# Estimation of probability of more that k events for recurrent events process Estimation of probability of more that k events for recurrent events process where there is terminal event, based on this also estimate of variance of recurrent events. The estimator is based on cumulative incidence of exceeding "k" events. In contrast the probability of exceeding k events can also be computed as a counting process integral, and this is implemented in prob.exceedRecurrent ```r prob.exceed.recurrent( data, type, status = "status", death = "death", start = "start", stop = "stop", id = "id", times = NULL, exceed = NULL, cifmets = TRUE, strata = NULL, all.cifs = FALSE, ... ) ``` ## Arguments - `data`: data-frame - `type`: type of evnent (code) related to status - `status`: name of status - `death`: name of death indicator - `start`: start stop call of Hist() of prodlim - `stop`: start stop call of Hist() of prodlim - `id`: id - `times`: time at which to get probabilites P(N1(t) >= n) - `exceed`: n's for which which to compute probabilites P(N1(t) >= n) - `cifmets`: if true uses cif of mets package rather than prodlim - `strata`: to stratify according to variable, only for cifmets=TRUE, when strata is given then only consider the output in the all.cifs - `all.cifs`: if true then returns list of all fitted objects in cif.exceed - `...`: Additional arguments to lower level funtions ## Examples ```r ######################################## ## getting some rates to mimick ######################################## data(base1cumhaz) data(base4cumhaz) data(drcumhaz) dr <- drcumhaz base1 <- base1cumhaz base4 <- base4cumhaz cor.mat <- corM <- rbind(c(1.0, 0.6, 0.9), c(0.6, 1.0, 0.5), c(0.9, 0.5, 1.0)) rr <- simRecurrentII(1000,base4,cumhaz2=base4,death.cumhaz=dr,cens=2/5000) rr <- count.history(rr) dtable(rr,~death+status) oo <- prob.exceedRecurrent(rr,1) bplot(oo) par(mfrow=c(1,2)) with(oo,plot(time,mu,col=2,type="l")) ### with(oo,plot(time,varN,type="l")) ### Bivariate probability of exceeding oo <- prob.exceedBiRecurrent(rr,1,2,exceed1=c(1,5),exceed2=c(1,2)) with(oo, matplot(time,pe1e2,type="s")) nc <- ncol(oo$pe1e2) legend("topleft",legend=colnames(oo$pe1e2),lty=1:nc,col=1:nc) ### do not test to avoid dependence on prodlim ### now estimation based on cumualative incidence, but do not test to avoid dependence on prodlim ### library(prodlim) pp <- prob.exceed.recurrent(rr,1,status="status",death="death",start="entry",stop="time",id="id") with(pp, matplot(times,prob,type="s")) ### with(pp, matlines(times,se.lower,type="s")) with(pp, matlines(times,se.upper,type="s")) ``` ## References Scheike, Eriksson, Tribler (2019) The mean, variance and correlation for bivariate recurrent events with a terminal event, JRSS-C ## Author(s) Thomas Scheike

prob.exceed.recurrent function