Introduction

Predicted disease intensity alone does not fully describe the potential agronomic consequences of an epidemic.

In many pathosystems, researchers also want to estimate how the predicted disease response may translate into reduced crop yield and economic losses.

EpiExposure connects three modeling stages:

1. environmental exposure profiles;
2. expected disease outcomes from the fitted DLNM;
3. user-defined disease-yield and economic relationships.

This section demonstrates how scenario predictions can be translated into:

• expected remaining yield;
• yield loss;
• proportional yield loss;
• economic loss;
• comparisons across production scenarios.

Yield and economic losses are not estimated by the DLNM alone. They depend on additional assumptions supplied by the user, including the disease-yield relationship, attainable yield, commodity price, and unit conversions.

The resulting quantities are model-based projections under those assumptions. They should not automatically be interpreted as observed losses or causal effects.

Preparing the epidemiological model

This section uses the same example dataset and DLNM specification introduced in the previous tutorials.

library(EpiExposure)
library(ggplot2)

data("epi_data")

Define the exposure-lag structures:

cb <- define_exposures(
  data = epi_data,
  vars = c(
    "tmean",
    "rain",
    "wetness"
  ),
  max_lag = 85,
  df_var = 3,
  df_lag = 2
)

Build the epidemic-level design:

dat <- build_design(
  data = epi_data,
  cb_templates = cb
)

Prepare the disease response:

dat <- prepare_response(
  data = dat,
  response = "y",
  family = "beta"
)

Fit the DLNM:

fit <- fit_epidlnm(
  data = dat,
  model_engine = "glmmTMB",
  family = "beta",
  random_effect = NULL,
  epiexposure_spec = attr(
    cb,
    "spec"
  )
)

The fitted model is now used to predict disease responses across environmental scenarios and translate those predictions into agronomic and economic quantities.

Translating disease predictions into losses

Generating disease scenarios

Define biologically meaningful lag periods:

periods <- define_periods(
  max_lag = 85,
  cuts = c(
    20,
    40,
    60
  ),
  prefix = "Period"
)

Generate a scenario grid in which rainfall varies continuously across selected temperature and leaf wetness conditions:

range_losses <- simulate_ranges(
  periods = periods,
  vary = list(
    tmean = c(
      20,
      34
    ),
    rain = seq(
      0,
      15,
      by = 1
    ),
    wetness = c(
      2,
      10
    )
  ),
  scenario_type = "grid",
  scenario_var = "rain"
)

The fine rainfall sequence provides a smooth grid for visualizing the modeled disease and loss relationships. It should not be interpreted as additional observed information.

Predict expected disease outcomes and propagate coefficient uncertainty:

scenarios_losses <- simulate_scenarios(
  fit = fit,
  scenarios = range_losses,
  data = epi_data,
  uncertainty = TRUE,
  output = "summary",
  n_samples = 5,
  seed = 123
)

The Beta-model predictions are proportions. Convert the central estimates and interval limits to percentage points because the damage coefficient used below was defined for percentage disease severity:

scenarios_losses$prediction <- (
  scenarios_losses$prediction * 100
)

scenarios_losses$prediction_lower <- (
  scenarios_losses$prediction_lower * 100
)

scenarios_losses$prediction_upper <- (
  scenarios_losses$prediction_upper * 100
)

Simulating yield and economic losses

intercept = 9691.0
slope = 49.3

losses <- simulate_losses(
  data = scenarios_losses,
  lower = "prediction_lower",
  upper = "prediction_upper",
  y = "prediction",
  slope = 49.3,
  parameter_mode = "values",
  intercept = 9691.0,
  attainable_yield = seq(
    4000,
    10000,
    by = 50
  ),
  price = 300
)

names(
  losses
)
#>  [1] "scenario"          "scenario_point"    "tmean"            
#>  [4] "rain"              "wetness"           "prediction"       
#>  [7] "prediction_sd"     "prediction_lower"  "prediction_upper" 
#> [10] ".loss_row_id"      ".sim"              "slope_sim"        
#> [13] "intercept_sim"     "rand_eff"          "ref_yield"        
#> [16] "att_yield"         "price"             "y_used"           
#> [19] "y_lower"           "y_upper"           "yl_prop_raw"      
#> [22] "yl_capped"         "pred_yield"        "rl_prop"          
#> [25] "rl_pct"            "yl_prop"           "yl_pct"           
#> [28] "ap_yield"          "yield_loss"        "econ_loss"        
#> [31] "yl_prop_raw_lower" "yl_prop_raw_upper" "pred_yield_lower" 
#> [34] "pred_yield_upper"  "rl_prop_lower"     "rl_prop_upper"    
#> [37] "rl_pct_lower"      "rl_pct_upper"      "yl_prop_lower"    
#> [40] "yl_prop_upper"     "yl_pct_lower"      "yl_pct_upper"     
#> [43] "ap_yield_lower"    "ap_yield_upper"    "yield_loss_lower" 
#> [46] "yield_loss_upper"  "econ_loss_lower"   "econ_loss_upper"  
#> [49] "yl_capped_lower"   "yl_capped_upper"

