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authorNaeem Model <me@nmode.ca>2023-06-29 23:47:01 +0000
committerNaeem Model <me@nmode.ca>2023-06-29 23:47:01 +0000
commit80df3ed7a280f86a3b9b5443309487d428f4fe95 (patch)
treebad65796f40c62320ce0d92d6940d7c8685e7685
parentf4327720b605385e68039af924b9cafef2416717 (diff)
Re-style code and enforce 80 character line limit
-rw-r--r--R/ID.R56
-rw-r--r--R/IDEA.R72
-rw-r--r--R/WP.R164
-rw-r--r--R/WP_internal.R132
-rw-r--r--R/seqB.R201
5 files changed, 324 insertions, 301 deletions
diff --git a/R/ID.R b/R/ID.R
index 0e3cc35..7e8a04d 100644
--- a/R/ID.R
+++ b/R/ID.R
@@ -1,48 +1,46 @@
#' ID method
#'
-#' This function implements a least squares estimation method of R0 due to Fisman et al. (PloS One, 2013).
-#' See details for implementation notes.
+#' This function implements a least squares estimation method of R0 due to
+#' Fisman et al. (PloS One, 2013). See details for implementation notes.
#'
-#' The method is based on a straightforward incidence decay model. The estimate of R0 is the value which
-#' minimizes the sum of squares between observed case counts and cases counts 'expected' under the model.
+#' The method is based on a straightforward incidence decay model. The estimate
+#' of R0 is the value which minimizes the sum of squares between observed case
+#' counts and cases counts 'expected' under the model.
#'
-#' 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.
+#' 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.
#'
#' @param NT Vector of case counts.
-#' @param 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.
+#' @param 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.
#'
#' @return \code{ID} returns a single value, the estimate of R0.
#'
#' @examples
-#' ## ===================================================== ##
-#' ## Illustrate on weekly data ##
-#' ## ===================================================== ##
-#'
+#' # Weekly data:
#' NT <- c(1, 4, 10, 5, 3, 4, 19, 3, 3, 14, 4)
-#' ## obtain Rhat when serial distribution has mean of five days
-#' ID(NT=NT, mu=5/7)
-#' ## obtain Rhat when serial distribution has mean of three days
-#' ID(NT=NT, mu=3/7)
#'
-#' ## ========================================================= ##
-#' ## Compute Rhat using only the first five weeks of data ##
-#' ## ========================================================= ##
+#' # Obtain R0 when the serial distribution has a mean of five days.
+#' ID(NT, mu = 5 / 7)
#'
-#' ID(NT=NT[1:5], mu=5/7) # serial distribution has mean of five days
+#' # Obtain R0 when the serial distribution has a mean of three days.
+#' ID(NT, mu = 3 / 7)
#'
#' @export
ID <- function(NT, mu) {
- NT <- as.numeric(NT)
- TT <- length(NT)
- s <- (1:TT) / mu
- y <- log(NT) / s
+ NT <- as.numeric(NT)
+ TT <- length(NT)
+ s <- (1:TT) / mu
+ y <- log(NT) / s
- R0_ID <- exp(sum(y) / TT)
+ R0_ID <- exp(sum(y) / TT)
- return(R0_ID)
+ return(R0_ID)
}
diff --git a/R/IDEA.R b/R/IDEA.R
index 854acd7..53fa653 100644
--- a/R/IDEA.R
+++ b/R/IDEA.R
@@ -1,58 +1,56 @@
#' IDEA method
#'
-#' This function implements a least squares estimation method of R0 due to Fisman et al. (PloS One, 2013).
-#' See details for implementation notes.
+#' This function implements a least squares estimation method of R0 due to
+#' Fisman et al. (PloS One, 2013). See details for implementation notes.
#'
-#' This method is closely related to that implemented in \code{ID}. The method is based on an incidence decay model.
-#' The estimate of R0 is the value which minimizes the sum of squares between observed case counts and cases counts
+#' This method is closely related to that implemented in \code{ID}. The method
+#' is based on an incidence decay model. The estimate of R0 is the value which
+#' minimizes the sum of squares between observed case counts and cases counts
#' expected under the model.
