Calculating AUDPS in R and Julia.

Previously we introduced Julia, a programming language that is similar to R or Python and demonstrated how AUDPC can be calculated using the trapezoidal method in R as shown in the “Disease Progress Over Time” module of the “Epidemiology and Ecology in R,” Sparks et al. (2008). Then we looked at how the function could be optimised in R before writing a Julia function to calculate the same value.

Now we will take a look at a similar calculation, Area Under the Disease Stairs (AUDPS) (Simko and Piepho 2012). AUDPS can give better estimates of the disease progress by giving a weight closer to the optimal first and last observations.

This function is not the fully optimised version like what we showed for AUDPC, using `sum()`

would help make this faster but possibly at the expense of readability so we’ll stick with using the regular `+`

and `-`

here for readability.

Both of the R packages that were previously discussed when showing how to calculate AUDPC, *agricolae* (Mendiburu 2021) and *epifitter* (Alves and Del Ponte 2021), provide easy to use functions to calculate AUDPS, `audps()`

and `AUDPS()`

, respectively. The following code uses an example from *agricolae’s* help showing how to calculate AUDPS in R using our own function, `r_audps()`

.

```
> dates <- c(14, 21, 28) # days
> evaluation <- c(40, 80, 90)
> r_audps(evaluation, dates)
```

`[1] 14 21 28`

`[1] 40 80 90`

`[1] 1470`

Since we’ve already introduced Julia, here we’ll just build an AUDPS function in Julia to illustrate how it can be done.

```
function j_audps(evaluation, dates)
# find how many observations there are and calculate that minus 1 as well
= length(dates)
n = length(dates) - 1
n_1
# initialise our objects outside the loop
= 0
i = 0
out # the for loop looks roughly the same but here we just use 1:n
for j in 1:n_1
= i + evaluation[j] * (dates[j + 1] - dates[j])
i
= i + evaluation[n] * (dates[n] - dates[n_1])
out end
# return the object, `out` from the for loop
return out
# end the function (no curly brackets!)
end
```

`j_audps (generic function with 1 method)`

```
> dates = [14, 21, 28] # days
julia> evaulation = [40, 80, 90]
julia> j_audps(evaulation, dates) julia
```

```
3-element Vector{Int64}:
14
21
28
```

```
3-element Vector{Int64}:
40
80
90
```

`1470`

The AUDPS values match!

This is just a quick follow-up example of how you can use Julia in plant pathology to show new users how it compares with R with a another commonly used function. If you’re curious to know more, the Julia docs are a great place to start. In particular, the noteworthy differences is a useful bit to refer to if you’re familiar with R.

For a more detailed comparison of complete Julia and R packages that offer an existing plant disease model, EPIRICE (Savary et al. 2012), see Epicrop.jl (Sparks 2022), a port of epicrop (Sparks et al. 2021) to Julia, which has demonstrated faster speeds in benchmarking tests for the same rice disease predictions.

This post was constructed using R Version `4.1.2`

(R Core Team 2021) and Julia Version `1.7.1`

(Bezanson et al. 2017) using *JuliaCall* Pull Request #174.

Alves, K. dos S., and Del Ponte, E. M. 2021. *epifitter: Analysis and Simulation of Plant Disease Progress Curves*. Available at: https://CRAN.R-project.org/package=epifitter.

Bezanson, J., Edelman, A., Karpinski, S., and Shah, V. B. 2017. Julia: A fresh approach to numerical computing. SIAM review. 59:65–98.

Mendiburu, F. de. 2021. *agricolae: Statistical Procedures for Agricultural Research*. Available at: https://CRAN.R-project.org/package=agricolae.

R Core Team. 2021. *R: A language and environment for statistical computing*. Vienna, Austria: R Foundation for Statistical Computing. Available at: https://www.R-project.org/.

Savary, S., Nelson, A., Willocquet, L., Pangga, I., and Aunario, J. 2012. Modeling and mapping potential epidemics of rice diseases globally. Crop Protection. 34:6–17.

Simko, I., and Piepho, H.-P. 2012. The area under the disease progress stairs: Calculation, advantage, and application. Phytopathology. 102:381–389.

Sparks, A. 2022. *Simulation modelling of crop diseases using a healthy-latent-infectious-postinfectious (HLIP) model in Julia*. Available at: https://github.com/adamhsparks/Epicrop.jl.

Sparks, A. H., Hijmans, R., Savary, S., Pangga, I., and Aunario, J. 2021. *epicrop: Simulation modelling of crop diseases using a susceptible-exposed-infectious-removed (seir) model*. Available at: https://github.com/adamhsparks/epicrop.

Sparks, A., Esker, P. D., Bates, M., Dall’Acqua, W., Guo, Z., Segovia, V., et al. 2008. Ecology and epidemiology in R: Disease progress over time. The Plant Health Instructor.

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