Today we had a data set come in that the researcher requested AUDPC (Area Under the Disease Progress Curve) (Shaner and Finney 1977) be calculated from two points. This is a common request as it’s quite time and labour intensive to collect these data, especially in breeding trials and can be done with a simple formula from Jeger and Viljanen-Rollinson (2001). However, I wasn’t aware of any R package that implemented this calculation, so I wrote a function to do it.

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audpc_2_points <- function(time, y0, yT) {
  # eqn. 3 from Jeger and Viljanen-Rollinson (2001), rate parameter r
  r <- (log(yT / (1 - yT)) - log(y0 / (1 - y0))) / time
  
  # eqn. 2 from Jeger and Viljanen-Rollinson (2001), AUDPC estimation
  return(time + log(y0 / yT) / r)
}

Using the example as seen in the documentation for AUDPC from dos S. Alves and Del Ponte (2021) we can calculate AUDPC using the trapezoidal method.

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library(epifitter)

epi <- sim_logistic(N = 30, y0 = 0.01,dt = 5, r = 0.3, alpha = 0.5, n = 1)

(eg_1 <- AUDPC(time = epi$time, y = epi$y, y_proportion = TRUE))

## [1] 14.69147

Using the same data, we can calculate AUDPC from two points.

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# time using the last time-step point
epi$time[7]

## [1] 30

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# y0 using the first disease incidence point
epi$y[1]

## [1] 0.01

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# yT using the last disease incidence point
epi$y[7]

## [1] 0.9879302

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(eg_2 <- audpc_2_points(time = epi$time[7], y0 = epi$y[1], yT = epi$y[7]))

## [1] 14.68996

We can see that the values are very similar, but not identical, i.e., our two point method results in 14.6899594, while the traditional method provides, 14.6914735, which is what Jeger and Viljanen-Rollinson (2001) proposes we should expect, values that are close enough to be useful but not identical.

References