syndromic Combination Antibiogram.

WISCA is a Bayesian approach that integrates:

  • Pathogen prevalence (how often each species causes the syndrome),
  • Regimen susceptibility (how often a regimen works if the pathogen is known),

to estimate the overall empirical coverage of antimicrobial regimens, with quantified uncertainty.

This vignette explains how WISCA works, why it is useful, and how to apply it using the AMR package.

Why traditional antibiograms fall short

A standard antibiogram gives you:

Species → Antibiotic → Susceptibility %

But clinicians don’t know the species a priori. They need to choose a regimen that covers the likely pathogens, without knowing which one is present.

Traditional antibiograms calculate the susceptibility % as just the number of resistant isolates divided by the total number of tested isolates. Therefore, traditional antibiograms:

  • Fragment information by organism,
  • Do not weight by real-world prevalence,
  • Do not account for combination therapy or sample size,
  • Do not provide uncertainty.

The idea of WISCA

WISCA asks:

“What is the probability that this regimen will cover the pathogen, given the syndrome?”

This means combining two things:

  • Incidence of each pathogen in the syndrome,
  • Susceptibility of each pathogen to the regimen.

We can write this as:

Coverage=∑i(Incidencei×Susceptibilityi)\text{Coverage} = \sum_i (\text{Incidence}_i \times \text{Susceptibility}_i)

For example, suppose:

  • E. coli causes 60% of cases, and 90% of E. coli are susceptible to a drug.
  • Klebsiella causes 40% of cases, and 70% of Klebsiella are susceptible.

Then:

Coverage=(0.6×0.9)+(0.4×0.7)=0.82\text{Coverage} = (0.6 \times 0.9) + (0.4 \times 0.7) = 0.82

But in real data, incidence and susceptibility are estimated from samples, so they carry uncertainty. WISCA models this probabilistically, using conjugate Bayesian distributions.

The Bayesian engine behind WISCA

Pathogen incidence

Let:

  • KK be the number of pathogens,
  • α=(1,1,…,1)\alpha = (1, 1, \ldots, 1) be a Dirichlet prior (uniform),
  • n=(n1,…,nK)n = (n_1, \ldots, n_K) be the observed counts per species.

Then the posterior incidence is:

p∼Dirichlet(α1+n1,…,αK+nK)p \sim \text{Dirichlet}(\alpha_1 + n_1, \ldots, \alpha_K + n_K)

To simulate from this, we use:

xi∼Gamma(αi+ni,1),pi=xi∑j=1Kxjx_i \sim \text{Gamma}(\alpha_i + n_i,\ 1), \quad p_i = \frac{x_i}{\sum_{j=1}^{K} x_j}

Susceptibility

Each pathogen–regimen pair has a prior and data:

  • Prior: Beta(α0,β0)\text{Beta}(\alpha_0, \beta_0), with default α0=β0=1\alpha_0 = \beta_0 = 1
  • Data: SS susceptible out of NN tested

The SS category could also include values SDD (susceptible, dose-dependent) and I (intermediate [CLSI], or susceptible, increased exposure [EUCAST]).

Then the posterior is:

θ∼Beta(α0+S,β0+N−S)\theta \sim \text{Beta}(\alpha_0 + S,\ \beta_0 + N - S)

Final coverage estimate

Putting it together:

  1. Simulate pathogen incidence: 𝐩∼Dirichlet\boldsymbol{p} \sim \text{Dirichlet}
  2. Simulate susceptibility: θi∼Beta(1+Si,1+Ri)\theta_i \sim \text{Beta}(1 + S_i,\ 1 + R_i)
  3. Combine:

Coverage=∑i=1Kpi⋅θi\text{Coverage} = \sum_{i=1}^{K} p_i \cdot \theta_i

Repeat this simulation (e.g. 1000×) and summarise:

