Function to transform forecasts and true values before scoring.

## Arguments

- data
A data.frame or data.table with the predictions and observations. For scoring using

`score()`

, the following columns need to be present:`true_value`

- the true observed values`prediction`

- predictions or predictive samples for one true value. (You only don't need to provide a prediction column if you want to score quantile forecasts in a wide range format.)

For scoring integer and continuous forecasts a

`sample`

column is needed:`sample`

- an index to identify the predictive samples in the prediction column generated by one model for one true value. Only necessary for continuous and integer forecasts, not for binary predictions.

For scoring predictions in a quantile-format forecast you should provide a column called

`quantile`

:`quantile`

: quantile to which the prediction corresponds

In addition a

`model`

column is suggested and if not present this will be flagged and added to the input data with all forecasts assigned as an "unspecified model").You can check the format of your data using

`check_forecasts()`

and there are examples for each format (example_quantile, example_continuous, example_integer, and example_binary).- fun
A function used to transform both true values and predictions. The default function is

`log_shift()`

, a custom function that is essentially the same as`log()`

, but has an additional arguments (`offset`

) that allows you add an offset before applying the logarithm. This is often helpful as the natural log transformation is not defined at zero. A common, and pragmatic solution, is to add a small offset to the data before applying the log transformation. In our work we have often used an offset of 1 but the precise value will depend on your application.- append
Logical, defaults to

`TRUE`

. Whether or not to append a transformed version of the data to the currently existing data (`TRUE`

). If selected, the data gets transformed and appended to the existing data frame, making it possible to use the outcome directly in`score()`

. An additional column, 'scale', gets created that denotes which rows or untransformed ('scale' has the value "natural") and which have been transformed ('scale' has the value passed to the argument`label`

).- label
A string for the newly created 'scale' column to denote the newly transformed values. Only relevant if

`append = TRUE`

.- ...
Additional parameters to pass to the function you supplied. For the default option of

`log_shift()`

this could be the`offset`

argument.

## Value

A `data.table`

with either a transformed version of the data, or one
with both the untransformed and the transformed data. includes the original
data as well as a transformation of the original data. There will be one
additional column, `scale', present which will be set to "natural" for the
untransformed forecasts.

## Details

There are a few reasons, depending on the circumstances, for why this might be desirable (check out the linked reference for more info). In epidemiology, for example, it may be useful to log-transform incidence counts before evaluating forecasts using scores such as the weighted interval score (WIS) or the continuous ranked probability score (CRPS). Log-transforming forecasts and observations changes the interpretation of the score from a measure of absolute distance between forecast and observation to a score that evaluates a forecast of the exponential growth rate. Another motivation can be to apply a variance-stabilising transformation or to standardise incidence counts by population.

Note that if you want to apply a transformation, it is important to transform the forecasts and observations and then apply the score. Applying a transformation after the score risks losing propriety of the proper scoring rule.

## References

Transformation of forecasts for evaluating predictive performance in an epidemiological context Nikos I. Bosse, Sam Abbott, Anne Cori, Edwin van Leeuwen, Johannes Bracher, Sebastian Funk medRxiv 2023.01.23.23284722 doi:10.1101/2023.01.23.23284722 https://www.medrxiv.org/content/10.1101/2023.01.23.23284722v1

