Reporting delays and right-truncation of line list data

If you are unfamiliar with the {simulist} package or the sim_linelist() function Get Started vignette is a great place to start.

This vignette covers reporting delays in line list data, how to use {simulist} to produce line list data with a delay between symptom onset and reporting, explains right truncation in outbreak data sets and shows how to use the truncate_linelist() function in {simulist} to augment a simulated line list to resemble real-time outbreak data.

Reporting delays

Reporting delays in line list data during an infectious disease outbreak refer to the time lag between when an event (e.g., infection, symptom onset, or hospitalisation) occurs and when it is officially recorded or reported. These delays can arise from factors like diagnostic testing turnaround times, administrative processing, or delayed healthcare-seeking behaviour. In line list data sets, these delays are captured as separate times/dates for different event types, such as the dates of symptom onset, specimen collection, laboratory confirmation, or case reporting. For each case, the delay is the difference between these times/dates, allowing researchers to quantify and adjust for reporting delays when analysing outbreak dynamics. Accurate recording of these dates is crucial for reconstructing the epidemic curve and assessing the timeliness of public health responses.

In {simulist}, sim_linelist() outputs a line list with a date of reporting ($date_reporting column), which by default will be identical to the date of symptom onset ($date_onset). However, it is possible to parameterise a reporting delay that can be used by sim_linelist() to simulate a delay between symptom onset and reporting. In {simulist} we assume that the reporting delay is the delay between symptom onset and it being reported, it does not reflect reporting of hospitalisation or outcome times.

library(simulist)
library(epiparameter)
library(tidyr)
library(dplyr)
#> 
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union
library(ggplot2)
library(incidence2)
#> Loading required package: grates

First we load the required delay distributions using the {epiparameter} package.

contact_distribution <- epiparameter(
  disease = "COVID-19",
  epi_name = "contact distribution",
  prob_distribution = create_prob_distribution(
    prob_distribution = "pois",
    prob_distribution_params = c(mean = 2)
  )
)
#> Citation cannot be created as author, year, journal or title is missing

infectious_period <- epiparameter(
  disease = "COVID-19",
  epi_name = "infectious period",
  prob_distribution = create_prob_distribution(
    prob_distribution = "gamma",
    prob_distribution_params = c(shape = 3, scale = 2)
  )
)
#> Citation cannot be created as author, year, journal or title is missing

onset_to_hosp <- epiparameter(
  disease = "COVID-19",
  epi_name = "onset to hospitalisation",
  prob_distribution = create_prob_distribution(
    prob_distribution = "lnorm",
    prob_distribution_params = c(meanlog = 1, sdlog = 0.5)
  )
)
#> Citation cannot be created as author, year, journal or title is missing

# get onset to death from {epiparameter} database
onset_to_death <- epiparameter_db(
  disease = "COVID-19",
  epi_name = "onset to death",
  single_epiparameter = TRUE
)
#> Using Linton N, Kobayashi T, Yang Y, Hayashi K, Akhmetzhanov A, Jung S, Yuan
#> B, Kinoshita R, Nishiura H (2020). "Incubation Period and Other
#> Epidemiological Characteristics of 2019 Novel Coronavirus Infections
#> with Right Truncation: A Statistical Analysis of Publicly Available
#> Case Data." _Journal of Clinical Medicine_. doi:10.3390/jcm9020538
#> <https://doi.org/10.3390/jcm9020538>.. 
#> To retrieve the citation use the 'get_citation' function

Setting the seed ensures we have the same output each time the vignette is rendered. When using {simulist}, setting the seed is not required unless you need to simulate the same line list multiple times.

set.seed(123)

Using a simple line list simulation without specifying a reporting delay will produce reporting times identical to symptom onset times:

linelist <- sim_linelist(
  contact_distribution = contact_distribution,
  infectious_period = infectious_period,
  prob_infection = 0.5,
  onset_to_hosp = onset_to_hosp,
  onset_to_death = onset_to_death
)
identical(linelist$date_onset, linelist$date_reporting)
#> [1] TRUE

The reporting delay can be specified as a (random) number generating function to the reporting_delay argument in sim_linelist().

