---
title: "Example to estimate incubation period"
author: "Flavio Finger"
date: "`r Sys.Date()`"
output:
   rmarkdown::html_vignette:
     toc: true
     toc_depth: 2
vignette: >
  %\VignetteIndexEntry{Estimating Incubation Period}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, echo = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.width=7,
  fig.height=5,
  fig.path="figs-overview/"
)
```

# 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:

```{r, echo = TRUE, message=FALSE}
library(magrittr)
library(epitrix)
library(distcrete)
library(ggplot2)
```

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

```{r, echo = TRUE}
ll <- sim_linelist(15)

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)
```

Empirical distribution:

```{r}
incubation_period_dist <- empirical_incubation_dist(ll, date_of_onset, dates_exposure)
print(incubation_period_dist)

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

Fit discrete gamma:

```{r}
fit <- fit_gamma_incubation_dist(ll, date_of_onset, dates_exposure)
print(fit)

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).