---
title: "Estimating Empirical Coverage with WISCA"
output: 
  rmarkdown::html_vignette:
    toc: true
    toc_depth: 3
vignette: >
  %\VignetteIndexEntry{Estimating Empirical Coverage with WISCA}
  %\VignetteEncoding{UTF-8}
  %\VignetteEngine{knitr::rmarkdown}
editor_options: 
  chunk_output_type: console
---

```{r setup, include = FALSE}
knitr::opts_chunk$set(
  warning = FALSE,
  collapse = TRUE,
  comment = "#>",
  fig.width = 7.5,
  fig.height = 5
)
```

## 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 in **AMR**.

---

## 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:
- 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 = ∑ (pathogen incidence × susceptibility)

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

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:
- K be the number of pathogens,
- ``` α = (1, 1, ..., 1) be a **Dirichlet** prior (uniform),
- ``` n = (n₁, ..., nₖ) be the observed counts per species.

Then the posterior incidence follows:

``` incidence ∼ Dirichlet(α + n)

In simulations, we draw from this posterior using:

``` xᵢ ∼ Gamma(αᵢ + nᵢ, 1)

``` incidenceᵢ = xᵢ / ∑ xⱼ

---

### Susceptibility

Each pathogen–regimen pair has:
- ``` prior: Beta(1, 1)
- ``` data: S susceptible out of N tested

Then:

``` susceptibility ∼ Beta(1 + S, 1 + (N - S))

In each simulation, we draw random susceptibility per species from this Beta distribution.

---

### Final coverage estimate

Putting it together:

``` For each simulation:
    - Draw incidence ∼ Dirichlet
    - Draw susceptibility ∼ Beta
    - Multiply → coverage estimate

We repeat this (e.g. 1000×) and summarise:
- **Mean**: expected coverage
- **Quantiles**: credible interval (default 95%)

---

## Practical use in AMR

### Simulate a synthetic syndrome

```{r}
library(AMR)
data <- example_isolates

# Add a fake syndrome column for stratification
data$syndrome <- ifelse(data$mo %like% "coli", "UTI", "Other")

```

### Basic WISCA antibiogram

```{r}
antibiogram(data,
            wisca = TRUE)
```

### Stratify by syndrome

```{r}
antibiogram(data,
            syndromic_group = "syndrome",
            wisca = TRUE)
```

### Use combination regimens

The `antibiogram()` function supports combination regimens:

```{r}
antibiogram(data,
            antimicrobials = c("AMC", "GEN", "AMC + GEN", "CIP"),
            wisca = TRUE)
```

---

## Interpretation

Suppose you get this output:

| Regimen     | Coverage | Lower_CI | Upper_CI |
|-------------|----------|----------|----------|
| AMC         | 0.72     | 0.65     | 0.78     |
| AMC + GEN   | 0.88     | 0.83     | 0.93     |

Interpretation:

> *“AMC + GEN covers 88% of expected pathogens for this syndrome, with 95% certainty that the true coverage lies between 83% and 93%.”*

Regimens with few tested isolates will show **wider intervals**.

---

## Sensible defaults, but you can customise

- `minimum = 30`: exclude regimens with <30 isolates tested.
- `simulations = 1000`: number of Monte Carlo samples.
- `conf_interval = 0.95`: coverage interval width.
- `combine_SI = TRUE`: count “I”/“SDD” as susceptible.

---

## Limitations

- WISCA does not model time trends or temporal resistance shifts.
- It assumes data are representative of current clinical practice.
- It does not account for patient-level covariates (yet).
- Species-specific data are abstracted into syndrome-level estimates.

---

## Reference

Bielicki JA et al. (2016).  
*Weighted-incidence syndromic combination antibiograms to guide empiric treatment in pediatric bloodstream infections.*  
**J Antimicrob Chemother**, 71(2):529–536. doi:10.1093/jac/dkv397

---

## Conclusion

WISCA shifts empirical therapy from simple percent susceptible toward **probabilistic, syndrome-based decision support**. It is a statistically principled, clinically intuitive method to guide regimen selection — and easy to use via the `antibiogram()` function in the **AMR** package.

For antimicrobial stewardship teams, it enables **disease-specific, reproducible, and data-driven guidance** — even in the face of sparse data.