In this example we assume the reporting delays are distributed according to a lognormal distribution with parameters: meanlog = 1 and sdlog = 1 (or a mean of approximately 4.5 days and standard deviation of 5.9 days).

linelist <- sim_linelist(
  contact_distribution = contact_distribution,
  infectious_period = infectious_period,
  prob_infection = 0.5,
  onset_to_hosp = onset_to_hosp,
  onset_to_death = onset_to_death,
  reporting_delay = function(x) rlnorm(n = x, meanlog = 1, sdlog = 1)
)
head(linelist)
#>   id        case_name case_type sex age date_onset date_reporting
#> 1  1  Oscar Jaracuaro  probable   m  66 2023-01-01     2023-01-06
#> 2  2     Jose Herrera  probable   m  21 2023-01-04     2023-01-17
#> 3  3 Mamoon el-Hakeem confirmed   m   8 2023-01-05     2023-01-19
#> 4  4     Gettay Penny confirmed   f  33 2023-01-05     2023-01-16
#> 5  5     Miguel Leyba confirmed   m  79 2023-01-05     2023-01-06
#> 6  6     Mary Monahan confirmed   f  88 2023-01-11     2023-01-16
#>   date_admission   outcome date_outcome date_first_contact date_last_contact
#> 1     2023-01-05 recovered         <NA>               <NA>              <NA>
#> 2           <NA> recovered         <NA>         2023-01-03        2023-01-04
#> 3           <NA> recovered         <NA>         2023-01-07        2023-01-09
#> 4     2023-01-10 recovered         <NA>         2023-01-03        2023-01-06
#> 5           <NA> recovered         <NA>         2023-01-04        2023-01-07
#> 6           <NA> recovered         <NA>         2023-01-06        2023-01-08
#>   ct_value
#> 1       NA
#> 2       NA
#> 3     26.5
#> 4     25.2
#> 5     24.0
#> 6     28.7

Here from the first 6 rows of the line list you can see differences between the $date_onset column and the $date_reporting column.

tidy_linelist <- linelist %>%
  pivot_longer(
    cols = c("date_onset", "date_reporting", "date_admission", "date_outcome")
  ) %>%
  mutate(ordering_value = ifelse(name == "date_onset", value, NA)) %>% # nolint consecutive_mutate_linter
  mutate(case_name = reorder(case_name, ordering_value, min, na.rm = TRUE)) # nolint consecutive_mutate_linter

ggplot(data = tidy_linelist) +
  geom_line(
    mapping = aes(x = value, y = case_name),
    linewidth = 0.25
  ) +
  geom_point(
    mapping = aes(
      x = value,
      y = case_name,
      shape = name,
      col = name
    ), size = 2
  ) +
  scale_x_date(name = "Event date", date_breaks = "week") +
  scale_y_discrete(name = "Case name") +
  scale_color_brewer(
    palette = "Set1",
    name = "Event type",
    labels = c("Date Admission", "Date Onset", "Date Outcome", "Date Reporting")
  ) +
  scale_shape_manual(
    name = "Event type",
    labels = c(
      "Date Admission", "Date Onset", "Date Outcome", "Date Reporting"
    ),
    values = c(15, 16, 17, 18)
  ) +
  theme_bw() +
  theme(legend.position = "bottom", axis.text.y = element_text(size = 4))
#> Warning: Removed 159 rows containing missing values or values outside the scale range
#> (`geom_line()`).
#> Warning: Removed 159 rows containing missing values or values outside the scale range
#> (`geom_point()`).

