mcmodule

Modular Monte-Carlo Risk Analysis

Introduction

mcmodule is a framework for building modular Monte Carlo risk analysis models. It extends the capabilities of mc2d to make working with multiple risk pathways, variates, and scenarios easier. It was developed by epidemiologists, for the farmrisk project, and now it aims to help epidemiologists and other risk modellers save time and evaluate ambitious, complex risk pathways in R.

The mc2d R package (Pouillot and Delignette-Muller 2010) provides tools to build and analyse models involving multiple variables and uncertainties based on Monte Carlo simulations. The mcmodule package includes additional tools to:

1. Organize risk analysis in independent flexible modules
2. Perform multivariate mcnode operations
3. Automate the creation of mcnodes
4. visualise risk analysis models

Multivariate Monte-Carlo simulations

Quantitative risk analysis is the numerical assessment of risk to facilitate decision making in the face of uncertainty. Monte Carlo simulation is a technique used to model and analyse uncertainty (Vose 2008).

In mc2d, parameters are stored as mcnode class objects. These objects are arrays of numbers that represent random variables and have three dimensions: variability × uncertainty × variates. For more information, see the mc2d package vignette.

In the mcmodule framework an mcnode is an array of dimensions (u × 1 × i):

• We combine variability and uncertainty into one dimension¹ (u)

• We use variates (representing different groups or categories) in the other dimension (i)

• The variables that define and distinguish these variates are called keys and are stored as metadata

In this document we will use the term “uncertainty dimension” to refer to the combined dimension of variability and uncertainty.

Example

If we are buying a number of cows and heifers from a specific region, an mcnode for herd prevalence would have:

• Multiple variates (rows), defined by two keys: “animal category” and “pathogen”

• Probability values generated through a PERT distribution, using minimum, mode, and maximum parameters across u iterations (columns) to model the uncertainty in these estimates

An mcnode representing herd prevalence of three pathogens, tuberculosis (TB), infectious bovine rhinotracheitis (IBR), and bovine viral diarrhoea (BVD), and two animal categories (cows and heifers). The herd prevalence is the same for both animal categories, but values differ due to the stochastic nature of random sampling from the PERT distribution.

Risk assessment

This section provides a brief introduction to risk assessment in R. Although this package is not intended for beginners in risk assessment, it can help you understand the logic behind mcmodule and its purpose.

A simple risk assessment

Consider a scenario where we need to purchase a cow from a farm that we know is infected with a disease our farm is free from. To reduce the risk of introducing the disease to our farm, we plan to perform a diagnostic test on the cow before bringing it to our farm. We want to calculate the probability of introducing the disease by purchasing one cow that tests negative.

We have an estimation (with some uncertainty) of both the probability of animal infection within a herd and the test sensitivity, so we want to conduct a stochastic risk assessment that properly accounts for this uncertainty.

The risk assessment for our cattle purchase can be performed using base R (2024) random sampling functions, or mc2d (Pouillot and Delignette-Muller 2010), a package provides additional probability distributions (such as rpert) and other useful tools for analysing stochastic (Monte-Carlo) simulations.

library(mc2d)
set.seed(123)
n_iterations <- 10000

# Within-herd prevalence
w_prev <- mcstoc(runif,
  min = 0.15, max = 0.2,
  nsu = n_iterations, type = "U"
)
# Test sensitivity
test_sensi <- mcstoc(rpert,
  min = 0.89, mode = 0.9, max = 0.91,
  nsu = n_iterations, type = "U"
)
# Probability an animal is tested in origin
test_origin <- mcdata(1, type = "0") # Yes


# EXPRESSIONS
# Probability that an animal in an infected herd is infected (a = animal)
infected <- w_prev
# Probability an animal is tested and is a false negative
# (test specificity assumed to be 100%)
false_neg <- infected * test_origin * (1 - test_sensi)
# Probability an animal is not tested
no_test <- infected * (1 - test_origin)
# Probability an animal is not detected
no_detect <- false_neg + no_test

mc_model <- mc(
  w_prev, infected, test_origin, test_sensi,
  false_neg, no_test, no_detect
)

# RESULT
hist(mc_model)

no_detect
#>   node    mode nsv   nsu nva variate    min   mean median    max Nas type outm
#> 1    x numeric   1 10000   1       1 0.0138 0.0175 0.0174 0.0218   0    U each

Multiple risk assessments at once

In the previous example, we calculated the risk for one specific case. However, we know that this farm is also positive for pathogen B, so it would be also interesting to calculate the risk of introducing it as well. Pathogen B has different within-herd prevalence and test sensitivity than Pathogen A.

To estimate the risk for both pathogens with our previous models, we could:

• Copy and paste the code twice with different parameters (against all good coding practices)

• Wrap the code in a function and call it twice using each pathogen’s parameters as arguments

• Create a loop

While these options work, they become messy or computationally intensive when the number of parameters or different situations to simulate increases.

The package mc2d offers a clever solution to this scalability problem: variates. In the previous example, our stochastic nodes only had uncertainty dimension. However, we can now use the variates dimension to calculate the risk of introduction of both pathogens at the same time.

set.seed(123)
n_iterations <- 10000

# Within-herd prevalence
w_prev_min <- mcdata(c(a = 0.15, b = 0.45), nvariates = 2, type = "0")
w_prev_max <- mcdata(c(a = 0.2, b = 0.6), nvariates = 2, type = "0")

w_prev <- mcstoc(runif,
  min = w_prev_min, max = w_prev_max,
  nsu = n_iterations, nvariates = 2, type = "U"
)

# Test sensitivity
test_sensi_min <- mcdata(c(a = 0.89, b = 0.80), nvariates = 2, type = "0")
test_sensi_mode <- mcdata(c(a = 0.9, b = 0.85), nvariates = 2, type = "0")
test_sensi_max <- mcdata(c(a = 0.91, b = 0.90), nvariates = 2, type = "0")

test_sensi <- mcstoc(rpert,
  min = test_sensi_min,
  mode = test_sensi_mode, max = test_sensi_max,
  nsu = n_iterations, nvariates = 2, type = "U"
)

# Probability an animal is tested in origin
test_origin <- mcdata(c(a = 1, b = 1), nvariates = 2, type = "0")


# EXPRESSIONS
# Probability that an animal in an infected herd is infected (a = animal)
infected <- w_prev
# Probability an animal is tested and is a false negative
# (test specificity assumed to be 100%)
false_neg <- infected * test_origin * (1 - test_sensi)
# Probability an animal is not tested
no_test <- infected * (1 - test_origin)
# Probability an animal is not detected
no_detect <- false_neg + no_test

mc_model <- mc(
  w_prev, infected, test_origin, test_sensi,
  false_neg, no_test, no_detect
)

# RESULT
no_detect
#>   node    mode nsv   nsu nva variate    min   mean median    max Nas type outm
#> 1    x numeric   1 10000   2       1 0.0139 0.0175 0.0174 0.0217   0    U each
#> 2    x numeric   1 10000   2       2 0.0477 0.0787 0.0783 0.1178   0    U each

When to use mcmodule?

