R/Idist.R

In EpiLPS: A Fast and Flexible Bayesian Tool for Estimating Epidemiological Parameters

#' Density function and discrete distribution for a disease interval
#'
#' @description
#' This function computes the probability density function and probability mass
#' function for a disease interval (e.g. the serial interval defined as the time
#' elapsed between the symptom onset in an infector and the onset of
#' symptoms in the secondary cases generated by that infector). It takes as
#' input the mean and the standard deviation of the disease interval (expressed
#'  in days) and gives as an output the interval distribution based on
#' a chosen parametric family.
#'
#' @usage Idist(mean, sd, dist = c("gamma", "weibull", "lognorm"), probs = NULL)
#'
#' @param mean The mean of the disease interval (must be larger than 1).
#' @param sd A positive and finite real number corresponding to the standard
#' deviation of the disease interval.
#' @param dist A choice among a Gamma, Weibull or Log-normal distribution for
#' the disease interval.
#' @param probs A vector of probabilities for the interval distribution.
#'
#' @return A list of class \code{Idist} containing a vector of probabilities
#' corresponding to the discrete distribution of the disease interval,
#' the name of the chosen parametric distribution and its parameters.
#'
#' @details The discretization is based on the formula in Held et al. (2019).
#'
#' @author Oswaldo Gressani \email{oswaldo_gressani@hotmail.fr}
#'
#' @references Held, L., Hens, N., D O'Neill, P., and Wallinga, J. (2019).
#' Handbook of infectious disease data analysis. \emph{CRC Press}.
#'
#' @examples
#' Idist(mean = 2.6, sd = 1.5)
#'
#' @export


Idist <- function(mean, sd, dist = c("gamma", "weibull", "lognorm"),
                  probs = NULL){

  if(is.null(probs)){
    if(mean <= 1)
      stop("mean must be larger than 1")
    if(sd < 0)
      stop("sd must be strictly positive")
    # If Gamma distribution with shape rate parameterization
    cdist <- match.arg(dist)
    if (cdist == "gamma") {
      shape <- (mean / sd) ^ 2
      rate <- mean / (sd ^ 2)
      # Discrete upper bound (largest possible generatio time for instance)
      Dmax <- floor(stats::qgamma(0.9999, shape, rate))
      # gt pmf
      gt <- function(t){
        val <- (stats::pgamma(t + 0.5, shape, rate)-
                  stats::pgamma(t - 0.5, shape, rate))/
          (stats::pgamma(Dmax + 0.5, shape, rate)-
             stats::pgamma(0.5, shape, rate))
        return(val)
      }
      pvec <- sapply(seq_len(Dmax), gt)
      outlist <- list(pvec = pvec, dist = cdist, shape = shape, rate = rate)
    } else if (cdist == "weibull"){ # Weibull with shape scale

      fa <- function(a) {
        val <- (mean / gamma(1 + (1 / a))) ^ 2 *
          (gamma(1 + (2 / a)) - gamma(1 + (1 / a)) ^ 2) - (sd ^ 2)
        return(val)
      }
      # Approach lower bound from the left
      lb <- 1e-5
      fa_lb <- fa(lb)
      while(is.na(fa_lb) || is.infinite(fa_lb)){
        lb <- lb + 0.001
        fa_lb <- fa(lb)
      }
      shape <- stats::uniroot(fa, lower = lb, upper = 2*mean)$root
      scale <- mean / (gamma(1 + (1 / shape)))
      Dmax <- floor(stats::qweibull(0.9999, shape, scale))
      # gt pmf
      gt <- function(t){
        val <- (stats::pweibull(t + 0.5, shape, scale)-
                  stats::pweibull(t - 0.5, shape, scale))/
          (stats::pweibull(Dmax + 0.5, shape, scale)-
             stats::pweibull(0.5, shape, scale))
        return(val)
      }
      pvec <- sapply(seq_len(Dmax), gt)
      outlist <- list(pvec = pvec, dist = cdist, shape = shape, scale = scale)
    } else if (cdist == "lognorm"){ # Log normal with location scale
      fmu <- function(mu) {
        val <- exp(4 * log(mean) - 2 * mu) - mean^2 - (sd ^ 2)
        return(val)
      }
      # Approach lower bound from the left
      lb <- 1e-5
      fmu_lb <- fmu(lb)
      while(is.na(fmu_lb) || is.infinite(fmu_lb)){
        lb <- lb + 0.001
        fmu_lb <- fmu(lb)
      }
      location <- stats::uniroot(fmu, lower = lb, upper = 2 * mean)$root
      scale2 <- 2 * (log(mean)-location)
      scale <- sqrt(scale2)
      Dmax <- floor(stats::qlnorm(0.9999, meanlog = location,
                                  sdlog = sqrt(scale2)))
      # gt pmf
      gt <- function(t){
        val <- (stats::plnorm(t + 0.5, meanlog = location, sdlog = scale)-
                  stats::plnorm(t - 0.5, meanlog = location, sdlog = scale))/
          (stats::plnorm(Dmax + 0.5, meanlog = location, sdlog = scale)-
             stats::plnorm(0.5, meanlog = location, sdlog = scale))
        return(val)
      }
      pvec <- sapply(seq_len(Dmax), gt)
      outlist <- list(pvec = pvec, dist = cdist, location = location,
                      scale = scale)
    }
  } else {
    mean <- NA
    sd <- NA
    outlist <- list(pvec = probs)
  }
  attr(outlist, "class") <- "Idist"
  outlist
}