## Author

Nikos Bosse nikosbosse@gmail.com

## Examples

```
library(magrittr) # pipe operator
# transform forecasts using the natural logarithm
# negative values need to be handled (here by replacing them with 0)
example_quantile %>%
.[, true_value := ifelse(true_value < 0, 0, true_value)] %>%
# Here we use the default function log_shift() which is essentially the same
# as log(), but has an additional arguments (offset) that allows you add an
# offset before applying the logarithm.
transform_forecasts(append = FALSE) %>%
head()
#> Warning: Detected zeros in input values.Try specifying offset = 1 (or any other offset).
#> Warning: Detected zeros in input values.Try specifying offset = 1 (or any other offset).
#> location target_end_date target_type true_value location_name forecast_date
#> 1: DE 2021-01-02 Cases 11.754302 Germany <NA>
#> 2: DE 2021-01-02 Deaths 8.419360 Germany <NA>
#> 3: DE 2021-01-09 Cases 11.950677 Germany <NA>
#> 4: DE 2021-01-09 Deaths 8.718827 Germany <NA>
#> 5: DE 2021-01-16 Cases 11.609898 Germany <NA>
#> 6: DE 2021-01-16 Deaths 8.677099 Germany <NA>
#> quantile prediction model horizon
#> 1: NA NA <NA> NA
#> 2: NA NA <NA> NA
#> 3: NA NA <NA> NA
#> 4: NA NA <NA> NA
#> 5: NA NA <NA> NA
#> 6: NA NA <NA> NA
# alternatively, integrating the truncation in the transformation function:
example_quantile %>%
transform_forecasts(
fun = function(x) {log_shift(pmax(0, x))}, append = FALSE
) %>%
head()
#> Warning: Detected zeros in input values.Try specifying offset = 1 (or any other offset).
#> Warning: Detected zeros in input values.Try specifying offset = 1 (or any other offset).
#> location target_end_date target_type true_value location_name forecast_date
#> 1: DE 2021-01-02 Cases 11.754302 Germany <NA>
#> 2: DE 2021-01-02 Deaths 8.419360 Germany <NA>
#> 3: DE 2021-01-09 Cases 11.950677 Germany <NA>
#> 4: DE 2021-01-09 Deaths 8.718827 Germany <NA>
#> 5: DE 2021-01-16 Cases 11.609898 Germany <NA>
#> 6: DE 2021-01-16 Deaths 8.677099 Germany <NA>
#> quantile prediction model horizon
#> 1: NA NA <NA> NA
#> 2: NA NA <NA> NA
#> 3: NA NA <NA> NA
#> 4: NA NA <NA> NA
#> 5: NA NA <NA> NA
#> 6: NA NA <NA> NA
# specifying an offset for the log transformation removes the
# warning caused by zeros in the data
example_quantile %>%
.[, true_value := ifelse(true_value < 0, 0, true_value)] %>%
transform_forecasts(offset = 1, append = FALSE) %>%
head()
#> location target_end_date target_type true_value location_name forecast_date
#> 1: DE 2021-01-02 Cases 11.754310 Germany <NA>
#> 2: DE 2021-01-02 Deaths 8.419580 Germany <NA>
#> 3: DE 2021-01-09 Cases 11.950683 Germany <NA>
#> 4: DE 2021-01-09 Deaths 8.718991 Germany <NA>
#> 5: DE 2021-01-16 Cases 11.609907 Germany <NA>
#> 6: DE 2021-01-16 Deaths 8.677269 Germany <NA>
#> quantile prediction model horizon
#> 1: NA NA <NA> NA
#> 2: NA NA <NA> NA
#> 3: NA NA <NA> NA
#> 4: NA NA <NA> NA
#> 5: NA NA <NA> NA
#> 6: NA NA <NA> NA
# adding square root transformed forecasts to the original ones
example_quantile %>%
.[, true_value := ifelse(true_value < 0, 0, true_value)] %>%
transform_forecasts(fun = sqrt, label = "sqrt") %>%
score() %>%
summarise_scores(by = c("model", "scale"))
#> The following messages were produced when checking inputs:
#> 1. 288 values for `prediction` are NA in the data provided and the corresponding rows were removed. This may indicate a problem if unexpected.
#> model scale interval_score dispersion underprediction
#> 1: EuroCOVIDhub-baseline natural 11124.930667 2096.9535954 5143.5356658
#> 2: EuroCOVIDhub-baseline sqrt 27.742316 7.7296761 9.5936380
#> 3: EuroCOVIDhub-ensemble natural 5796.064569 1846.8527819 2120.6402853
#> 4: EuroCOVIDhub-ensemble sqrt 14.974344 4.2878323 5.1827454
#> 5: epiforecasts-EpiNow2 natural 7514.375476 2950.7342158 1697.2341137
#> 6: epiforecasts-EpiNow2 sqrt 17.704899 5.4112770 5.7235785
#> 7: UMass-MechBayes natural 52.651946 26.8723947 16.8009511
#> 8: UMass-MechBayes sqrt 1.328653 0.5993586 0.4019195
#> overprediction coverage_deviation bias ae_median
#> 1: 3884.4414062 0.003369565 0.21816406 16156.871094
#> 2: 10.4190016 0.003369565 0.21816406 39.185406
#> 3: 1828.5715014 0.048716033 0.00812500 8880.542969
#> 4: 5.5037665 0.048716033 0.00812500 22.458900
#> 5: 2866.4071466 -0.055169864 -0.04336032 11208.072874
#> 6: 6.5700431 -0.055169864 -0.04336032 25.585018
#> 7: 8.9786005 -0.023125000 -0.02234375 78.476562
#> 8: 0.3273746 -0.023125000 -0.02234375 2.069103
# adding multiple transformations
example_quantile %>%
.[, true_value := ifelse(true_value < 0, 0, true_value)] %>%
transform_forecasts(fun = log_shift, offset = 1) %>%
transform_forecasts(fun = sqrt, label = "sqrt") %>%
head()
#> location target_end_date target_type true_value location_name forecast_date
#> 1: DE 2021-01-02 Cases 127300 Germany <NA>
#> 2: DE 2021-01-02 Deaths 4534 Germany <NA>
#> 3: DE 2021-01-09 Cases 154922 Germany <NA>
#> 4: DE 2021-01-09 Deaths 6117 Germany <NA>
#> 5: DE 2021-01-16 Cases 110183 Germany <NA>
#> 6: DE 2021-01-16 Deaths 5867 Germany <NA>
#> quantile prediction model horizon scale
#> 1: NA NA <NA> NA natural
#> 2: NA NA <NA> NA natural
#> 3: NA NA <NA> NA natural
#> 4: NA NA <NA> NA natural
#> 5: NA NA <NA> NA natural
#> 6: NA NA <NA> NA natural
```