The mc2d multivariate approach works well for basic multivariate risk analysis. However, if instead of purchasing one cow, you’re dealing with multiple cattle purchases, from different farms, across different pathogens, scenarios, and age categories, or modelling multiple risk pathways with different what-if scenarios, this approach becomes unwieldy.

mcmodule addresses these challenges by providing functions for multivariate operations and modular management of the risk model. It automates the process of creating mcnodes and assigns metadata to them (making it easy to identify which variate corresponds to which data row). Thanks to this mcnode metadata, it enables row-matching between nodes with different variates, combines probabilities across variates, and calculates multilevel trials. As your risk analysis grows, you can create separate modules for different pathways, each with independent parameters, expressions, and scenarios that can later be connected into a complete model.

This package is particularly useful for:

• Working with complex models that involve multiple pathways, pathogens, or scenarios simultaneously

• Dealing with large parameter sets (hundreds or thousands of parameters)

• Handling different numbers of variates across different parts of your model that need to be combined

• Creating modular risk assessments where different components need to be developed independently but later integrated (for example in collaborative projects)

• Performing sophisticated sensitivity analyses across multiple model components

However, for simpler analyses, such as single pathway models, exploratory work, small models with few parameters, one-off analyses or learning risk assessment mcmodule’s additional structure may be unnecessary.

Installing mcmodule

Now, let’s explore the package! We can install it from CRAN:

install.packages("mcmodule")
library("mcmodule")

Or install latest development version from GitHub (requires devtool package):

# install.packages("devtools")
devtools::install_github("NataliaCiria/mcmodule")
library("mcmodule")

Other recommended packages to load along with mcmodule are:

# install.packages(c("dplyr","ggplot2","igraph","visNetwork"))
library(dplyr) # Data manipulation
library(igraph) # Network analysis
library(visNetwork) # Interactive network visualization

Building an mcmodule

To quickly understand the key components of an mcmodule, we’ll start by building one using the animal imports example included in the package.

Data

Let’s consider a scenario where we want to evaluate the risk of introducing pathogen A and pathogen B into our region from animal imports from different regions (north, south, east, and west). We have gathered the following data:

• animal_imports: number of animal imports with their mean and standard deviation values per region, and the number of exporting farms in each region.

  animal_imports
  #>   origin farms_n animals_n_mean animals_n_sd
  #> 1   nord       5            100            6
  #> 2  south      10            130           10
  #> 3   east       7            140           12

• prevalence_region: estimates for both herd and within-herd prevalence ranges for pathogens A and B, as well as an indicator of how often tests are performed in origin

  prevalence_region
  #>   pathogen origin h_prev_min h_prev_max w_prev_min w_prev_max test_origin
  #> 1        a   nord       0.08       0.10       0.15        0.2   sometimes
  #> 2        a  south       0.02       0.05       0.15        0.2   sometimes
  #> 3        a   east       0.10       0.15       0.15        0.2       never
  #> 4        b   nord       0.50       0.70       0.45        0.6      always
  #> 5        b  south       0.25       0.30       0.37        0.4   sometimes
  #> 6        b   east       0.30       0.50       0.45        0.6     unknown

• test_sensitivity: estimates of test sensitivity values for pathogen A and B

  test_sensitivity
  #>   pathogen test_sensi_min test_sensi_mode test_sensi_max
  #> 1        a           0.89            0.90           0.91
  #> 2        b           0.80            0.85           0.90

Now we will use dplyr::left_join() to create our imports module data:

imports_data <- prevalence_region %>%
  left_join(animal_imports) %>%
  left_join(test_sensitivity) %>%
  relocate(pathogen, origin, test_origin)
#> Joining with `by = join_by(origin)`
#> Joining with `by = join_by(pathogen)`

Data keys

From now on we will use only the merged imports_data table. However, it is useful to understand which input dataset each parameter comes from, as each dataset provides information for different keys. In this context, keys are fields that (combined) uniquely identify each row in a table. In our example:

• animal_imports provided information by region of "origin"

• prevalence_region provided information by "pathogen" and region of "origin"

• test_sensitivity provided information by "pathogen" only

The resulting merged table, imports_data, will therefore have two keys: "pathogen" and "origin". However, not all parameters will use both keys, for example, "test_sensi" only has information by "pathogen". Knowing the keys for each parameter is crucial when performing multivariate operations, such as calculating totals.

To make these relationships explicit in the model, we need to provide the data keys. These are defined in a list with one element for each input dataset, specifying both the columns and the keys for each dataset.

imports_data_keys <- list(
  animal_imports = list(
    cols = names(animal_imports),
    keys = "origin"
  ),
  prevalence_region = list(
    cols = names(prevalence_region),
    keys = c("pathogen", "origin")
  ),
  test_sensitivity = list(
    cols = names(test_sensitivity),
    keys = "pathogen"
  )
)

mcnodes table

With values and keys established, we still need some information to build our stochastic parameters. The mcnode table specifies how to build mcnodes from the data table. It specifies which parameters are included in the model, the type of parameters (those with an mc_func are stochastic), and what columns to look for in the data table to build these mcnodes (the name of the mcnode, or another variable in the data columns), as well as transformations that are useful to encode categorical data values into mcnodes that must always be numeric.

• mcnode: Name of the Monte Carlo node (required)

• description: Description of the parameter

• mc_func: Probability distribution

• from_variable: Column name, if it comes from a column with a name different to the mcnode

• transformation: Transformation to be applied to the original column values

• sensi_baseline: Parameters for baseline mock distribution ²

• sensi_variation: OAT variation expression using value placeholder³

Here we have the imports_mctable for our example. While the mctable can be hard-coded in R, it’s more efficient to prepare it in a CSV or other external file. This approach also allows the table to be included as part of the model documentation.

mcnode	description	mc_func	from_variable	transformation	sensi_baseline	sensi_variation
h_prev	Herd prevalence	runif	NA	NA	min = 0.1, max = 0.3	pmin(1, pmax(0, value * 1.5))
w_prev	Within herd prevalence	runif	NA	NA	min = 0.1, max = 0.3	pmin(1, pmax(0, value * 1.5))
test_sensi	Test sensitivity	rpert	NA	NA	min = 0.7, mode = 0.85, max = 0.95	pmin(1, pmax(0, value * 1.5))
farms_n	Number of farms exporting animals	NA	NA	NA	value = 10	value * 1.5
animals_n	Number of animals exported per farm	rnorm	NA	NA	mean = 50, sd = 10	value * 1.5
test_origin_unk	Unknown probability of the animals being tested in origin (true = unknown)	NA	test_origin	value==“unknown”	value = “unknown”	ifelse(value == “unknown”, “always”, value)
test_origin	Probability of the animals being tested in origin	NA	NA	ifelse(value == “always”, 1, ifelse(value == “sometimes”, 0.5, ifelse(value == “never”, 0, NA)))	value = 0.5	pmin(1, pmax(0, value * 1.5))

