Example to estimate incubation period

Flavio Finger

2019-05-13

Description

This package contains two functions useful to compute the incubation period distribution from outbreak data. The inputs needed for each patient are given as a data.frame or linelist object and must contain:

• the date of onset of symptoms
• a list/vector of possible dates of exposure.

The function empirical_incubation_dist() computes the discrete probability distribution by giving equal weight to each patient. Thus, in the case of N patients, the n possible exposure dates of a given patient get the overall weight 1/(n*N). The function returns a data frame with column incubation_period containing the different incubation periods with a time step of one day and their relative_frequency.

The function fit_gamma_incubation_dist() takes the same inputs, but directly samples from the empirical distribution and fits a discrete gamma distribution to it by the means of fit_disc_gamma.

Example

Load environment:

library(magrittr)
library(linelist)
library(epitrix)
library(distcrete)
library(ggplot2)

Make a linelist object containing toy data with several possible exposure dates for each case:

ll <- messy_data() %>% clean_data()

x <- 0:15
y <- distcrete("gamma", 1, shape = 12, rate = 3, w = 0)$d(x)
mkexposures <- function(i) i - sample(x, size = sample.int(5, size = 1), replace = FALSE, prob = y)
exposures <- sapply(ll$date_of_onset, mkexposures)
ll$dates_exposure <- exposures

print(ll)
#>        id date_of_onset  discharge gender epi_case_definition messy_dates
#> 1  ujfkwq    2018-01-03 2018-01-13 female          not_a_case  2001-12-01
#> 2  eyxzua    2018-01-07 2018-01-17   male           confirmed        <NA>
#> 3  doulii    2018-01-05 2018-01-15   male          not_a_case        <NA>
#> 4  owvlbu    2018-01-02 2018-01-12 female           confirmed        <NA>
#> 5  wqbbyq    2018-01-05 2018-01-15 female           suspected        <NA>
#> 6  mauyjn    2018-01-02 2018-01-12   male          not_a_case  2001-12-01
#> 7  wahzsb    2018-01-09 2018-01-19   male            probable        <NA>
#> 8  wyhlwc    2018-01-02 2018-01-12 female           suspected        <NA>
#> 9  tbnecx    2018-01-02 2018-01-12   male           suspected        <NA>
#> 10 brithg    2018-01-08 2018-01-18   male           confirmed  2018-10-18
#> 11 kfezyj    2018-01-08 2018-01-18   male           suspected        <NA>
#> 12 anykpl    2018-01-02 2018-01-12 female            probable  1989-12-24
#> 13 ndffve    2018-01-09 2018-01-19 female          not_a_case  2001-12-01
#> 14 qykakh    2018-01-09 2018-01-19   male          not_a_case        <NA>
#> 15 aprglr    2018-01-06 2018-01-16 female          not_a_case        <NA>
#> 16 hwepnc    2018-01-07 2018-01-17 female            probable  2018-10-18
#> 17 nlmqas    2018-01-08 2018-01-18 female            probable  2018-10-17
#> 18 wuzznf    2018-01-06 2018-01-16   male           suspected        <NA>
#> 19 obzshh    2018-01-04 2018-01-14   male           suspected  1989-12-24
#> 20 nvlxer    2018-01-04 2018-01-14 female           suspected  2018-10-17
#>          lat      lon                    dates_exposure
#> 1  12.688208 48.36797               17530, 17529, 17531
#> 2   9.496732 48.10133                      17535, 17536
#> 3  13.276658 49.10333 17533, 17532, 17535, 17527, 17534
#> 4  15.443281 50.26166        17529, 17530, 17528, 17531
#> 5  12.186121 47.46422        17534, 17533, 17532, 17531
#> 6  10.887826 48.27850        17528, 17531, 17529, 17530
#> 7  11.755842 47.69728                             17539
#> 8  12.484501 50.46869               17528, 17527, 17531
#> 9  11.566569 47.99664               17528, 17529, 17530
#> 10 13.635864 48.10328 17537, 17534, 17535, 17536, 17533
#> 11 15.703823 48.67810                             17536
#> 12 12.643401 48.12971               17531, 17530, 17529
#> 13 15.226172 48.88853        17536, 17537, 17538, 17535
#> 14 13.603475 46.06085                             17538
#> 15 10.708423 48.01061 17534, 17533, 17531, 17535, 17536
#> 16 14.720354 47.77516 17535, 17534, 17533, 17531, 17536
#> 17 12.902306 49.15254                             17536
#> 18 14.379251 46.48828        17535, 17534, 17532, 17530
#> 19 14.677445 47.84708 17532, 17533, 17531, 17530, 17529
#> 20 15.894964 48.53582 17532, 17531, 17530, 17533, 17529

Empirical distribution:

incubation_period_dist <- empirical_incubation_dist(ll, date_of_onset, dates_exposure)
print(incubation_period_dist)
#> # A tibble: 10 x 2
#>    incubation_period relative_frequency
#>                <dbl>              <dbl>
#>  1                 0             0     
#>  2                 1             0.0700
#>  3                 2             0.231 
#>  4                 3             0.298 
#>  5                 4             0.16  
#>  6                 5             0.152 
#>  7                 6             0.0567
#>  8                 7             0.0225
#>  9                 8             0     
#> 10                 9             0.01

ggplot(incubation_period_dist, aes(incubation_period, relative_frequency)) +
  geom_col()

Fit discrete gamma:

fit <- fit_gamma_incubation_dist(ll, date_of_onset, dates_exposure)
print(fit)
#> $mu
#> [1] 3.984821
#> 
#> $cv
#> [1] 0.3827553
#> 
#> $sd
#> [1] 1.525211
#> 
#> $ll
#> [1] -1812.963
#> 
#> $converged
#> [1] TRUE
#> 
#> $distribution
#> A discrete distribution
#>   name: gamma
#>   parameters:
#>     shape: 6.82586216220056
#>     scale: 0.58378274853449

x = c(0:10)
y = fit$distribution$d(x)
ggplot(data.frame(x = x, y = y), aes(x, y)) +
  geom_col(data = incubation_period_dist, aes(incubation_period, relative_frequency)) +
  geom_point(stat="identity", col = "red", size = 3) +
  geom_line(stat="identity", col = "red")

Note that if the possible exposure dates are consecutive for all patients then empirical_incubation_dist() and fit_gamma_incubation_dist() can take date ranges as inputs instead of lists of individual exposure dates (see help for details).