#'
-#' 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.
+#' 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.
#'
#' @param NT Vector of case counts.
-#' @param 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.
+#' @param 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.
#'
#' @return \code{IDEA} returns a single value, the estimate of R0.
#'
#' @examples
-#' ## ===================================================== ##
-#' ## Illustrate on weekly data ##
-#' ## ===================================================== ##
-#'
+#' # Weekly data.
#' NT <- c(1, 4, 10, 5, 3, 4, 19, 3, 3, 14, 4)
-#' ## obtain Rhat when serial distribution has mean of five days
-#' IDEA(NT=NT, mu=5/7)
-#' ## obtain Rhat when serial distribution has mean of three days
-#' IDEA(NT=NT, mu=3/7)
#'
-#' ## ========================================================= ##
-#' ## Compute Rhat using only the first five weeks of data ##
-#' ## ========================================================= ##
+#' # Obtain R0 when the serial distribution has a mean of five days.
+#' IDEA(NT, mu = 5 / 7)
#'
-#' IDEA(NT=NT[1:5], mu=5/7) # serial distribution has mean of five days
+#' # Obtain R0 when the serial distribution has a mean of three days.
+#' IDEA(NT, mu = 3 / 7)
#'
#' @export
IDEA <- function(NT, mu) {
- if (length(NT) < 2)
- print("Warning: length of NT should be at least two.")
- else {
- NT <- as.numeric(NT)
- TT <- length(NT)
- s <- (1:TT) / mu
+ if (length(NT) < 2)
+ print("Warning: length of NT should be at least two.")
+ else {
+ NT <- as.numeric(NT)
+ TT <- length(NT)
+ s <- (1:TT) / mu
- y1 <- log(NT) / s
- y2 <- s^2
- y3 <- log(NT)
+ y1 <- log(NT) / s
+ y2 <- s^2
+ y3 <- log(NT)
- IDEA1 <- sum(y2) * sum(y1) - sum(s) * sum(y3)
- IDEA2 <- TT * sum(y2) - sum(s)^2
- IDEA <- exp(IDEA1 / IDEA2)
+ IDEA1 <- sum(y2) * sum(y1) - sum(s) * sum(y3)
+ IDEA2 <- TT * sum(y2) - sum(s)^2
+ IDEA <- exp(IDEA1 / IDEA2)
- return(IDEA)
- }
+ return(IDEA)
+ }
}
diff --git a/R/WP.R b/R/WP.R
index c8178b7..a6e5354 100644
--- a/R/WP.R
+++ b/R/WP.R
@@ -1,98 +1,112 @@
#' WP method
#'
-#' This function implements an R0 estimation due to White and Pagano (Statistics in Medicine, 2008).
-#' The method is based on maximum likelihood estimation in a Poisson transmission model.
-#' See details for important implementation notes.
+#' This function implements an R0 estimation due to White and Pagano (Statistics
+#' in Medicine, 2008). The method is based on maximum likelihood estimation in a
+#' Poisson transmission model. See details for important implementation notes.
#'
-#' This method is based on a Poisson transmission model, and hence may be most most valid at the beginning
-#' of an epidemic. In their model, the serial distribution is assumed to be discrete with a finite number
-#' of posible values. In this implementation, if \code{mu} is not {NA}, the serial distribution is taken to
-#' be a discretized version of a gamma distribution with mean \code{mu}, shape parameter one, and largest
-#' possible value based on parameter \code{tol}. When \code{mu} is \code{NA}, the function implements a
-#' grid search algorithm to find the maximum likelihood estimator over all possible gamma distributions
-#' with unknown mean and variance, restricting these to a prespecified grid (see \code{search} parameter).