The data table and the mctable must complement each other:

• mcnodes without an mc_func (like farms_n), needs the matching column name ("farms_n") in the data table

• mcnodes with an mc_func, you need columns for each probability distribution argument in the data table. For example:

  • h_prev with runif distribution requires "h_prev_min" and "h_prev_max"

  • animals_n with rnorm distribution requires "animals_n_mean" and "animals_n_sd"

For encoding categorical variables as mcnodes (or any other data transformation), you can use any R code with value as a placeholder for the mcnode name or column name (specified in from_variable)

Expressions

Finally, we need to write the model’s mathematical expression. These expressions should ideally include only arithmetic operations, not R functions (with some exceptions that will be covered later in “tricks and tweaks”). We’ll wrap them using quote() so they aren’t executed immediately but stored for later evaluation with eval_model().

imports_exp <- quote({
  # Probability that an animal in an infected herd is infected (a = animal)
  infected <- w_prev
  # Probability an animal is tested and is a false negative
  # (test specificity assumed to be 100%)
  false_neg <- infected * test_origin * (1 - test_sensi)
  # Probability an animal is not tested
  no_test <- infected * (1 - test_origin)
  # Probability an animal is not detected
  no_detect <- false_neg + no_test
})

Creating mcnodes within expressions

Starting with version 1.2.0, you can create mcnodes directly inside expressions using mcstoc() or mcdata() from the mc2d package. However, these functions do not behave exactly as they do in mc2d when used within mcmodule. Keep the following points in mind:

• Do not set nvariates. It is automatically set to match the number of rows in your data.
• Use type = "V" (variability, the default) or type = "0" (deterministic).
• All other mcstoc() and mcdata() arguments behave as documented in mc2d.

# Example expression with mcnodes created on-the-fly
imports_exp_inline <- quote({
  # Probability that an animal in an infected herd is infected
  infected <- w_prev
  
  # Create a clinic sensitivity parameter directly in the expression
  # (no need to specify nvariates, it's inferred from data rows)
  clinic_sensi <- mcstoc(runif, min = 0.6, max = 0.8)
  
  # Probability an animal is tested and is a false negative
  # Now accounting for both test sensitivity and clinic sensitivity
  false_neg <- infected * test_origin * (1 - test_sensi) * (1 - clinic_sensi)
  
  # Probability an animal is not tested but detected at clinic
  no_test <- infected * (1 - test_origin) * (1 - clinic_sensi)
  
  # Probability an animal is not detected
  no_detect <- false_neg + no_test
})

Evaluating an mcmodule

With all components in place, we’re now ready to create our first mcmodule using eval_module().

imports <- eval_module(
  exp = c(imports = imports_exp_inline),
  data = imports_data,
  mctable = imports_mctable,
  data_keys = imports_data_keys
)
#> imports evaluated
#> mcmodule created (expressions: imports)

class(imports)
#> [1] "mcmodule"

An mcmodule is an S3 object class, and it is essentially a list that contains all risk assessment components in a structured format.

names(imports)
#> [1] "data"      "exp"       "node_list"

The mcmodule contains the input data and mathematical expressions (exp) that ensure traceability. All input and calculated parameters are stored in node_list. Each node contains not only the mcnode itself but also important metadata: node type (input or output), source dataset and columns, keys, calculation method, and more. The specific metadata varies depending on the node’s characteristics. Here are a few examples:

imports$node_list$w_prev
#> $type
#> [1] "in_node"
#> 
#> $mc_func
#> [1] "runif"
#> 
#> $description
#> [1] "Within herd prevalence"
#> 
#> $inputs_col
#> [1] "w_prev_min" "w_prev_max"
#> 
#> $input_dataset
#> [1] "prevalence_region"
#> 
#> $keys
#> [1] "pathogen" "origin"  
#> 
#> $exp_name
#> [1] "imports"
#> 
#> $mc_name
#> [1] "w_prev"
#> 
#> $mcnode
#>   node    mode  nsv nsu nva variate  min  mean median max Nas type outm
#> 1    x numeric 1001   1   6       1 0.15 0.175  0.175 0.2   0    V each
#> 2    x numeric 1001   1   6       2 0.15 0.175  0.173 0.2   0    V each
#> 3    x numeric 1001   1   6       3 0.15 0.176  0.176 0.2   0    V each
#> 4    x numeric 1001   1   6       4 0.45 0.524  0.524 0.6   0    V each
#> 5    x numeric 1001   1   6       5 0.37 0.385  0.385 0.4   0    V each
#> 6    x numeric 1001   1   6       6 0.45 0.525  0.525 0.6   0    V each
#> 
#> $data_name
#> [1] "imports_data"
imports$node_list$no_detect
#> $function_call
#> [1] TRUE
#> 
#> $type
#> [1] "out_node"
#> 
#> $node_exp
#> [1] "false_neg + no_test"
#> 
#> $inputs
#> [1] "false_neg" "no_test"  
#> 
#> $exp_name
#> [1] "imports"
#> 
#> $mc_name
#> [1] "no_detect"
#> 
#> $keys
#> [1] "pathogen" "origin"  
#> 
#> $exp_param
#> [1] "false_neg" "no_test"  
#> 
#> $mcnode
#>   node    mode  nsv nsu nva variate    min   mean median    max Nas type outm
#> 1    x numeric 1001   1   6       1 0.0169 0.0288 0.0286 0.0435   0    V each
#> 2    x numeric 1001   1   6       2 0.0173 0.0288 0.0288 0.0433   0    V each
#> 3    x numeric 1001   1   6       3 0.0305 0.0522 0.0519 0.0795   0    V each
#> 4    x numeric 1001   1   6       4 0.0113 0.0237 0.0231 0.0415   0    V each
#> 5    x numeric 1001   1   6       5 0.0427 0.0665 0.0659 0.0936   0    V each
#> 6    x numeric 1001   1   6       6 0.0910 0.1566 0.1550 0.2357   0    V each
#> 
#> $data_name
#> [1] "imports_data"

And now that we have an mcmodule, we can begin exploring its possibilities!

Understanding mcnodes operations

When arithmetic operations are performed between nodes in mcmodule, they are applied on matching elements and keep the original dimensions, allowing uncertainties and variates to propagate through the calculations.

