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Diffstat (limited to 'man/seqB.Rd')
| -rw-r--r-- | man/seqB.Rd | 117 |
1 files changed, 59 insertions, 58 deletions
diff --git a/man/seqB.Rd b/man/seqB.Rd index 184f476..0864294 100644 --- a/man/seqB.Rd +++ b/man/seqB.Rd @@ -9,82 +9,83 @@ 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{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.} +\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{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). +\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. +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 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. } \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 - -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) +Rpost$supp[loc] # Posterior mode. +res1$Rhat # Compare with the posterior mean. -## ========================================================= ## -## Compute Rhat using only the first five weeks of data ## -## ========================================================= ## +par(mfrow = c(2, 1), mar = c(2, 2, 1, 1)) -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) } |