If we plot the difference between the date of symptom onset and reporting then the distribution is roughly lognormally distributed.

ggplot(data = linelist) +
  geom_histogram(
    mapping = aes(x = as.numeric(date_reporting - date_onset)),
    binwidth = 2
  ) +
  scale_x_continuous(
    name = paste0(
      "Reporting delay (",
      attr(linelist$date_reporting - linelist$date_onset, "units"),
      ")"
    )
  ) +
  theme_bw() +
  theme(axis.title.y = element_blank())

If instead of a variable reporting delay you want to simulate a fixed reporting delay, for example, the date of reporting is always 5 days after the date of symptom onset, then a different function can be supplied. One option is to set the parameter that controls the variance of the probability distribution to zero (in the case of the lognormal distribution, setting sdlog = 0), but a simpler and more readable option would be to give a number generating function that always returned 5.

We once again simulate to produce a line list with a fixed reporting delay.

linelist <- sim_linelist(
  contact_distribution = contact_distribution,
  infectious_period = infectious_period,
  prob_infection = 0.5,
  onset_to_hosp = onset_to_hosp,
  onset_to_death = onset_to_death,
  reporting_delay = function(x) rep(5, times = x)
)
head(linelist)
#>   id          case_name case_type sex age date_onset date_reporting
#> 1  1 Francisco Gardunio  probable   m  26 2023-01-01     2023-01-06
#> 2  4       Kiley Morris confirmed   f  73 2023-01-04     2023-01-09
#> 3  5      Joseph Abrams confirmed   m  14 2023-01-02     2023-01-07
#> 4  7    Allison Worsham  probable   f   3 2023-01-04     2023-01-09
#> 5  8       Sou Guerrero confirmed   m  85 2023-01-08     2023-01-13
#> 6  9    Kayla Crawleigh confirmed   f  68 2023-01-04     2023-01-09
#>   date_admission   outcome date_outcome date_first_contact date_last_contact
#> 1     2023-01-04 recovered         <NA>               <NA>              <NA>
#> 2           <NA> recovered         <NA>         2023-01-03        2023-01-05
#> 3     2023-01-04 recovered         <NA>         2022-12-31        2023-01-03
#> 4           <NA> recovered         <NA>         2023-01-06        2023-01-06
#> 5           <NA> recovered         <NA>         2023-01-09        2023-01-11
#> 6           <NA> recovered         <NA>         2023-01-03        2023-01-05
#>   ct_value
#> 1       NA
#> 2     26.8
#> 3     23.5
#> 4       NA
#> 5     24.0
#> 6     23.7
linelist$date_reporting - linelist$date_onset
#> Time differences in days
#>  [1] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

Truncation

Right truncation in infectious disease data occurs when only individuals who have experienced a specific event by a certain time can be included in the linelist. This leads to an underestimate of recent cases or death, and is especially relevant for ongoing outbreaks where recent cases might not have been recorded. It can also happen if cases are no longer recorded after a certain point in time.

Right-truncated outbreak data, in particular line list data, can give the impression that the incidence is decreasing (R < 1), however this can be an artefact resulting from the fact the data is right-truncated, and the outbreak can be stable or growing.

By default {simulist} simulates an outbreak from start to finish. Therefore, the line list or contact data contain all cases and outcomes. In order to get data that is more representative of ongoing outbreak dynamics where recent cases are not yet recorded and may be revised upwards in the future the truncate_linelist() function can be applied.

Re-simulating a simple line list using sim_linelist().

# set seed to produce small line list
set.seed(1)
linelist <- sim_linelist(
  contact_distribution = contact_distribution,
  infectious_period = infectious_period,
  prob_infection = 0.5,
  onset_to_hosp = onset_to_hosp,
  onset_to_death = onset_to_death
)