Working with an mcmodule

Visualizing

We can visualise an mc_module with the mc_network() function. For this, you will need to have igraph (Csardi and Nepusz 2006) and visNetwork (Almende B. V. and Benoit Thieurmel 2025) installed.

In these network visualizations, input datasets appear in blue, input data files, input columns and input mcnodes appear in different shades of dark-grey-blue, output mcnodes in green, and total mcnodes (as we will see later) in orange. The numbers displayed when clicked correspond to the median and the 95% confidence interval of the first variate of each mcnode.

mc_network(imports, legend = TRUE)

Summarizing

In the imports mcmodule, we can already see the raw mcnode results for the probability of an imported animal not being detected (no_detect). However, it’s difficult to determine which pathogen or region these results refer to. The mc_summary() function solves this problem by linking mcnode results with their key columns in the data.

Note that while the printed summary looks similar to the raw mcnode, it’s actually just a dataframe containing statistical measures, whereas the actual mcnode is a large array of numbers with dimensions (uncertainty × 1 × variates),

mc_summary(mcmodule = imports, mc_name = "no_detect")
#>     mc_name pathogen origin       mean          sd        Min       2.5%
#> 1 no_detect        a   nord 0.02876295 0.005883480 0.01687456 0.01875305
#> 2 no_detect        a  south 0.02876181 0.005994587 0.01726271 0.01870397
#> 3 no_detect        a   east 0.05221667 0.011010899 0.03050241 0.03392336
#> 4 no_detect        b   nord 0.02368331 0.005669560 0.01132022 0.01435750
#> 5 no_detect        b  south 0.06651522 0.012734194 0.04266336 0.04540683
#> 6 no_detect        b   east 0.15664447 0.033952337 0.09097242 0.09980820
#>          25%        50%        75%      97.5%        Max  nsv Na's
#> 1 0.02387016 0.02863349 0.03333063 0.03959466 0.04351491 1001    0
#> 2 0.02375014 0.02877089 0.03307491 0.04063392 0.04326582 1001    0
#> 3 0.04312578 0.05186702 0.06064605 0.07355557 0.07948500 1001    0
#> 4 0.01930997 0.02309890 0.02751195 0.03579437 0.04150531 1001    0
#> 5 0.05585011 0.06591137 0.07797919 0.08748444 0.09355962 1001    0
#> 6 0.12933887 0.15496802 0.18097518 0.22205690 0.23574153 1001    0

Filtering

Sometimes you may want to focus your analysis on specific subsets of your data, such as a particular pathogen or region. The mc_filter() function allows you to filter mcnodes based on conditions, similar to dplyr::filter().

Filtering a single condition

Let’s filter the no_detect node to only include results for pathogen “a”:

# Filter for pathogen a only
imports <- mc_filter(
  imports,
  "no_detect",
  pathogen == "a",
  name = "no_detect_pathogen_a"
)

# View the filtered results
imports$node_list$no_detect_pathogen_a$summary
#>                         mc_name pathogen origin       mean          sd
#> 1 no_detect_pathogen_a_filtered        a   nord 0.02876295 0.005883480
#> 2 no_detect_pathogen_a_filtered        a  south 0.02876181 0.005994587
#> 3 no_detect_pathogen_a_filtered        a   east 0.05221667 0.011010899
#>          Min       2.5%        25%        50%        75%      97.5%        Max
#> 1 0.01687456 0.01875305 0.02387016 0.02863349 0.03333063 0.03959466 0.04351491
#> 2 0.01726271 0.01870397 0.02375014 0.02877089 0.03307491 0.04063392 0.04326582
#> 3 0.03050241 0.03392336 0.04312578 0.05186702 0.06064605 0.07355557 0.07948500
#>    nsv Na's
#> 1 1001    0
#> 2 1001    0
#> 3 1001    0

Filtering with multiple conditions

You can also apply multiple filter conditions at once. For example, to analyze only pathogen “b” from the “nord” region:

# Filter for pathogen b from nord region
imports <- mc_filter(
  imports,
  "no_detect",
  pathogen == "b",
  origin == "nord",
  name = "no_detect_b_nord"
)

# View the filtered results
imports$node_list$no_detect_b_nord$summary
#>                     mc_name pathogen origin       mean         sd        Min
#> 4 no_detect_b_nord_filtered        b   nord 0.02368331 0.00566956 0.01132022
#>        2.5%        25%       50%        75%      97.5%        Max  nsv Na's
#> 4 0.0143575 0.01930997 0.0230989 0.02751195 0.03579437 0.04150531 1001    0

The filtered nodes maintain all the metadata from the original node and can be used in subsequent calculations just like any other node in the mcmodule.

Calculating totals

Most of the following probability calculations are based on Chapter 5 of the Handbook on Import Risk Analysis for Animals and Animal Products Volume 2. Quantitative risk assessment (Murray 2004). More details can be found on the Multivariate operations vignette.

Single-level trials

In imports, we know the probability that an infected animal from an infected farm goes undetected ("no_detect"). We can use the total number of animals selected per farm ("animals_n") as the number of trials (trials_n) to determine the probability that at least one infected animal from an infected farm is not detected (no_detect_set).

In single-level trials, each trial is independent with the same probability of success ($trial\_p$). For a set of $trials\_n$ trials, the probability of at least one success is:

$$set\_p= 1-(1-trial\_p)^{trials\_n}$$

# Probability of at least one imported animal from an infected herd is not detected
imports <- trial_totals(
  mcmodule = imports,
  mc_names = "no_detect",
  trials_n = "animals_n",
  mctable = imports_mctable
)

The trial_totals() function returns the mcmodule with some additional nodes: the probability of at least one success and the expected number of successes. These total nodes have special metadata fields, and always include a summary by default.

# Probability of at least one
imports$node_list$no_detect_set$summary
#>         mc_name pathogen origin      mean           sd       Min      2.5%
#> 1 no_detect_set        a   nord 0.9353649 3.883557e-02 0.7861311 0.8430134
#> 2 no_detect_set        a  south 0.9688685 2.434001e-02 0.8521708 0.9053670
#> 3 no_detect_set        a   east 0.9982705 2.713104e-03 0.9779484 0.9896240
#> 4 no_detect_set        b   nord 0.8925258 5.809912e-02 0.6801729 0.7620536
#> 5 no_detect_set        b  south 0.9994921 8.394029e-04 0.9937705 0.9971897
#> 6 no_detect_set        b   east 0.9999999 1.007295e-06 0.9999716 0.9999996
#>         25%       50%       75%     97.5%       Max  nsv Na's
#> 1 0.9110563 0.9449214 0.9664750 0.9839338 0.9903200 1001    0
#> 2 0.9556170 0.9767071 0.9875921 0.9960537 0.9987422 1001    0
#> 3 0.9978473 0.9994127 0.9998526 0.9999866 0.9999976 1001    0
#> 4 0.8568207 0.9028213 0.9383441 0.9732375 0.9913663 1001    0
#> 5 0.9993476 0.9998565 0.9999701 0.9999948 0.9999994 1001    0
#> 6 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1001    0