Visualizing the loss scenarios

plot_losses() can display the yield and economic consequences across the environmental scenario grid.

losses_plot <- plot_losses(
  data = losses,
  x = "rain",
  y = "att_yield",
  facet = c(
    "tmean",
    "wetness"
  ),
  type = "heatmap",
  x_breaks = seq(
    0,
    15,
    by = 3
  ),
  y_breaks = seq(
    4000,
    10000,
    by = 2000
  ),
  x_label = "Daily precipitation (mm)",
  nrow = 2,
  facet_ncol = 4
)

losses_plot

The heatmap summarizes the complete modeling chain:

rainfall, temperature, and leaf wetness scenarios
                         ↓
predicted disease severity
                         ↓
linear damage relationship
                         ↓
estimated yield and economic losses

Rainfall should not be interpreted in isolation because the panels also represent different temperature and leaf wetness conditions.

Sensitivity to damage-function parameters

Damage-function parameters may vary among studies, cultivars, production systems, or experimental conditions. simulate_losses() can evaluate multiple parameter values to show how agronomic conclusions depend on the selected disease-yield relationship.

The following example compares two parameter combinations:

Damage relationship 1: intercept = 9691.0, slope = 49.3
Damage relationship 2: intercept = 12000, slope = 80

losses_sensitivity <- simulate_losses(
  data = scenarios_losses,
  lower = "prediction_lower",
  upper = "prediction_upper",
  y = "prediction",
  slope = c(
    49.3,
    80
  ),
  parameter_mode = "values",
  intercept = c(
    9691.0,
    12000
  ),
  attainable_yield = seq(
    4000,
    10000,
    by = 50
  ),
  price = 300
)

The parameter combinations represent alternative damage relationships rather than uncertainty intervals around one damage function. Their scientific source and interpretation should be stated explicitly in a real analysis.

Visualize the modeled relationship between rainfall and predicted yield for a selected attainable yield:

plot_losses(
  data = losses_sensitivity,
  x = "rain",
  y = "att_yield",
  facet = c(
    "tmean",
    "wetness"
  ),
  type = "regression",
  reg_y = "ap_yield",
  att_yield = 10000,
  x_breaks = seq(
    0,
    15,
    by = 3
  ),
  x_label = "Daily precipitation (mm)"
)

This sensitivity analysis helps determine whether the agronomic conclusions remain similar across plausible disease-yield relationships.

Interpreting the loss results

The outputs combine assumptions from several stages:

1. the fitted exposure-lag-response model;
2. the simulated environmental scenarios;
3. the conversion of disease predictions into percentage severity;
4. the selected slope and intercept;
5. the attainable-yield range;
6. the commodity price.

The lower and upper disease-prediction limits are transformed through the damage relationship to obtain corresponding loss limits. This interval transformation does not automatically represent full draw-by-draw propagation of every source of uncertainty.

The resulting limits do not automatically include uncertainty in:

• slope;
• intercept;
• attainable yield;
• commodity price;
• environmental scenario assumptions.

The second analysis varies slope and intercept explicitly, but these values are alternative parameter combinations rather than random draws from an estimated joint parameter distribution.

Practical applications

When supported by appropriate data and assumptions, yield and economic loss simulations can help researchers:

• translate disease predictions into agronomic units;
• compare hypothetical environmental scenarios;
• examine sensitivity to attainable yield;
• evaluate sensitivity to commodity price;
• identify scenarios associated with larger modeled losses;
• connect disease forecasting with production consequences;
• explore assumptions used in management or climate scenarios.

These applications remain conditional on the fitted epidemiological model and the disease-yield relationship supplied by the user.

Reporting checklist

When reporting loss estimates, specify:

1. the response family and disease scale;
2. the fitted DLNM specification;
3. the environmental profiles or scenarios;
4. the disease-yield equation;
5. the source and units of the slope and intercept;
6. the range and units of attainable yield;
7. the commodity price and price unit;
8. any conversion between kilograms and metric tons;
9. the uncertainty sources that were propagated;
10. whether the results are associational projections or causal estimates.

Summary

This section demonstrated how EpiExposure connects exposure-lag-response modeling with agronomic and economic outcomes.

The workflow is:

complete exposure profiles
            ↓
fitted DLNM
            ↓
expected disease response
            ↓
user-supplied disease-yield relationship
            ↓
expected remaining yield
            ↓
yield loss
            ↓
economic loss

The DLNM describes the modeled association between environmental profiles and disease. The damage function translates predicted disease into expected yield, and commodity price translates yield loss into economic units.

Each stage introduces assumptions that should be documented and evaluated through sensitivity analysis.

Next steps

The next section focuses on model selection and ensemble prediction.

Topics include:

• find_bestfit();
• model ranking;
• cross-validation;
• ensemble_bestfit().

These tools help compare candidate exposure-lag specifications and evaluate their predictive performance.