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@@ -1,49 +1,62 @@ % Generated by roxygen2: do not edit by hand -% Please edit documentation in R/WP.R -\name{WP} -\alias{WP} -\title{WP method} +% Please edit documentation in R/wp.R +\name{wp} +\alias{wp} +\title{White and Pagano (WP)} \usage{ -WP( - NT, +wp( + cases, mu = NA, - search = list(B = 100, shape.max = 10, scale.max = 10), - tol = 0.999 + serial = FALSE, + grid_length = 100, + max_shape = 10, + max_scale = 10 ) } \arguments{ -\item{NT}{Vector of case counts.} +\item{cases}{Vector of case counts. The vector must be of length at least two +and only contain positive integers.} -\item{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}.} +\item{mu}{Mean of the serial distribution. This must be a positive number or +\code{NA}. If a number is specified, the value should match the 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 \code{1}. If +case counts are daily and the serial distribution has a mean of seven days, +then \code{mu} should be set to \code{7}.} -\item{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}.} +\item{serial}{Whether to return the estimated serial distribution in addition +to the estimate of R0. This must be a value identical to \code{TRUE} or \code{FALSE}.} -\item{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).} +\item{grid_length}{The length of the grid in the grid search (defaults to +100). This must be a positive integer. It will only be used if \code{mu} is set +to \code{NA}. The grid search will go through all combinations of the shape and +scale parameters for the gamma distribution, which are \code{grid_length} evenly +spaced values from \code{0} (exclusive) to \code{max_shape} and \code{max_scale} +(inclusive), respectively. Note that larger values will result in a longer +search time.} + +\item{max_shape}{The largest possible value of the shape parameter in the +grid search (defaults to 10). This must be a positive number. It will only +be used if \code{mu} is set to \code{NA}. Note that larger values will result in a +longer search time, and may cause numerical instabilities.} + +\item{max_scale}{The largest possible value of the scale parameter in the +grid search (defaults to 10). This must be a positive number. It will only +be used if \code{mu} is set to \code{NA}. Note that larger values will result in a +longer search time, and may cause numerical instabilities.} } \value{ -\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). +If \code{serial} is identical to \code{TRUE}, a list containing the following +components is returned: +\itemize{ +\item \code{r0} - the estimate of R0 +\item \code{supp} - the support of the estimated serial distribution +\item \code{pmf} - the probability mass function of the estimated serial +distribution +} + +Otherwise, if \code{serial} is identical to \code{FALSE}, only the estimate of R0 is +returned. } \description{ This function implements an R0 estimation due to White and Pagano (Statistics @@ -53,51 +66,63 @@ Poisson transmission model. See details for important implementation notes. \details{ 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). +distribution is assumed to be discrete with a finite number of possible +values. In this implementation, if \code{mu} is not \code{NA}, the serial distribution +is taken to be a discretized version of a gamma distribution with shape +parameter \code{1} and scale parameter \code{mu} (and hence mean \code{mu}). 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 shape +and scale, restricting these to a prespecified grid (see the parameters +\code{grid_length}, \code{max_shape} and \code{max_scale}). In both cases, the largest value +of the support is chosen such that the cumulative distribution function of +the original (pre-discretized) gamma distribution has cumulative probability +of no more than 0.999 at this value. -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, -and is caused by the discretization. +value \code{mu} is that of a continuous distribution. The algorithm discretizes +this input, and so the mean of the estimated serial distribution returned +(when \code{serial} is set to \code{TRUE}) will differ from \code{mu} somewhat. That is to +say, if the user notices that the input \code{mu} and the mean of the estimated +serial distribution are different, this is to be expected, and is caused by +the discretization. } \examples{ # Weekly data. -NT <- c(1, 4, 10, 5, 3, 4, 19, 3, 3, 14, 4) +cases <- 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 <- WP(NT, mu = 5 / 7) -res1$Rhat +wp(cases, mu = 5 / 7) # Obtain R0 when the serial distribution has a mean of three days. -res2 <- WP(NT, mu = 3 / 7) -res2$Rhat +wp(cases, mu = 3 / 7) # Obtain R0 when the serial distribution is unknown. -# NOTE: This implementation will take longer to run. -res3 <- WP(NT) -res3$Rhat +# Note that this will take longer to run than when `mu` is known. +wp(cases) + +# Same as above, but specify custom grid search parameters. The larger any of +# the parameters, the longer the search will take, but with potentially more +# accurate estimates. +wp(cases, grid_length = 40, max_shape = 4, max_scale = 4) -# Find the mean of the estimated serial distribution. -serial <- res3$SD -sum(serial$supp * serial$pmf) +# Return the estimated serial distribution in addition to the estimate of R0. +estimate <- wp(cases, serial = TRUE) +# Display the estimate of R0, as well as the support and probability mass +# function of the estimated serial distribution returned by the grid search. +estimate$r0 +estimate$supp +estimate$pmf +} +\references{ +\href{https://doi.org/10.1002/sim.3136}{White and Pagano (Statistics in Medicine, 2008)} } |