+#' This method is based on a Poisson transmission model, and hence may be most
+#' most valid at the beginning of an epidemic. In their model, the serial
+#' distribution is assumed to be discrete with a finite number of posible
+#' values. In this implementation, if \code{mu} is not {NA}, the serial
+#' distribution is taken to be a discretized version of a gamma distribution
+#' with mean \code{mu}, shape parameter one, and largest possible value based on
+#' parameter \code{tol}. When \code{mu} is \code{NA}, the function implements a
+#' grid search algorithm to find the maximum likelihood estimator over all
+#' possible gamma distributions with unknown mean and variance, restricting
+#' these to a prespecified grid (see \code{search} parameter).
#'
-#' When the serial distribution is known (i.e., \code{mu} is not \code{NA}), sensitivity testing of \code{mu}
-#' is strongly recommended. If the serial distribution is unknown (i.e., \code{mu} is \code{NA}), the
-#' likelihood function can be flat near the maximum, resulting in numerical instability of the optimizer.
-#' When \code{mu} is \code{NA}, the implementation takes considerably longer to run. Users should be careful
-#' about units of time (e.g., are counts observed daily or weekly?) when implementing.
+#' When the serial distribution is known (i.e., \code{mu} is not \code{NA}),
+#' sensitivity testing of \code{mu} is strongly recommended. If the serial
+#' distribution is unknown (i.e., \code{mu} is \code{NA}), the likelihood
+#' function can be flat near the maximum, resulting in numerical instability of
+#' the optimizer. When \code{mu} is \code{NA}, the implementation takes
+#' considerably longer to run. Users should be careful about units of time
+#' (e.g., are counts observed daily or weekly?) when implementing.
#'
-#' The model developed in White and Pagano (2008) is discrete, and hence the serial distribution is finite
-#' discrete. In our implementation, the input value \code{mu} is that of a continuous distribution. The
-#' algorithm discretizes this input when \code{mu} is not \code{NA}, and hence the mean of the serial
-#' distribution returned in the list \code{SD} will differ from \code{mu} somewhat. That is to say, if the
-#' user notices that the input \code{mu} and output mean of \code{SD} are different, this is to be expected,
+#' The model developed in White and Pagano (2008) is discrete, and hence the
+#' serial distribution is finite discrete. In our implementation, the input
+#' value \code{mu} is that of a continuous distribution. The algorithm
+#' discretizes this input when \code{mu} is not \code{NA}, and hence the mean of
+#' the serial distribution returned in the list \code{SD} will differ from
+#' \code{mu} somewhat. That is to say, if the user notices that the input
+#' \code{mu} and output mean of \code{SD} are different, this is to be expected,
#' and is caused by the discretization.
#'
#' @param NT Vector of case counts.
-#' @param mu Mean of the serial distribution (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). The default value of \code{mu} is set to \code{NA}.
-#' @param search List of default values for the grid search algorithm. The list includes three elements: the
-#' first is \code{B}, which is the length of the grid in one dimension; the second is
-#' \code{scale.max}, which is the largest possible value of the scale parameter; and the third
-#' is \code{shape.max}, which is the largest possible value of the shape parameter. Defaults to
-#' \code{B=100, scale.max=10, shape.max=10}. For both shape and scale, the smallest possible
-#' value is 1/\code{B}.
-#' @param tol Cutoff value for cumulative distribution function of the pre-discretization gamma serial
-#' distribution. Defaults to 0.999 (i.e. in the discretization, the maximum is chosen such that the
-#' original gamma distribution has cumulative probability of no more than 0.999 at this maximum).
+#' @param mu Mean of the serial distribution (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). The default value of \code{mu} is set to \code{NA}.
+#' @param search List of default values for the grid search algorithm. The list
+#' includes three elements: the first is \code{B}, which is the
+#' length of the grid in one dimension; the second is
+#' \code{scale.max}, which is the largest possible value of the
+#' scale parameter; and the third is \code{shape.max}, which is
+#' the largest possible value of the shape parameter. Defaults to
+#' \code{B=100, scale.max=10, shape.max=10}. For both shape and
+#' scale, the smallest possible value is 1/\code{B}.