# first 6 rows of linelist
head(linelist)
#>   id           case_name case_type sex age date_onset date_reporting
#> 1  1    Munsif al-Demian suspected   m  35 2023-01-01     2023-01-01
#> 2  2       Zachary Nault confirmed   m  43 2023-01-01     2023-01-01
#> 3  3      Tae Woo Ralpho confirmed   m   1 2023-01-02     2023-01-02
#> 4  5 Abdul Kader el-Diab suspected   m  78 2023-01-05     2023-01-05
#> 5  6      Katelyn Catlin confirmed   f  22 2023-01-02     2023-01-02
#> 6  8        Lynsey Duron confirmed   f  28 2023-01-04     2023-01-04
#>   date_admission   outcome date_outcome date_first_contact date_last_contact
#> 1           <NA> recovered         <NA>               <NA>              <NA>
#> 2     2023-01-05 recovered         <NA>         2022-12-30        2023-01-05
#> 3           <NA> recovered         <NA>         2022-12-30        2023-01-02
#> 4     2023-01-07      died   2023-01-25         2022-12-29        2023-01-02
#> 5     2023-01-07      died   2023-01-11         2023-01-02        2023-01-04
#> 6           <NA> recovered         <NA>         2023-01-04        2023-01-05
#>   ct_value
#> 1       NA
#> 2     25.3
#> 3     25.8
#> 4       NA
#> 5     24.9
#> 6     24.5

Variable truncation point (default)

The right-truncation point for each individual (row) in the line list might not be equal, if for example there are regional differences in time taken to input data into a health information system. The truncate_linelist() function has a delay argument, which accepts a function that generates random numbers from which the truncation point can be sampled.

Here we define the time between the latest, or user-specified date, and the time point at which data is truncated as the truncation point.

In the plot below we show the truncation points as a cross for each case. If the cross falls before the truncation event, in this case date of reporting, then the case is removed from the linelist, if it falls after the date of reporting but before the hospital admission and/or outcome date they are set to NA.

tidy_linelist <- linelist %>%
  pivot_longer(
    cols = c("date_onset", "date_reporting", "date_admission", "date_outcome")
  ) %>%
  mutate(ordering_value = ifelse(name == "date_onset", value, NA)) %>% # nolint consecutive_mutate_linter
  mutate(case_name = reorder(case_name, ordering_value, min, na.rm = TRUE)) # nolint consecutive_mutate_linter

trunc_point <- data.frame(
  case_name = linelist$case_name,
  trunc_point = as.Date(
    max(
      unlist(
        linelist[grep(pattern = "date_", x = colnames(linelist), fixed = TRUE)]
      ),
      na.rm = TRUE
    ) - rlnorm(n = nrow(linelist), meanlog = 2.75, sdlog = 0.5),
    origin = "1970-01-01"
  )
)

ggplot(data = tidy_linelist) +
  geom_line(
    mapping = aes(x = value, y = case_name),
    linewidth = 0.25
  ) +
  geom_point(
    mapping = aes(
      x = value,
      y = case_name,
      shape = name,
      col = name
    ),
    size = 2
  ) +
  geom_point(
    data = trunc_point,
    mapping = aes(
      x = trunc_point,
      y = case_name
    ),
    shape = 4
  ) +
  scale_x_date(name = "Event date", date_breaks = "2 week") +
  scale_y_discrete(name = "Case name") +
  scale_color_brewer(
    palette = "Set1",
    name = "Event type",
    labels = c("Date Admission", "Date Onset", "Date Outcome", "Date Reporting")
  ) +
  scale_shape_manual(
    name = "Event type",
    labels = c(
      "Date Admission", "Date Onset", "Date Outcome", "Date Reporting"
    ),
    values = c(15, 16, 17, 18)
  ) +
  theme_bw() +
  theme(legend.position = "bottom", axis.text.y = element_text(size = 4))
#> Warning: Removed 17 rows containing missing values or values outside the scale range
#> (`geom_line()`).
#> Warning: Removed 17 rows containing missing values or values outside the scale range
#> (`geom_point()`).

In this example one case is removed (Vladmir Sanchez) and two outcome times are set to NA (Benito Redding and Abdul Kadar el-Diab).

linelist_trunc <- truncate_linelist(
  linelist = linelist,
  delay = function(x) rlnorm(n = x, meanlog = 1, sdlog = 0.5)
)

By default truncate_linelist() will assume the event which is pertinent to the truncation of the data is the date of reporting ($date_reporting), as this is likely the date the data was input, even if this date is before the date of hospital admission ($date_admission) or date of outcome ($date_outcome). It also assumes that the date you want to sample the truncation times from is the end of the outbreak, which is defined as the latest date in any of the date columns of the line list.

