Estimate a delay distribution from a reporting triangle

Provides an estimate of the reporting delay as a function of the delay, based on the reporting triangle and the number of reference date observations to be used in the estimation. This point estimate of the delay is computed empirically, using an iterative algorithm starting from the most recent observations. Use truncate_to_delay() if you want to limit the maximum delay before estimation. This code was adapted from code written (under an MIT license) by the Karlsruhe Institute of Technology RESPINOW German Hospitalization Nowcasting Hub. Modified from: https://github.com/KITmetricslab/RESPINOW-Hub/blob/7cce3ae2728116e8c8cc0e4ab29074462c24650e/code/baseline/functions.R#L55 #nolint

Usage

estimate_delay(
  reporting_triangle,
  n = nrow(reporting_triangle),
  preprocess = preprocess_negative_values,
  validate = TRUE
)

Arguments

reporting_triangle

A reporting_triangle object with rows representing reference times and columns representing delays. Can be a reporting matrix or incomplete reporting matrix. Can also be a ragged reporting triangle, where multiple columns are reported for the same row (e.g., weekly reporting of daily data).

n

Integer indicating the number of reference times (observations) to be used in the estimate of the reporting delay, always starting from the most recent reporting delay. The default is to use the whole reporting triangle, so nrow(reporting_triangle).

preprocess

Function to apply to the truncated triangle before estimation, or NULL to skip preprocessing. Default is preprocess_negative_values(), which handles negative values by redistributing them to earlier delays. Set to NULL if you want to preserve negative PMF entries (e.g., when working with downward corrections where negative probabilities reflect systematic adjustments). Custom preprocess functions must accept a validate parameter (defaults to TRUE) to enable validation optimisation in internal function chains.

validate

Logical. If TRUE (default), validates the object. Set to FALSE only when called from functions that already validated.

Value

Vector indexed at 0 of length ncol(reporting_triangle) with columns indicating the point estimate of the empirical probability mass on each delay.

See also

Delay distribution estimation functions preprocess_negative_values()

Examples

# Example 1: Standard usage with default preprocessing
delay_pmf <- estimate_delay(
  reporting_triangle = example_reporting_triangle
)
delay_pmf
#>          0          1          2          3 
#> 0.52654815 0.28277586 0.13006993 0.06060606 

# Example 2: Using data with downward corrections without preprocessing
# This preserves negative PMF entries reflecting systematic corrections
triangle_ex2 <- example_downward_corr_rt
delay_pmf_negative <- estimate_delay(
  reporting_triangle = triangle_ex2,
  n = 5,
  preprocess = NULL
)
delay_pmf_negative
#>           0           1           2           3 
#>  0.66544955  0.38806216 -0.14046823  0.08695652 
# Note: PMF may contain negative values and not sum to 1
sum(delay_pmf_negative)
#> [1] 1