+#' @param tol Cutoff value for cumulative distribution function of the
+#' pre-discretization gamma serial distribution. Defaults to 0.999
+#' (i.e. in the discretization, the maximum is chosen such that the
+#' original gamma distribution has cumulative probability of no more
+#' than 0.999 at this maximum).
#'
-#' @return \code{WP} returns a list containing the following components: \code{Rhat} is the estimate of R0,
-#' and \code{SD} is either the discretized serial distribution (if \code{mu} is not \code{NA}), or the
-#' estimated discretized serial distribution (if \code{mu} is \code{NA}). The list also returns the
-#' variable \code{check}, which is equal to the number of non-unique maximum likelihood estimators.
-#' The serial distribution \code{SD} is returned as a list made up of \code{supp} (the support of
-#' the distribution) and \code{pmf} (the probability mass function).
+#' @return \code{WP} returns a list containing the following components:
+#' \code{Rhat} is the estimate of R0, and \code{SD} is either the
+#' discretized serial distribution (if \code{mu} is not \code{NA}), or
+#' the estimated discretized serial distribution (if \code{mu} is
+#' \code{NA}). The list also returns the variable \code{check}, which is
+#' equal to the number of non-unique maximum likelihood estimators. The
+#' serial distribution \code{SD} is returned as a list made up of
+#' \code{supp} (the support of the distribution) and \code{pmf} (the
+#' probability mass function).
#'
#' @examples
-#' ## ===================================================== ##
-#' ## Illustrate on weekly data ##
-#' ## ===================================================== ##
-#'
+#' # Weekly data.
#' NT <- c(1, 4, 10, 5, 3, 4, 19, 3, 3, 14, 4)
-#' ## obtain Rhat when serial distribution has mean of five days
-#' res1 <- WP(NT=NT, mu=5/7)
+#'
+#' # Obtain R0 when the serial distribution has a mean of five days.
+#' res1 <- WP(NT, mu = 5 / 7)
#' res1$Rhat
-#' ## obtain Rhat when serial distribution has mean of three days
-#' res2 <- WP(NT=NT, mu=3/7)
+#'
+#' # Obtain R0 when the serial distribution has a mean of three days.
+#' res2 <- WP(NT, mu = 3 / 7)
#' res2$Rhat
-#' ## obtain Rhat when serial distribution is unknown
-#' ## NOTE: this implementation will take longer to run
-#' res3 <- WP(NT=NT)
+#'
+#' # Obtain R0 when the serial distribution is unknown.
+#' # NOTE: This implementation will take longer to run.
+#' res3 <- WP(NT)
#' res3$Rhat
-#' ## find mean of estimated serial distribution
+#'
+#' # Find the mean of the estimated serial distribution.
#' serial <- res3$SD
#' sum(serial$supp * serial$pmf)
#'
-#' ## ========================================================= ##
-#' ## Compute Rhat using only the first five weeks of data ##
-#' ## ========================================================= ##
-#'
-#' res4 <- WP(NT=NT[1:5], mu=5/7) # serial distribution has mean of five days
-#' res4$Rhat
-#'
#' @importFrom stats pexp qexp
#'
#' @export
-WP <- function(NT, mu=NA, search=list(B=100, shape.max=10, scale.max=10), tol=0.999) {
- if (is.na(mu)) {
- print("You have assumed that the serial distribution is unknown.")
- res <- WP_unknown(NT=NT, B=search$B, shape.max=search$shape.max, scale.max=search$scale.max, tol=tol)
- Rhat <- res$Rhat
- p <- res$p
- range.max <- res$range.max
- JJ <- res$JJ
- } else {
- print("You have assumed that the serial distribution is known.")
- range.max <- ceiling(qexp(tol, rate=1/mu))
- p <- diff(pexp(0:range.max, 1/mu))
- p <- p / sum(p)
- res <- WP_known(NT=NT, p=p)
- Rhat <- res
- JJ <- NA
- }
+WP <- function(NT, mu = NA,
+ search = list(B = 100, shape.max = 10, scale.max = 10),
+ tol = 0.999) {
+ if (is.na(mu)) {
+ print("You have assumed that the serial distribution is unknown.")