# Expected number of animals
imports$node_list$no_detect_set_n$summary
#>           mc_name pathogen origin      mean        sd      Min      2.5%
#> 1 no_detect_set_n        a   nord  2.881746 0.6124382 1.529033  1.833821
#> 2 no_detect_set_n        a  south  3.740006 0.8357107 1.894541  2.335889
#> 3 no_detect_set_n        a   east  7.330762 1.6711952 3.754963  4.480383
#> 4 no_detect_set_n        b   nord  2.361640 0.5839372 1.132675  1.423825
#> 5 no_detect_set_n        b  south  8.613970 1.7498539 4.958773  5.733913
#> 6 no_detect_set_n        b   east 22.012662 5.1394951 9.971617 13.895154
#>         25%       50%       75%     97.5%       Max  nsv Na's
#> 1  2.391553  2.857134  3.339671  4.051653  4.536046 1001    0
#> 2  3.079032  3.707894  4.320097  5.424437  6.535555 1001    0
#> 3  6.003530  7.242773  8.544794 10.827406 12.409943 1001    0
#> 4  1.923674  2.303978  2.749540  3.555514  4.654709 1001    0
#> 5  7.123986  8.552104 10.002242 11.658403 13.687274 1001    0
#> 6 18.048291 21.529684 25.817968 32.375069 36.016324 1001    0

Multilevel trials

Simple multilevel

We can also calculate the probability that at least one infected animal from at least one infected farm is not detected, but here, we need to consider two levels: animals and farms.

Selection (in blue) of 4 animals from 3 farms, with a 20% regional herd prevalence and 50% within-herd prevalence.

We import animals from "farms_n" farms. Each farm has a probability "h_prev" (regional herd prevalence) of being infected. From each farm, we import "animals_n" animals. In an infected farm, each animal has a probability "w_prev" (within-herd prevalence) of being infected. We’ve already used this to calculate "no_detect", which is the probability that an infected animal is not detected.

The probability of at least one success in this hierarchical structure is given by:

$$set\_p= 1-(1-subset\_p \cdot (1-(1-trial\_p)^{trial\_n}))^{subset\_n}$$

Where:

• trials_p represents the probability of a trial in a subset being a success

• trials_n represents the number of trials in subset

• subset_p represents the probability of a subset being selected

• subset_n represents the number of subsets

• set_p represents the probability of a at least one trial of at least one subset being a success

# Probability of at least one animal from at least one herd being is not detected (probability of a herd being infected: h_prev)
imports <- trial_totals(
  mcmodule = imports,
  mc_names = "no_detect",
  trials_n = "animals_n",
  subsets_n = "farms_n",
  subsets_p = "h_prev",
  mctable = imports_mctable,
)

# Result
imports$node_list$no_detect_set$summary
#>         mc_name pathogen origin      mean          sd       Min      2.5%
#> 1 no_detect_set        a   nord 0.3554524 0.022994131 0.2879914 0.3121972
#> 2 no_detect_set        a  south 0.2918725 0.062035936 0.1707131 0.1841581
#> 3 no_detect_set        a   east 0.6031702 0.044184854 0.5206358 0.5262034
#> 4 no_detect_set        b   nord 0.9746355 0.016235524 0.9080894 0.9353931
#> 5 no_detect_set        b  south 0.9593916 0.008324214 0.9435923 0.9445593
#> 6 no_detect_set        b   east 0.9662035 0.021220418 0.9176483 0.9211130
#>         25%       50%       75%     97.5%       Max  nsv Na's
#> 1 0.3379731 0.3553841 0.3732035 0.3966264 0.4037282 1001    0
#> 2 0.2363502 0.2957188 0.3458267 0.3884192 0.3984394 1001    0
#> 3 0.5662145 0.6055760 0.6393578 0.6753059 0.6787207 1001    0
#> 4 0.9653477 0.9783262 0.9873528 0.9947945 0.9963197 1001    0
#> 5 0.9523539 0.9602221 0.9666917 0.9714390 0.9717183 1001    0
#> 6 0.9508097 0.9717442 0.9848915 0.9915584 0.9921264 1001    0

It also provides the probability of at least one and the expected number of infected animals by subset (in this case a farm)

# Probability of at least one in a farm
imports$node_list$no_detect_subset$summary
#>            mc_name pathogen origin       mean          sd        Min       2.5%
#> 1 no_detect_subset        a   nord 0.08418689 0.006531174 0.06567697 0.07211792
#> 2 no_detect_subset        a  south 0.03425691 0.008450613 0.01854480 0.02014774
#> 3 no_detect_subset        a   east 0.12435837 0.013995100 0.09971337 0.10121463
#> 4 no_detect_subset        b   nord 0.53616683 0.061836633 0.37959809 0.42182969
#> 5 no_detect_subset        b  south 0.27549957 0.014904524 0.24987461 0.25117068
#> 6 no_detect_subset        b   east 0.39950577 0.057881309 0.30000310 0.30428818
#>         25%        50%       75%      97.5%        Max  nsv Na's
#> 1 0.0791792 0.08407440 0.0891952 0.09610651 0.09824438 1001    0
#> 2 0.0266043 0.03445036 0.0415504 0.04798151 0.04955292 1001    0
#> 3 0.1124718 0.12445096 0.1355792 0.14844909 0.14973428 1001    0
#> 4 0.4895580 0.53528475 0.5827474 0.65062396 0.67403048 1001    0
#> 5 0.2624308 0.27562373 0.2883684 0.29922709 0.29991533 1001    0
#> 6 0.3496821 0.39920048 0.4505998 0.49443719 0.49944352 1001    0

Multiple group multilevel trials

This trial_totals() application is beyond the scope of this vignette, but there are cases where you might have several variates from the same subset. For example we could deal with different animal categories (cow, calf, bull…) from the same farm. In this case, the infection probability of animals within the same farm is not independent, and this should be taken into account. For more information, see Multilevel trials in the Multivariate operations vignette.

Selection (in blue) of 2 cows and 5 calves from 3 farms, with a 20% regional herd prevalence and 50% within-herd prevalence for adult animals and 30% within-herd prevalence for young animals.

