% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/seqB.R
\name{seqB}
\alias{seqB}
\title{seqB method}
\usage{
seqB(NT, mu, kappa = 20)
}
\arguments{
\item{NT}{Vector of case counts.}

\item{mu}{Mean of the serial distribution. This needs to match case counts in
time units. For example, if case counts are weekly and the serial
distribution has a mean of seven days, then \code{mu} should be set
to one. If case counts are daily and the serial distribution has a
mean of seven days, then \code{mu} should be set to seven.}

\item{kappa}{Largest possible value of uniform prior (defaults to 20). This
describes the prior belief on ranges of R0, and should be set to
a higher value if R0 is believed to be larger.}
}
\value{
\code{seqB} returns a list containing the following components:
        \code{Rhat} is the estimate of R0 (the posterior mean),
        \code{posterior} is the posterior distribution of R0 from which
        alternate estimates can be obtained (see examples), and \code{group}
        is an indicator variable (if \code{group == TRUE}, zero values of NT
        were input and grouping was done to obtain \code{Rhat}). The variable
        \code{posterior} is returned as a list made up of \code{supp} (the
        support of the distribution) and \code{pmf} (the probability mass
        function).
}
\description{
This function implements a sequential Bayesian estimation method of R0 due to
Bettencourt and Riberio (PloS One, 2008). See details for important
implementation notes.
}
\details{
The method sets a uniform prior distribution on R0 with possible values
between zero and \code{kappa}, discretized to a fine grid. The distribution
of R0 is then updated sequentially, with one update for each new case count
observation. The final estimate of R0 is \code{Rhat}, the mean of the (last)
posterior distribution. The prior distribution is the initial belief of the
distribution of R0, which is the uninformative uniform distribution with
values between zero and \code{kappa}. Users can change the value of
\code{kappa} only (i.e., the prior distribution cannot be changed from the
uniform). As more case counts are observed, the influence of the prior
distribution should lessen on the final estimate \code{Rhat}.

This method is based on an approximation of the SIR model, which is most
valid at the beginning of an epidemic. The method assumes that the mean of
the serial distribution (sometimes called the serial interval) is known. The
final estimate can be quite sensitive to this value, so sensitivity testing
is strongly recommended. Users should be careful about units of time (e.g.,
are counts observed daily or weekly?) when implementing.

Our code has been modified to provide an estimate even if case counts equal
to zero are present in some time intervals. This is done by grouping the
counts over such periods of time. Without grouping, and in the presence of
zero counts, no estimate can be provided.
}
\examples{
# Weekly data.
NT <- c(1, 4, 10, 5, 3, 4, 19, 3, 3, 14, 4)

## Obtain R0 when the serial distribution has a mean of five days.
res1 <- seqB(NT, mu = 5 / 7)
res1$Rhat

## Obtain R0 when the serial distribution has a mean of three days.
res2 <- seqB(NT, mu = 3 / 7)
res2$Rhat

# Compute posterior mode instead of posterior mean and plot.

Rpost <- res1$posterior
loc <- which(Rpost$pmf == max(Rpost$pmf))
Rpost$supp[loc] # Posterior mode.
res1$Rhat # Compare with the posterior mean.

par(mfrow = c(2, 1), mar = c(2, 2, 1, 1))

plot(Rpost$supp, Rpost$pmf, col = "black", type = "l", xlab = "", ylab = "")
abline(h = 1 / (20 / 0.01 + 1), col = "red")
abline(v = res1$Rhat, col = "blue")
abline(v = Rpost$supp[loc], col = "purple")
legend("topright",
  legend = c("Prior", "Posterior", "Posterior mean", "Posterior mode"),
  col = c("red", "black", "blue", "purple"), lty = 1)

}