+ res <- WP_unknown(NT, B = search$B, shape.max = search$shape.max,
+ scale.max = search$scale.max, tol = tol)
+ Rhat <- res$Rhat
+ p <- res$p
+ range.max <- res$range.max
+ JJ <- res$JJ
+ } else {
+ print("You have assumed that the serial distribution is known.")
+ range.max <- ceiling(qexp(tol, rate = 1 / mu))
+ p <- diff(pexp(0:range.max, 1 / mu))
+ p <- p / sum(p)
+ res <- WP_known(NT = NT, p = p)
+ Rhat <- res
+ JJ <- NA
+ }
- return(list(Rhat=Rhat, check=length(JJ), SD=list(supp=1:range.max, pmf=p)))
+ return(list(Rhat = Rhat,
+ check = length(JJ),
+ SD = list(supp = 1:range.max, pmf = p)))
}
diff --git a/R/WP_internal.R b/R/WP_internal.R
index 54744b9..420d0c0 100644
--- a/R/WP_internal.R
+++ b/R/WP_internal.R
@@ -1,7 +1,8 @@
#' WP method background function WP_known
#'
-#' This is a background/internal function called by \code{WP}. It computes the maximum
-#' likelihood estimator of R0 assuming that the serial distribution is known and finite discrete.
+#' This is a background/internal function called by \code{WP}. It computes the
+#' maximum likelihood estimator of R0 assuming that the serial distribution is
+#' known and finite discrete.
#'
#' @param NT Vector of case counts.
#' @param p Discretized version of the serial distribution.
@@ -10,97 +11,106 @@
#'
#' @keywords internal
WP_known <- function(NT, p) {
- k <- length(p)
- TT <- length(NT) - 1
- mu_t <- rep(0, TT)
+ k <- length(p)
+ TT <- length(NT) - 1
+ mu_t <- rep(0, TT)
- for (i in 1:TT) {
- Nt <- NT[i:max(1, i-k+1)]
- mu_t[i] <- sum(p[1:min(k, i)] * Nt)
- }
+ for (i in 1:TT) {
+ Nt <- NT[i:max(1, i - k + 1)]
+ mu_t[i] <- sum(p[1:min(k, i)] * Nt)
+ }
- Rhat <- sum(NT[-1]) / sum(mu_t)
- return(Rhat)
+ Rhat <- sum(NT[-1]) / sum(mu_t)
+ return(Rhat)
}
#' WP method background function WP_unknown
#'
-#' This is a background/internal function called by \code{WP}. It computes the maximum likelihood estimator
-#' of R0 assuming that the serial distribution is unknown but comes from a discretized gamma distribution.
-#' The function then implements a simple grid search algorithm to obtain the maximum likelihood estimator
-#' of R0 as well as the gamma parameters.
+#' This is a background/internal function called by \code{WP}. It computes the
+#' maximum likelihood estimator of R0 assuming that the serial distribution is
+#' unknown but comes from a discretized gamma distribution. The function then
+#' implements a simple grid search algorithm to obtain the maximum likelihood
+#' estimator of R0 as well as the gamma parameters.
#'
#' @param NT Vector of case counts.
#' @param B Length of grid for shape and scale (grid search parameter).
#' @param shape.max Maximum shape value (grid \code{search} parameter).
#' @param scale.max Maximum scale value (grid \code{search} parameter).
-#' @param tol cutoff value for cumulative distribution function of the serial distribution (defaults to 0.999).
+#' @param tol cutoff value for cumulative distribution function of the serial
+#' distribution (defaults to 0.999).
#'
-#' @return The function returns \code{Rhat}, the maximum likelihood estimator of R0, as well as the maximum
-#' likelihood estimator of the discretized serial distribution given by \code{p} (the probability mass
-#' function) and \code{range.max} (the distribution has support on the integers one to \code{range.max}).
