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Calculate Area-Under-the-Curve (AUC) Metrics for Delay Discounting Data

Source: R/utils.R
calc_aucs.Rd

Calculates three area-under-the-curve (AUC) metrics for delay-discounting data: regular AUC (using raw delays), log10 AUC (using logarithmically scaled delays), and ordinal AUC (using ordinally scaled delays). The three differ only in how the delays are scaled before the area is computed. Metrics are computed separately for each id, so a data frame with several subjects returns one row per subject.

Usage

calc_aucs(dat)

Arguments

dat

A data frame containing delay discounting data. It must include the following columns:

  • id: Participant or group identifier.

  • x: Delay values (e.g., in days).

  • y: Indifference points as a proportion of the larger later reward (the area is normalized by the delay range times 1, so y must be on the 0–1 scale).

Missing y or x values and duplicate delays within a subject are errors.

Value

A tibble with the following columns:

  • id: The participant or group identifier.

  • auc_regular: The regular AUC, calculated using the raw delay values.

  • auc_log10: The log10 AUC, calculated on log10(x + 1) delays scaled to their maximum.

  • auc_ord: The ordinal AUC, calculated using ordinally scaled delay values.

Details

Each area is the trapezoidal area under the indifference points divided by the width of the delay axis, so a subject who does not discount scores 1. auc_log10 transforms delays as log10(x + 1) (the + 1 keeps a zero delay finite, the convention usually attributed to Borges et al., 2016) and rescales them by their maximum. Because of the + 1, auc_log10 depends on the delay unit: the same series scores differently in days and in weeks, so compare auc_log10 only across data recorded in one delay unit. auc_regular and auc_ord are unit-free.

References

Borges, A. M., Kuang, J., Milhorn, H., & Yi, R. (2016). An alternative approach to calculating area-under-the-curve (AUC) in delay discounting research. Journal of the Experimental Analysis of Behavior, 106, 145–155. doi:10.1002/jeab.219

Examples

# Example data
data <- data.frame(
  id = rep("P1", 6),
  x = c(1, 7, 30, 90, 180, 365),
  y = c(0.8, 0.5, 0.3, 0.2, 0.1, 0.05)
)

# Calculate AUC metrics for a single participant
calc_aucs(data)
#> # A tibble: 1 × 4
#>   id    auc_regular auc_log10 auc_ord
#>   <chr>       <dbl>     <dbl>   <dbl>
#> 1 P1          0.152     0.359   0.305