Aggregated totals

Until this point, all mcnode operations were element-wise, keeping the original dimensions, and allowing uncertainties and variates to propagate through the calculations. However, sometimes, we need to aggregate variates to calculate totals, for example, to total risk of introducing a pathogen across all regions. In this case, we want to preserve the uncertainty dimension but reduce the variates dimension. With agg_totals() we can calculate overall probabilities or sum quantities across groups.

imports <- agg_totals(
  mcmodule = imports,
  mc_name = "no_detect_set",
  agg_keys = "pathogen"
)
#> 3 variates per group for no_detect_set

# Result
imports$node_list$no_detect_set_agg$summary
#>             mc_name pathogen      mean           sd       Min      2.5%
#> 1 no_detect_set_agg        a 0.8188637 2.656678e-02 0.7330214 0.7635315
#> 4 no_detect_set_agg        b 0.9999646 3.709019e-05 0.9996568 0.9998676
#>         25%       50%       75%     97.5%       Max  nsv Na's
#> 1 0.8005996 0.8199115 0.8383779 0.8657543 0.8790562 1001    0
#> 4 0.9999557 0.9999769 0.9999892 0.9999968 0.9999988 1001    0

Now we can visualise our mcmodule again and see all these new nodes created by the totals functions.

mc_network(imports, legend = TRUE)

Working with what-if scenarios

So far, we’ve only tested our model using current data. But risk analysis is most useful when comparing different scenarios. In our example, we could compare the baseline risk with the risk if tests were always performed in all regions.

To do this this, we only need to add a column called “scenario_id”. This name is important as it is used to will recognize it specifically for scenario comparisons, not as regular variate categories. The baseline scenario should be called “0”. While not every scenario needs to contain all the variate categories included in the baseline, any variate categories present in alternative scenarios must exist in the baseline.

imports_data <- imports_data %>%
  mutate(scenario_id = "0")

imports_data_wif <- imports_data %>%
  mutate(
    scenario_id = "always_test",
    test_origin = "always"
  ) %>%
  bind_rows(imports_data) %>%
  relocate(scenario_id)

imports_data_wif[, 1:6]
#>    scenario_id pathogen origin test_origin h_prev_min h_prev_max
#> 1  always_test        a   nord      always       0.08       0.10
#> 2  always_test        a  south      always       0.02       0.05
#> 3  always_test        a   east      always       0.10       0.15
#> 4  always_test        b   nord      always       0.50       0.70
#> 5  always_test        b  south      always       0.25       0.30
#> 6  always_test        b   east      always       0.30       0.50
#> 7            0        a   nord   sometimes       0.08       0.10
#> 8            0        a  south   sometimes       0.02       0.05
#> 9            0        a   east       never       0.10       0.15
#> 10           0        b   nord      always       0.50       0.70
#> 11           0        b  south   sometimes       0.25       0.30
#> 12           0        b   east     unknown       0.30       0.50

Now we create the mcmodule and calculate the totals. Note that, since most functions for working with mcmodules both take and return mcmodules, you can use the pipe %>% to simplify your workflow

imports_wif <- eval_module(
  exp = c(imports = imports_exp),
  data = imports_data_wif,
  mctable = imports_mctable,
  data_keys = imports_data_keys
)
#> imports evaluated
#> mcmodule created (expressions: imports)

imports_wif <- imports_wif %>%
  trial_totals(
    mc_names = "no_detect",
    trials_n = "animals_n",
    subsets_n = "farms_n",
    subsets_p = "h_prev",
    mctable = imports_mctable,
  ) %>%
  agg_totals(
    mc_name = "no_detect_set",
    agg_keys = c("pathogen", "scenario_id")
  )
#> 3 variates per group for no_detect_set

# Result
imports_wif$node_list$no_detect_set_agg$summary
#>              mc_name scenario_id pathogen      mean           sd       Min
#> 1  no_detect_set_agg always_test        a 0.7874198 2.858463e-02 0.6926341
#> 4  no_detect_set_agg always_test        b 0.9999831 1.708178e-05 0.9998825
#> 7  no_detect_set_agg           0        a 0.8266259 2.563749e-02 0.7525038
#> 10 no_detect_set_agg           0        b 0.9999822 1.896049e-05 0.9998809
#>         2.5%       25%       50%       75%     97.5%       Max  nsv Na's
#> 1  0.7267729 0.7691942 0.7889077 0.8079228 0.8354961 0.8499450 1001    0
#> 4  0.9999376 0.9999776 0.9999892 0.9999945 0.9999985 0.9999992 1001    0
#> 7  0.7724774 0.8094927 0.8281388 0.8464569 0.8705576 0.8808379 1001    0
#> 10 0.9999266 0.9999768 0.9999894 0.9999947 0.9999985 0.9999993 1001    0

Working with multiple mcmodules

As your risk analysis grows in complexity, you may need to split your model into several independent modules and then combine them.

Inputs from previous mcmodules

Often, the output from one module serves as input for another. For example, after estimating the probability that an imported animal is not detected, you may want to model the probability that this animal transmits a pathogen via direct contact.

To do this, simply pass the previous mcmodule as the prev_mcmodule argument when creating the new module. This makes all nodes from the previous module available for use in expressions in the new module.

#  Create pathogen data table
transmission_data <- data.frame(
  pathogen = c("a", "b"),
  inf_dc_min = c(0.05, 0.3),
  inf_dc_max = c(0.08, 0.4)
)

transmission_data_keys <- list(transmission_data = list(
  cols = c("pathogen", "inf_dc_min", "inf_dc_max"),
  keys = c("pathogen")
))

transmission_mctable <- data.frame(
  mcnode = c("inf_dc"),
  description = c("Probability of infection via direct contact"),
  mc_func = c("runif")
)
dir_contact_exp <- quote({
  dir_contact <- no_detect * inf_dc
})

transmission <- eval_module(
  exp = c(dir_contact = dir_contact_exp),
  data = transmission_data,
  mctable = transmission_mctable,
  data_keys = transmission_data_keys,
  prev_mcmodule = imports_wif
)
#> Group by: pathogen
#> no_detect prev dim: [1001, 1, 12], new dim: [1001, 1, 12], 0 null matches
#> data prev dim: [2, 3], new dim: [12, 4], 0 null matches
#> dir_contact evaluated
#> mcmodule created (expressions: dir_contact)

mc_network(transmission, legend = TRUE)

Combining mcmodules

To merge two or more modules into a single unified model, use the combine_modules() function. This will join their data, nodes, and expressions, allowing you to perform further calculations or summaries across the combined structure.