-#' The function also returns \code{resLL} (all values of the log-likelihood) at \code{shape} (grid for
-#' shape parameter) and at \code{scale} (grid for scale parameter), as well as \code{resR0} (the full
-#' vector of maximum likelihood estimators), \code{JJ} (the locations for the likelihood for these), and
-#' \code{J0} (the location for the maximum likelihood estimator \code{Rhat}). If \code{JJ} and \code{J0}
-#' are not the same, this means that the maximum likelihood estimator is not unique.
+#' @return The function returns \code{Rhat}, the maximum likelihood estimator of
+#' R0, as well as the maximum likelihood estimator of the discretized
+#' serial distribution given by \code{p} (the probability mass function)
+#' and \code{range.max} (the distribution has support on the integers
+#' one to \code{range.max}). The function also returns \code{resLL} (all
+#' values of the log-likelihood) at \code{shape} (grid for shape
+#' parameter) and at \code{scale} (grid for scale parameter), as well as
+#' \code{resR0} (the full vector of maximum likelihood estimators),
+#' \code{JJ} (the locations for the likelihood for these), and \code{J0}
+#' (the location for the maximum likelihood estimator \code{Rhat}). If
+#' \code{JJ} and \code{J0} are not the same, this means that the maximum
+#' likelihood estimator is not unique.
#'
#' @importFrom stats pgamma qgamma
#'
#' @keywords internal
-WP_unknown <- function(NT, B=100, shape.max=10, scale.max=10, tol=0.999) {
- shape <- seq(0, shape.max, length.out=B+1)
- scale <- seq(0, scale.max, length.out=B+1)
- shape <- shape[-1]
- scale <- scale[-1]
+WP_unknown <- function(NT, B = 100, shape.max = 10, scale.max = 10,
+ tol = 0.999) {
+ shape <- seq(0, shape.max, length.out = B + 1)
+ scale <- seq(0, scale.max, length.out = B + 1)
+ shape <- shape[-1]
+ scale <- scale[-1]
- resLL <- matrix(0,B,B)
- resR0 <- matrix(0,B,B)
+ resLL <- matrix(0, B, B)
+ resR0 <- matrix(0, B, B)
- for (i in 1:B) {
- for (j in 1:B) {
- range.max <- ceiling(qgamma(tol, shape=shape[i], scale=scale[j]))
- p <- diff(pgamma(0:range.max, shape=shape[i], scale=scale[j]))
- p <- p / sum(p)
- mle <- WP_known(NT, p)
- resLL[i,j] <- computeLL(p, NT, mle)
- resR0[i,j] <- mle
- }
+ for (i in 1:B)
+ for (j in 1:B) {
+ range.max <- ceiling(qgamma(tol, shape = shape[i], scale = scale[j]))
+ p <- diff(pgamma(0:range.max, shape = shape[i], scale = scale[j]))
+ p <- p / sum(p)
+ mle <- WP_known(NT, p)
+ resLL[i, j] <- computeLL(p, NT, mle)
+ resR0[i, j] <- mle
}
-
- J0 <- which.max(resLL)
- R0hat <- resR0[J0]
- JJ <- which(resLL == resLL[J0], arr.ind=TRUE)
- range.max <- ceiling(qgamma(tol, shape=shape[JJ[1]], scale=scale[JJ[2]]))
- p <- diff(pgamma(0:range.max, shape=shape[JJ[1]], scale=scale[JJ[2]]))
- p <- p / sum(p)
-
- return(list(Rhat=R0hat, J0=J0, ll=resLL, Rs=resR0, scale=scale, shape=shape, JJ=JJ, p=p, range.max=range.max))
+
+ J0 <- which.max(resLL)
+ R0hat <- resR0[J0]
+ JJ <- which(resLL == resLL[J0], arr.ind = TRUE)
+ range.max <- ceiling(qgamma(tol, shape = shape[JJ[1]], scale = scale[JJ[2]]))
+ p <- diff(pgamma(0:range.max, shape = shape[JJ[1]], scale = scale[JJ[2]]))
+ p <- p / sum(p)
+
+ return(list(Rhat = R0hat, J0 = J0, ll = resLL, Rs = resR0, scale = scale,
+ shape = shape, JJ = JJ, p = p, range.max = range.max))
}
#' WP method background function computeLL
#'
-#' This is a background/internal function called by \code{WP}. It computes the log-likelihood.