  • Mean = expected coverage
  • Quantiles = credible interval

Practical use in the AMR package

Prepare data and simulate synthetic syndrome 

library(AMR)
data <- example_isolates

# Structure of our data
data
#> # A tibble: 2,000 × 46
#>    date       patient   age gender ward     mo           PEN   OXA   FLC   AMX  
#>    <date>     <chr>   <dbl> <chr>  <chr>    <mo>         <sir> <sir> <sir> <sir>
#>  1 2002-01-02 A77334     65 F      Clinical B_ESCHR_COLI   R     NA    NA    NA 
#>  2 2002-01-03 A77334     65 F      Clinical B_ESCHR_COLI   R     NA    NA    NA 
#>  3 2002-01-07 067927     45 F      ICU      B_STPHY_EPDR   R     NA    R     NA 
#>  4 2002-01-07 067927     45 F      ICU      B_STPHY_EPDR   R     NA    R     NA 
#>  5 2002-01-13 067927     45 F      ICU      B_STPHY_EPDR   R     NA    R     NA 
#>  6 2002-01-13 067927     45 F      ICU      B_STPHY_EPDR   R     NA    R     NA 
#>  7 2002-01-14 462729     78 M      Clinical B_STPHY_AURS   R     NA    S     R  
#>  8 2002-01-14 462729     78 M      Clinical B_STPHY_AURS   R     NA    S     R  
#>  9 2002-01-16 067927     45 F      ICU      B_STPHY_EPDR   R     NA    R     NA 
#> 10 2002-01-17 858515     79 F      ICU      B_STPHY_EPDR   R     NA    S     NA 
#> # ℹ 1,990 more rows
#> # ℹ 36 more variables: AMC <sir>, AMP <sir>, TZP <sir>, CZO <sir>, FEP <sir>,
#> #   CXM <sir>, FOX <sir>, CTX <sir>, CAZ <sir>, CRO <sir>, GEN <sir>,
#> #   TOB <sir>, AMK <sir>, KAN <sir>, TMP <sir>, SXT <sir>, NIT <sir>,
#> #   FOS <sir>, LNZ <sir>, CIP <sir>, MFX <sir>, VAN <sir>, TEC <sir>,
#> #   TCY <sir>, TGC <sir>, DOX <sir>, ERY <sir>, CLI <sir>, AZM <sir>,
#> #   IPM <sir>, MEM <sir>, MTR <sir>, CHL <sir>, COL <sir>, MUP <sir>, …

# Add a fake syndrome column
data$syndrome <- ifelse(data$mo %like% "coli", "UTI", "No UTI")

Basic WISCA antibiogram 

wisca(data,
      antimicrobials = c("AMC", "CIP", "GEN"))
Amoxicillin/clavulanic acid Ciprofloxacin Gentamicin
73.7% (71.7-75.8%) 77% (74.3-79.4%) 72.8% (70.7-74.8%)

Use combination regimens 

wisca(data,
      antimicrobials = c("AMC", "AMC + CIP", "AMC + GEN"))
Amoxicillin/clavulanic acid Amoxicillin/clavulanic acid + Ciprofloxacin Amoxicillin/clavulanic acid + Gentamicin
73.8% (71.8-75.7%) 87.5% (85.9-89%) 89.7% (88.2-91.1%)

Stratify by syndrome 

wisca(data,
      antimicrobials = c("AMC", "AMC + CIP", "AMC + GEN"),
      syndromic_group = "syndrome")
Syndromic Group Amoxicillin/clavulanic acid Amoxicillin/clavulanic acid + Ciprofloxacin Amoxicillin/clavulanic acid + Gentamicin
No UTI 70.1% (67.8-72.3%) 85.2% (83.1-87.2%) 87.1% (85.3-88.7%)
UTI 80.9% (77.7-83.8%) 88.2% (85.7-90.5%) 90.9% (88.7-93%)

The AMR package is available in 20 languages, which can all be used for the wisca() function too:

wisca(data,
      antimicrobials = c("AMC", "AMC + CIP", "AMC + GEN"),
      syndromic_group = gsub("UTI", "UCI", data$syndrome),
      language = "Spanish")
Grupo sindrómico Amoxicilina/ácido clavulánico Amoxicilina/ácido clavulánico + Ciprofloxacina Amoxicilina/ácido clavulánico + Gentamicina
No UCI 70% (67.8-72.4%) 85.3% (83.3-87.2%) 87% (85.3-88.8%)
UCI 80.9% (77.7-83.9%) 88.2% (85.5-90.6%) 90.9% (88.7-93%)

Sensible defaults, which can be customised

  • simulations = 1000: number of Monte Carlo draws
  • conf_interval = 0.95: coverage interval width
  • combine_SI = TRUE: count “I” and “SDD” as susceptible

Limitations

  • It assumes your data are representative
  • No adjustment for patient-level covariates, although these could be passed onto the syndromic_group argument
  • WISCA does not model resistance over time, you might want to use tidymodels for that, for which we wrote a basic introduction

Summary

WISCA enables:

  • Empirical regimen comparison,
  • Syndrome-specific coverage estimation,
  • Fully probabilistic interpretation.

It is available in the AMR package via either:

wisca(...)

antibiogram(..., wisca = TRUE)

Reference

Bielicki, JA, et al. (2016). Selecting appropriate empirical antibiotic regimens for paediatric bloodstream infections: application of a Bayesian decision model to local and pooled antimicrobial resistance surveillance data. J Antimicrob Chemother. 71(3):794-802. https://doi.org/10.1093/jac/dkv397