Right-truncating line list date using {simulist} removes individuals (rows) when the sampled truncation time is less recent than the truncation event time (e.g. reporting date). For cases where the rows are kept because the truncation time is more recent than the truncation event, but there are subsequent events, such as date of hospitalisation, that are more recent than the truncation time, these events dates are set to NA. The reasoning being that these events are assumed to have not been reported yet.

Different truncation events

If the date influencing the right-truncation of line list date is not the date of reporting, but instead the date of symptom onset, date of hospitalisation, or date of outcome then this can be specified in truncate_linelist() by setting the truncation_event argument. This argument accepts "reporting" (default), "onset", "admission", "outcome".

linelist_trunc <- truncate_linelist(
  linelist = linelist,
  delay = function(x) rlnorm(n = x, meanlog = 1, sdlog = 0.5),
  truncation_event = "outcome"
)

Fixed truncation point

The delay argument in truncate_linelist() is flexible to allow the use of a variety of random number generators, such as different parametric probability distributions or different distribution parameters. This enables variability in the truncation. However, it may be warranted that the truncation point is the same for all cases. This could be the case if the reporting of cases during an outbreak stopped on a given date.

To adjust the line list for right truncation using a fixed truncation point we can use the same setup as specifying a fixed reporting_delay as outlined above. This will remove all events more recent than this time slice.

delay <- function(x) rep(6, times = x)
delay(10)
#>  [1] 6 6 6 6 6 6 6 6 6 6
linelist_trunc <- truncate_linelist(linelist = linelist, delay = delay)

Truncate to emulate different stages of outbreak

It is not possible to simulate a line list with sim_linelist() that is mid-way through an outbreak1. This can make it difficult to generate outbreak data sets that resemble early outbreak dynamics where incidence is increasing, or mid-outbreak, or late in an outbreak as the disease approaches extinction. These types of data sets are useful for testing outbreak analytics method that are applied in real-time outbreak scenarios.

The truncate_linelist() function enables converting a complete line list from sim_linelist() into a within-outbreak line list.

We can simulate another outbreak, this time with more cases, and plot the complete line list by aggregating to daily incidence using the {incidence2} package.

For a full overview of how to visualise outbreak data simulated with {simulist} see the Visualising simulated data vignette.

# set seed to produce single wave outbreak
set.seed(3)
linelist <- sim_linelist(
  contact_distribution = contact_distribution,
  infectious_period = infectious_period,
  prob_infection = 0.5,
  onset_to_hosp = onset_to_hosp,
  onset_to_death = onset_to_death,
  outbreak_size = c(500, 5000)
)

# create incidence object
weekly_inci <- incidence(
  x = linelist,
  date_index = "date_onset",
  interval = "epiweek",
  complete_dates = TRUE
)
plot(weekly_inci)
Daily incidence of cases from symptom onset including days with zero cases.

Daily incidence of cases from symptom onset including days with zero cases.

By looking at the outbreak, we can pick three points to truncate: 1) early in the outbreak when the epicurve is growing (1st February 2023, epiweek 5), 2) in the middle of the outbreak (15th March 2023, epiweek 11), and 3) late in the outbreak when the number of cases is declining and the end of the outbreak is near (1st May 2023, epiweek 18).