+#' This is a background/internal function called by \code{WP}. It computes the
+#' log-likelihood.
#'
#' @param NT Vector of case counts.
#' @param p Discretized version of the serial distribution.
#' @param R0 Basic reproductive ratio.
#'
-#' @return This function returns the log-likelihood at the input variables and parameters.
+#' @return This function returns the log-likelihood at the input variables and
+#' parameters.
#'
#' @keywords internal
computeLL <- function(p, NT, R0) {
- k <- length(p)
- TT <- length(NT) - 1
- mu_t <- rep(0, TT)
+ k <- length(p)
+ TT <- length(NT) - 1
+ mu_t <- rep(0, TT)
- for (i in 1:TT) {
- Nt <- NT[i:max(1, i-k+1)]
- mu_t[i] <- sum(p[1:min(k, i)] * Nt)
- }
+ for (i in 1:TT) {
+ Nt <- NT[i:max(1, i - k + 1)]
+ mu_t[i] <- sum(p[1:min(k, i)] * Nt)
+ }
- mu_t <- R0 * mu_t
- LL <- sum(NT[-1] * log(mu_t)) - sum(mu_t)
+ mu_t <- R0 * mu_t
+ LL <- sum(NT[-1] * log(mu_t)) - sum(mu_t)
- return(LL)
+ return(LL)
}
diff --git a/R/seqB.R b/R/seqB.R
index 8685f39..e51117f 100644
--- a/R/seqB.R
+++ b/R/seqB.R
@@ -1,126 +1,129 @@
#' seqB method
#'
-#' This function implements a sequential Bayesian estimation method of R0 due to Bettencourt and Riberio (PloS One, 2008).
-#' See details for important implementation notes.
+#' This function implements a sequential Bayesian estimation method of R0 due to
+#' Bettencourt and Riberio (PloS One, 2008). See details for important
+#' implementation notes.
#'
-#' 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 in this implementation 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}.
+#' 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.
+#' 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.
+#' 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.
#'
#' @param NT Vector of case counts.
-#' @param 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.
-#' @param 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.
+#' @param 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.
+#' @param 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.
#'
-#' @return \code{secB} 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).
+#' @return \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).
#'
#' @examples
-#' ## ===================================================== ##
-#' ## Illustrate on weekly data ##
-#' ## ===================================================== ##
-#'
+#' # Weekly data.
#' NT <- c(1, 4, 10, 5, 3, 4, 19, 3, 3, 14, 4)
-#' ## obtain Rhat when serial distribution has mean of five days
-#' res1 <- seqB(NT=NT, mu=5/7)
+#'
+#' ## Obtain R0 when the serial distribution has a mean of five days.
+#' res1 <- seqB(NT, mu = 5 / 7)
#' res1$Rhat
-#' ## obtain Rhat when serial distribution has mean of three days
-#' res2 <- seqB(NT=NT, mu=3/7)
+#'
+#' ## Obtain R0 when the serial distribution has a mean of three days.
+#' res2 <- seqB(NT, mu = 3 / 7)
#' res2$Rhat
#'
-#' ## ============================================================= ##
-#' ## Compute posterior mode instead of posterior mean and plot ##
-#' ## ============================================================= ##
+#' # Compute posterior mode instead of posterior mean and plot.
