A function to estimate the relative case fatality ratio when reporting rates are time-varying and deaths are lagged because of survival time.

This function implements an EM algorithm to estimate the relative case fatality ratio between two groups when reporting rates are time-varying and deaths are lagged because of survival time.

Usage

EMforCFR(assumed.nu, alpha.start.values, full.data, max.iter = 50,
  verb = FALSE, tol = 1e-10, SEM.var = TRUE)

Arguments

assumed.nu: a vector of probabilities corresponding to the survival distribution, i.e. nu[i]=Pr(surviving i days | fatal case)
alpha.start.values: a vector starting values for the reporting rate parameter of the GLM model. This must have length which corresponds to one less than the number of unique integer values of full.dat[,"new.times"].
full.data: A matrix of observed data. See description below.
max.iter: The maximum number of iterations for the EM algorithm and the accompanying SEM algorithm (if used).
verb: An indicator for whether the function should print results as it runs.
tol: A tolerance to use to test for convergence of the EM algorithm.
SEM.var: If TRUE, the SEM algorithm will be run in addition to the EM algorithm to calculate the variance of the parameter estimates.

Value

A list with the following elements

naive.rel.cfr: the naive estimate of the relative case fatality ratio
glm.rel.cfr: the reporting-rate-adjusted estimate of the relative case fatality ratio
EM.rel.cfr: the lag-adjusted estimate of the relative case fatality ratio
EM.re.cfr.var: the variance for the log-scale lag-adjusted estimator taken from the final M-step
EM.rel.cfr.var.SEM: the Supplemented EM algorithm variance for the log-scale lag-adjusted estimator
EM.rel.cfr.chain: a vector of the EM algorithm iterates of the lag-adjusted relative CFR estimates
EMiter: the number of iterations needed for the EM algorithm to converge
EMconv: indicator for convergence of the EM algorithm. 0 indicates all parameters converged within max.iter iterations. 1 indicates that the estimate of the relative case fatality ratio converged but other did not. 2 indicates that the relative case fatality ratio did not converge.
SEMconv: indicator for convergence of SEM algorithm. Same scheme as EMconv.
ests: the coefficient estimates for the model
ests.chain: a matrix with all of the coefficient estimates, at each EM iteration
DM: the DM matrix from the SEM algorithm
DMiter: a vector showing how many iterations it took for the variance component to converge in the SEM algorithm

Details

The data matrix full.data must have the following columns:

grp: a 1 or a 2 indicating which of the two groups, j, the observation is for.
new.times: an integer value representing the time, t, of observation.
R: the count of recovered cases with onset at time t in group j.
D: the count of deaths which occurred at time t in groupo j (note that these deaths did not have disease onset at time t but rather died at time t).
N: the total cases at t, j, or the sum of R and D columns.

Examples

    ## This is code from the CFR vignette provided in the documentation.

data(simulated.outbreak.deaths)
min.cases <- 10
N.1 <- simulated.outbreak.deaths[1:60, "N"]
N.2 <- simulated.outbreak.deaths[61:120, "N"]
first.t <- min(which(N.1 > min.cases & N.2 > min.cases))
last.t <- max(which(N.1 > min.cases & N.2 > min.cases))
idx.for.Estep <- first.t:last.t
new.times <- 1:length(idx.for.Estep)
simulated.outbreak.deaths <- cbind(simulated.outbreak.deaths, new.times = NA)
simulated.outbreak.deaths[c(idx.for.Estep, idx.for.Estep + 60), "new.times"] <- rep(new.times, + 2)
assumed.nu = c(0, 0.3, 0.4, 0.3)
alpha.start <- rep(0, 22)

## caution! this next line may take several minutes (5-10, depanding on
##    the speed of your machine) to run.
if (FALSE) cfr.ests <- EMforCFR(assumed.nu = assumed.nu,
                              alpha.start.values = alpha.start,
                              full.data = simulated.outbreak.deaths,
                              verb = FALSE,
                              SEM.var = TRUE,
                              max.iter = 500,
                              tol = 1e-05)