We use the max_date argument in truncate_linelist() to specify the date we want to apply the right truncation to, i.e. the sample truncation times are applied to max_date and not the day the outbreak is considered over (day of last event, the default setting). For this example we will set the right-truncation delay distribution to zero so it does not remove any cases before the max_date, and use the default truncation event (reporting date).

linelist_early <- truncate_linelist(
  linelist = linelist,
  delay = function(x) rep(0, times = x),
  max_date = "2023-02-01"
)
#> Truncation max date is: 2023-02-01.
#> Assuming an origin of '1970-01-01' in line with R >= v4.3.0.
inci_early <- incidence(
  x = linelist_early,
  date_index = "date_onset",
  interval = "epiweek",
  complete_dates = TRUE
)
plot(inci_early) +
  ggtitle("Early") +
  theme(plot.title = element_text(size = 25, hjust = 0.5))
linelist_mid <- truncate_linelist(
  linelist = linelist,
  delay = function(x) rep(0, times = x),
  max_date = "2023-03-15"
)
#> Truncation max date is: 2023-03-15.
#> Assuming an origin of '1970-01-01' in line with R >= v4.3.0.
inci_mid <- incidence(
  x = linelist_mid,
  date_index = "date_onset",
  interval = "epiweek",
  complete_dates = TRUE
)
plot(inci_mid) +
  ggtitle("Mid") +
  theme(plot.title = element_text(size = 25, hjust = 0.5))
linelist_late <- truncate_linelist(
  linelist = linelist,
  delay = function(x) rep(0, times = x),
  max_date = "2023-05-01"
)
#> Truncation max date is: 2023-05-01.
#> Assuming an origin of '1970-01-01' in line with R >= v4.3.0.
inci_late <- incidence(
  x = linelist_late,
  date_index = "date_onset",
  interval = "epiweek",
  complete_dates = TRUE
)
plot(inci_late) +
  ggtitle("Late") +
  theme(plot.title = element_text(size = 25, hjust = 0.5))

Next we repeat this procedure of creating data sets for early, mid, and late in the outbreak. For this example we will use the default right-truncation delay distribution (lognormal with meanlog = 0.58 and sdlog = 0.47) and default truncation event (reporting date).

linelist_early <- truncate_linelist(
  linelist = linelist,
  max_date = "2023-02-01"
)
#> Truncation max date is: 2023-02-01.
#> Assuming an origin of '1970-01-01' in line with R >= v4.3.0.
inci_early <- incidence(
  x = linelist_early,
  date_index = "date_onset",
  interval = "epiweek",
  complete_dates = TRUE
)
plot(inci_early) +
  ggtitle("Early") +
  theme(plot.title = element_text(size = 25, hjust = 0.5))
linelist_mid <- truncate_linelist(
  linelist = linelist,
  delay = function(x) rlnorm(n = x, meanlog = 1, sdlog = 0.5),
  max_date = "2023-03-15"
)
#> Truncation max date is: 2023-03-15.
#> Assuming an origin of '1970-01-01' in line with R >= v4.3.0.
inci_mid <- incidence(
  x = linelist_mid,
  date_index = "date_onset",
  interval = "epiweek",
  complete_dates = TRUE
)
plot(inci_mid) +
  ggtitle("Mid") +
  theme(plot.title = element_text(size = 25, hjust = 0.5))
linelist_late <- truncate_linelist(
  linelist = linelist,
  delay = function(x) rlnorm(n = x, meanlog = 1, sdlog = 0.5),
  max_date = "2023-05-01"
)
#> Truncation max date is: 2023-05-01.
#> Assuming an origin of '1970-01-01' in line with R >= v4.3.0.
inci_late <- incidence(
  x = linelist_late,
  date_index = "date_onset",
  interval = "epiweek",
  complete_dates = TRUE
)
plot(inci_late) +
  ggtitle("Late") +
  theme(plot.title = element_text(size = 25, hjust = 0.5))

Comparing the two sets of the three plots you can see how in the latter applying right truncation gives the impression that cases are declining.

These truncated line lists can be used to test methods that estimate the real-time reproduction number such as {EpiNow2} or {epinowcast}.

  1. sim_linelist() simulates an outbreak to extinction except in cases where the number of infected individuals exceeds the maximum outbreak size specified in the outbreak_size argument in sim_linelist(), which by default is 10^{4} where the line list returned is an ongoing outbreak.↩︎