intro <- combine_modules(imports_wif, transmission)
intro <- at_least_one(intro, c("no_detect", "dir_contact"), name = "total")
#> 2 variates per group for dir_contact
#> 2 variates per group for dir_contact
#> 2 variates per group for dir_contact
#> 2 variates per group for dir_contact
#> no_detect prev dim: [1001, 1, 12], new dim: [1001, 1, 24], 0 null matches
#> dir_contact prev dim: [1001, 1, 12], new dim: [1001, 1, 24], 0 null matches
intro$node_list$total$summary
#>    mc_name scenario_id pathogen origin       mean          sd        Min
#> 1    total always_test        a   nord 0.01860359 0.001686571 0.01508790
#> 2    total always_test        a   nord 0.02363784 0.001845052 0.01880110
#> 3    total always_test        a  south 0.01867499 0.001665734 0.01460705
#> 4    total always_test        a  south 0.02370747 0.001854541 0.01852406
#> 5    total always_test        a   east 0.01861293 0.001674509 0.01466754
#> 6    total always_test        a   east 0.02862368 0.002378809 0.02296087
#> 7    total always_test        b   nord 0.10490903 0.015742532 0.06520876
#> 8    total always_test        b   nord 0.10469136 0.012379656 0.06903792
#> 9    total always_test        b  south 0.07672860 0.009651204 0.05375472
#> 10   total always_test        b  south 0.13074539 0.009024516 0.10667734
#> 11   total always_test        b   east 0.10407889 0.015095180 0.06536057
#> 12   total always_test        b   east 0.24863722 0.022001480 0.18878599
#> 13   total           0        a   nord 0.09727192 0.008130946 0.08297629
#> 14   total           0        a   nord 0.10189818 0.008598009 0.08667225
#> 15   total           0        a  south 0.09699414 0.007975761 0.08316075
#> 16   total           0        a  south 0.10162070 0.008440121 0.08623578
#> 17   total           0        a   east 0.17549088 0.014408535 0.15081370
#> 18   total           0        a   east 0.18388670 0.015145401 0.15684902
#> 19   total           0        b   nord 0.10430305 0.012532288 0.07297195
#> 20   total           0        b   nord 0.10398150 0.015742025 0.06591324
#> 21   total           0        b  south 0.23734264 0.006291971 0.22156993
#> 22   total           0        b  south 0.28193053 0.008961662 0.25945590
#> 23   total           0        b   east 0.53951855 0.042747727 0.46283198
#> 24   total           0        b   east 0.61312548 0.043670514 0.52556879
#>          2.5%        25%        50%        75%      97.5%        Max  nsv Na's
#> 1  0.01565349 0.01724157 0.01852589 0.01997204 0.02165070 0.02310416 1001    0
#> 2  0.02010472 0.02227678 0.02360223 0.02498523 0.02708513 0.02868965 1001    0
#> 3  0.01572448 0.01746772 0.01863579 0.01993293 0.02172412 0.02283248 1001    0
#> 4  0.02036091 0.02229330 0.02372564 0.02506436 0.02718822 0.02928951 1001    0
#> 5  0.01563475 0.01726502 0.01860275 0.01991088 0.02173877 0.02316949 1001    0
#> 6  0.02429164 0.02688143 0.02856584 0.03032843 0.03327526 0.03532512 1001    0
#> 7  0.07672286 0.09347314 0.10385642 0.11635187 0.13451251 0.14829251 1001    0
#> 8  0.08183564 0.09614676 0.10465138 0.11338318 0.12871603 0.13858719 1001    0
#> 9  0.05889097 0.07015491 0.07611855 0.08333042 0.09500863 0.10635176 1001    0
#> 10 0.11307184 0.12437071 0.13077601 0.13743581 0.14810816 0.15352115 1001    0
#> 11 0.07565591 0.09404074 0.10326555 0.11423805 0.13545290 0.15049554 1001    0
#> 12 0.20996082 0.23302108 0.24762445 0.26344534 0.29385490 0.31056292 1001    0
#> 13 0.08417339 0.09020520 0.09674471 0.10468655 0.11035889 0.11161595 1001    0
#> 14 0.08803272 0.09455229 0.10160136 0.10970369 0.11577200 0.11767356 1001    0
#> 15 0.08413343 0.09007765 0.09693721 0.10356285 0.11051891 0.11161843 1001    0
#> 16 0.08793761 0.09424677 0.10170037 0.10863466 0.11618852 0.11760748 1001    0
#> 17 0.15216514 0.16290943 0.17553107 0.18810271 0.19973761 0.20086633 1001    0
#> 18 0.15936193 0.17057732 0.18392840 0.19742300 0.20933697 0.21240152 1001    0
#> 19 0.08008144 0.09578852 0.10434892 0.11232021 0.12958176 0.14191545 1001    0
#> 20 0.07432402 0.09310604 0.10358602 0.11387490 0.13534827 0.15441115 1001    0
#> 21 0.22546808 0.23289196 0.23711276 0.24187715 0.24958453 0.25546984 1001    0
#> 22 0.26422086 0.27551673 0.28189546 0.28842594 0.29946511 0.30642179 1001    0
#> 23 0.46821058 0.50286291 0.53933435 0.57726315 0.60757912 0.61336652 1001    0
#> 24 0.53663805 0.57576855 0.61398849 0.65143684 0.68281797 0.69399015 1001    0

mc_network(intro, legend = TRUE)

The combined module now contains all nodes and metadata from its components, enabling you to analyze interactions and aggregate results across the entire risk pathway.

Getting module information

The mcmodule_info() function provides comprehensive metadata about your mcmodule structure, including composition information, keys for each variate, and global keys used across the module.

info <- mcmodule_info(intro)

# Check if module is combined or raw
info$is_combined
#> [1] TRUE

# Number of component modules
info$n_modules
#> [1] 2

# Module and expression information
info$module_exp_data
#>         module         exp         data_name
#> 1  imports_wif     imports  imports_data_wif
#> 2 transmission dir_contact transmission_data

# Keys for each variate
head(info$data_keys)
#>   scenario_id pathogen origin variate        data_name
#> 1 always_test        a   nord       1 imports_data_wif
#> 2 always_test        a  south       2 imports_data_wif
#> 3 always_test        a   east       3 imports_data_wif
#> 4 always_test        b   nord       4 imports_data_wif
#> 5 always_test        b  south       5 imports_data_wif
#> 6 always_test        b   east       6 imports_data_wif

# Global key names
info$global_keys
#> [1] "pathogen"    "origin"      "scenario_id"

Model analysis

Correlation analysis

The mcmodule_corr() function calculates correlation coefficients between input and output nodes across your mcmodule. This helps identify which input parameters have the strongest influence on your results. It is based on mc2d::tornado() but applied to many distinct variates.

# Calculate correlations using Spearman's method (default)
cor_results <- mcmodule_corr(imports)

# View correlation results
head(cor_results)

# Use different correlation method
cor_pearson <- mcmodule_corr(imports, method = "pearson")
cor_kendall <- mcmodule_corr(imports, method = "kendall")

Convergence analysis

The mcmodule_converg() function assesses whether your Monte Carlo simulations have run for enough iterations to produce stable results. It tracks how statistics (mean, median, quantiles) change as iterations accumulate.