#'
-#' Rpost <- res1$posterior
+#' Rpost <- res1$posterior
#' loc <- which(Rpost$pmf == max(Rpost$pmf))
-#' Rpost$supp[loc] # posterior mode
-#' res1$Rhat # compare with posterior mean
+#' Rpost$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$supp[loc], col="purple")
-#' legend("topright", legend=c("prior", "posterior", "posterior mean (Rhat)", "posterior mode"),
-#' col=c("red", "black", "blue", "purple"), lty=1)
-#' plot(Rpost$supp, Rpost$pmf, col="black", type="l", xlim=c(0.5, 1.5), xlab="", ylab="")
-#' abline(h=1/(20/0.01+1), col="red")
-#' abline(v=res1$Rhat, col="blue")
-#' abline(v=Rpost$supp[loc], col="purple")
-#' legend("topright", legend=c("prior", "posterior", "posterior mean (Rhat)", "posterior mode"),
-#' col=c("red", "black", "blue", "purple"), lty=1)
+#' par(mfrow = c(2, 1), mar = c(2, 2, 1, 1))
#'
-#' ## ========================================================= ##
-#' ## Compute Rhat using only the first five weeks of data ##
-#' ## ========================================================= ##
-#'
-#' res3 <- seqB(NT=NT[1:5], mu=5/7) # serial distribution has mean of five days
-#' res3$Rhat
+#' 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)
#'
#' @export
-seqB <- function(NT, mu, kappa=20) {
- if (length(NT) < 2)
- print("Warning: length of NT should be at least two.")
- else {
- if (min(NT) > 0) {
- times <- 1:length(NT)
- tau <- diff(times)
- }
- group <- FALSE
- if (min(NT) == 0) {
- times <- which(NT > 0)
- NT <- NT[times]
- tau <- diff(times)
- group <- TRUE
- }
+seqB <- function(NT, mu, kappa = 20) {
+ if (length(NT) < 2) {
+ print("Warning: length of NT should be at least two.")
+ } else {
+ if (min(NT) > 0) {
+ times <- 1:length(NT)
+ tau <- diff(times)
+ }
+ group <- FALSE
+ if (min(NT) == 0) {
+ times <- which(NT > 0)
+ NT <- NT[times]
+ tau <- diff(times)
+ group <- TRUE
+ }
- R <- seq(0, kappa, 0.01)
- prior0 <- rep(1, kappa / 0.01 + 1)
- prior0 <- prior0 / sum(prior0)
- k <- length(NT) - 1
- R0.post <- matrix(0, nrow=k, ncol=length(R))
- prior <- prior0
- posterior <- seq(0, length(prior0))
- gamma <- 1 / mu
+ R <- seq(0, kappa, 0.01)
+ prior0 <- rep(1, kappa / 0.01 + 1)
+ prior0 <- prior0 / sum(prior0)
+ k <- length(NT) - 1
+ R0.post <- matrix(0, nrow = k, ncol = length(R))
+ prior <- prior0
+ posterior <- seq(0, length(prior0))
+ gamma <- 1 / mu
- for (i in 1:k) {
- mm1 <- NT[i]
- mm2 <- NT[i+1]
- lambda <- tau[i] * gamma * (R - 1)
- lambda <- log(mm1) + lambda
- loglik <- mm2 * lambda - exp(lambda)
- maxll <- max(loglik)
- const <- 0
+ for (i in 1:k) {
+ mm1 <- NT[i]
+ mm2 <- NT[i + 1]
+ lambda <- tau[i] * gamma * (R - 1)
+ lambda <- log(mm1) + lambda
+ loglik <- mm2 * lambda - exp(lambda)
+ maxll <- max(loglik)
+ const <- 0
- if (maxll > 700)
- const <- maxll - 700
+ if (maxll > 700)
+ const <- maxll - 700
- loglik <- loglik-const
- posterior <- exp(loglik) * prior
- posterior <- posterior / sum(posterior)
- prior <- posterior
- }
+ loglik <- loglik - const
+ posterior <- exp(loglik) * prior
+ posterior <- posterior / sum(posterior)
+ prior <- posterior
+ }
- Rhat <- sum(R * posterior)
+ Rhat <- sum(R * posterior)
- return(list(Rhat=Rhat, posterior=list(supp=R, pmf=posterior), group=group))
- }
+ return(list(Rhat = Rhat,
+ posterior = list(supp = R, pmf = posterior),
+ group = group))
+ }
}