# 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. ```r 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. ## Returns 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 ```r ## 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) ```

EMforCFR function