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Apply a time varying probability and convolution to count data

Source: R/simulation-utils.R
sim_convolution.Rd

Standard convolution assumes one delay distribution. This is actually not what we see in reality as delays can depend on any factors, including the day of week. This function applies a convolution to an input time-series when that convolution is expressed as a function (usually of time, but can be of anything in the input dataframe). The convolution is then sampled using a poisson or negative binomial

Usage

sim_convolution(
  df = i_sim_count_data,
  p_fn,
  delay_fn,
  ...,
  input = "infections",
  output,
  kappa = 1,
  from = c("count", "rate")
)

Arguments

df

a count dataframe from e.g. sim_poisson_model() or sim_summarise_linelist() - a dataframe with columns:

  • statistic (character) - An identifier for the statistic, whether that be infections, admissions, deaths

  • count (positive_integer) - Positive case counts associated with the specified time frame

  • time (ggoutbreak::time_period + group_unique) - A (usually complete) set of singular observations per unit time as a `time_period`

Minimally grouped by: statistic (and other groupings allowed).

p_fn

a function that takes a time parameter and potentially and returns probability of observation given something occurs. a no-op for this parameter is ~ 1.

delay_fn

a function that takes time and returns the probability of observation (given it occurred) over time since infection (i.e. tau) as an ip delay distribution. This does not have to sum to 1 (e.g. mapping incidence to prevalence) but if not then the combination of p_fn and delay_fn is less easy to interpret. This should behave sensibly if p changes halfway through a convolution. See cfg_weekly_ip_fn() and cfg_gamma_ip_fn() for helper functions to construct this parameter. A no-op for this parameter would be ~ ifelse(.x==0,1,0).

...

not used

input

the input statistic

output

the output statistic

kappa

dispersion. scaled such that poisson dispersion is 1. Values must be 0 (no dispersion), 1 (poisson dispersion) or greater than 1 for over-dispersion.

from

Controls if you base future counts on previous counts or on underlying rate, defaults to count but rate is a possibility if you want to base the convolution off a more theoretical value rather than observed cases. Either way the convolution generates a new rate which is in turn sampled into a poisson or negative binomial count.

Value

return the result of applying this convolution to the data.

Examples

weekday_delay = make_gamma_ip(median_of_mean = 5, median_of_sd = 2)
weekend_delay = make_gamma_ip(median_of_mean = 6, median_of_sd = 2)

delay_fn = ~ ifelse(.x %% 7 %in% c(6,7), list(weekend_delay), list(weekday_delay))
p_fn = ~ ifelse(.x < 20, 0.5, 0.75)

data = dplyr::tibble(
    time=1:40,
    count = rep(100,40),
    rate = rep(100,40),
    statistic="infections") %>% dplyr::group_by(statistic)
delayed = data %>%
    sim_convolution(p_fn,delay_fn,output="delayed") %>%
    dplyr::filter(statistic=="delayed")
if (interactive()) ggplot2::ggplot(delayed,ggplot2::aes(x=time))+
  ggplot2::geom_line(ggplot2::aes(y=rate))+
  ggplot2::geom_line(ggplot2::aes(y=count))

# other example delay functions
delay_fn = cfg_gamma_ip_fn( ~ ifelse(.x<5, 8, 4))