# Check convergence with default settings
converg_results <- mcmodule_converg(imports)

# Custom convergence analysis
# Check the last 10% of iterations with stricter threshold
converg_strict <- mcmodule_converg(
  imports,
  from_quantile = 0.90,
  conv_threshold = 0.01
)

Tricks and tweaks

Handling missing and infinite values in mcnodes

When building stochastic nodes, you may encounter missing (NA) or infinite (Inf, -Inf) values, especially after mathematical operations or data transformations. These can cause issues in downstream calculations. Use mcnode_na_rm() to clean your mcnode by replacing problematic values with another value (usually zero):

sample_mcnode <- mcstoc(runif,
  min = mcdata(c(NA, 0.2, -Inf), type = "0", nvariates = 3),
  max = mcdata(c(NA, 0.3, Inf), type = "0", nvariates = 3),
  nvariates = 3
)
#> Warning in (function (n, min = 0, max = 1) : NAs produced
#> Warning in (function (n, min = 0, max = 1) : NAs produced

# Replace NA and Inf with 0
clean_mcnode <- mcnode_na_rm(sample_mcnode)

This is especially useful in expressions where a denominator might be zero, resulting in Inf or NaN, but you want the output to be zero instead.

Customizing total node names

Functions like at_least_one(), agg_totals(), and trial_totals() automatically generate new mcnodes with informative suffixes. You can customize these names for clarity or documentation purposes:

# Custom name for at_least_one()
intro <- at_least_one(intro, c("no_detect", "dir_contact"), name = "custom_total")
#> 2 variates per group for dir_contact
#> 2 variates per group for dir_contact
#> 2 variates per group for dir_contact
#> 2 variates per group for dir_contact
#> no_detect prev dim: [1001, 1, 12], new dim: [1001, 1, 24], 0 null matches
#> dir_contact prev dim: [1001, 1, 12], new dim: [1001, 1, 24], 0 null matches

# Custom name for agg_totals()
intro <- agg_totals(intro, "no_detect_set", name = "custom_agg")
#> Keys to aggregate by not provided, using 'scenario_id' by default
#> 6 variates per group for no_detect_set

# Custom suffix for agg_totals()
intro <- agg_totals(intro, "no_detect_set",
  agg_keys = c("scenario_id", "pathogen"),
  agg_suffix = "aggregated"
)
#> 3 variates per group for no_detect_set

Prefixing mcmodules to avoid name duplication

If your project includes multiple modules with similar or repeated expressions, duplicated node names can cause problems when combining modules. Use add_prefix() to add a unique prefix to each module, making node names distinct:

imports_wif <- add_prefix(imports_wif)

By default, the prefix is the mcmodule name, but you can specify a custom prefix if needed.

Functions that work outside mcmodules

Some functions in mcmodule can be used independently of the full module workflow:

• create_mcnodes(): Quickly generate mcnodes from a data frame and mctable, useful for prototyping or testing

create_mcnodes(data = prevalence_region, mctable = imports_mctable)
# Nodes are created in the environment
h_prev
#>   node    mode  nsv nsu nva variate  min   mean median  max Nas type outm
#> 1    x numeric 1001   1   6       1 0.08 0.0898 0.0899 0.10   0    V each
#> 2    x numeric 1001   1   6       2 0.02 0.0347 0.0347 0.05   0    V each
#> 3    x numeric 1001   1   6       3 0.10 0.1248 0.1247 0.15   0    V each
#> 4    x numeric 1001   1   6       4 0.50 0.5992 0.5957 0.70   0    V each
#> 5    x numeric 1001   1   6       5 0.25 0.2750 0.2746 0.30   0    V each
#> 6    x numeric 1001   1   6       6 0.30 0.4004 0.3991 0.50   0    V each

• mc_summary(): Summarize a mcnode directly from data, without needing a full mcmodule

mc_summary(data = prevalence_region, mcnode = h_prev, keys_names = c("pathogen", "origin"))
#>   mc_name pathogen origin       mean          sd        Min       2.5%
#> 1  h_prev        a   nord 0.08978065 0.005724102 0.08002376 0.08043994
#> 2  h_prev        a  south 0.03470541 0.008504885 0.02001543 0.02084694
#> 3  h_prev        a   east 0.12481802 0.014858165 0.10001737 0.10087196
#> 4  h_prev        b   nord 0.59917835 0.056354382 0.50005262 0.50585667
#> 5  h_prev        b  south 0.27497915 0.014567291 0.25005631 0.25090975
#> 6  h_prev        b   east 0.40035896 0.058215707 0.30004424 0.30688182
#>          25%        50%        75%      97.5%        Max  nsv Na's
#> 1 0.08484119 0.08986064 0.09461528 0.09941119 0.09999418 1001    0
#> 2 0.02716204 0.03467646 0.04181022 0.04932608 0.04997037 1001    0
#> 3 0.11175195 0.12470867 0.13818939 0.14856349 0.14983727 1001    0
#> 4 0.55264482 0.59566340 0.64740407 0.69368987 0.69997201 1001    0
#> 5 0.26251251 0.27459805 0.28805483 0.29869293 0.29988814 1001    0
#> 6 0.34893812 0.39908466 0.44985631 0.49686042 0.49989177 1001    0

Next steps

We are currently planning to add global sensitivity analysis based on Morris screening, using the existing local sensitivity (OAT) support (see eval_module()).

We are also working on building compatibility with other R packages such as freedom, to facilitate integration with broader risk assessment workflows.

To stay updated on new releases and planned features, watch our repository: https://github.com/NataliaCiria/mcmodule. We encourage you to explore the package further, adapt it to your own use cases, and contribute feedback or improvements. To report bugs, please visit: https://github.com/NataliaCiria/mcmodule/issues or contact mail@nataliaciria.com.

References

Almende B. V., and Benoit Thieurmel. 2025. “Visnetwork: Network Visualization Using ’Vis. Js’ Library.” https://CRAN.R-project.org/package=visNetwork.

Csardi, Gabor, and Tamas Nepusz. 2006. “The Igraph Software Package for Complex Network Research” Complex Systems: 1695. https://igraph.org.

Murray, Noel. 2004. Handbook on Import Risk Analysis for Animals and Animal Products Volume 2 Quantitative Risk Assessment. Vol. 2. https://rr-africa.woah.org/app/uploads/2018/03/handbook_on_import_risk_analysis_-_oie_-_vol_ii.pdf.

Pouillot, R., and M.-L. Delignette-Muller. 2010. “Evaluating Variability and Uncertainty in Microbial Quantitative Risk Assessment Using Two r Packages” 142: 330–40.

R Core Team. 2024. “R: A Language and Environment for Statistical Computing.” https://www.R-project.org/.

Vose, David. 2008. Risk Analysis, a Quantitative Guide. Chichester, England: John Wiley & Sons.