EMforCFR: A function to estimate the relative case fatality ratio when...
In coarseDataTools: Analysis of Coarsely Observed Data

Description Usage Arguments Details Value Examples

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.

1 2	EMforCFR(assumed.nu, alpha.start.values, full.data, max.iter = 50, verb = FALSE, tol = 1e-10, SEM.var = TRUE)

`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.

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.

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

       
    ## 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.
## Not run: 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)
## End(Not run)