rec.ev.sim {survsim}

Generate a cohort with recurrent events

Description

Simulation of cohorts in a context of recurrent event survival analysis including several covariates, individual heterogeneity and periods at risk before and after the initial time of follow-up.

Recurrent event data is a type of multiple event where the subject can experience repeated occurences of the same type (Kelly, 2000), for example repeated asthma attacks or sick leave episodes. In practice, the hazard of an recurrent event can vary depending on the number of previous occurrences, in terms of shape and intensity (Reis, 2011; Navarro, 2012). However, simulations based on a mixture of distributions with different baseline hazard rates are quite rare (Bender, 2005; Metcalfe, 2006).

In a recurrent data context, each subject can present different number of episodes. We talk of episodes (or occurrences) rather than events since each occurrence is a new episode of the same event. This package supposes that there exists one different and independent Y_k distribution depending on k, the number of episode at risk. The simulating process for each Y_k is the same than for the multiple events situation (see mult.ev.sim), but in this case, obviously, a subject cannot be at risk for the k-th episode if he/she hadn't had the k-1-th.

Usage

rec.ev.sim(n, foltime, dist.ev, anc.ev, beta0.ev, dist.cens=rep("weibull",
length(beta0.cens)), anc.cens, beta0.cens, z=NULL, beta=NA, x=NA, lambda=NA, 
max.ep=Inf, priskb=0, max.old=0)

Arguments

n

integer value indicating the desired size of the cohort to be simulated.

foltime

real number that indicates the maximum time of follow-up of the simulated cohort.

dist.ev

vector of arbitrary size indicating the time to event distributions, with possible values weibull for the Weibull distribution, lnorm for the log-normal distribution and llogistic for the log-logistic distribution. If a subject suffers more episodes than specified distributions, the last distribution specified here is used to generate times corresponding to posterior episodes.

anc.ev

vector of arbitrary size of real components containing the ancillary parameters for the time to event distributions.

beta0.ev

vector of arbitrary size of real components containing the \beta_0 parameters for the time to event distributions.

dist.cens

string indicating the time to censoring distributions, with possible values weibull for the Weibull distribution, lnorm for the log-normal distribution, llogistic for the log-logistic distribution and unif for the uniform distribution. If no distribution is introduced, the time to censoring is assumed to follow a Weibull distribution.

anc.cens

real number containing the ancillary parameter for the time to censoring distribution or the maximum in case of uniform distributed time to censoring.

beta0.cens

real number containing the \beta_0 parameter for the time to censoring distribution or the minimum in case of uniform distributed time to censoring.

z

list of vectors with three elements containing information relative to a random effect used in order to introduce individual heterogeneity. Each vector in the list refers to a possible episode, so the number of vectors must be equal to nsit or equal to 1 if the same random effect will be used for all the episodes. The first element indicates the distribution: "unif" states for a uniform distribution, "gamma" states for a gamma distribution, "exp" states for an exponential distribution, "weibull" states for a Weibull distribution and "invgauss" states for an inverse gaussian distribution. The second and third elements indicates the minimum and maximum in the case of a uniform distribution (both must be positive) and the parameters in the case of the rest of distributions. Note that just one parameter is needed in the case of exponential distribution. Its default value is NULL, indicating that no individual heterogeneity is introduced.

beta

list of vectors indicating the effect of the corresponding covariate. The number of vectors in beta must match the number of covariates, and the length of each vector must match the number of events considered. Its default value is NA, indicating that no covariates are included.

x

list of vectors indicating the distribution and parameters of any covariate that the user need to introduce in the simulated cohort. The possible distributions are "normal" for a normal distribution, "unif" for a uniform distribution and "bern" for a Bernoulli distribution. Its default value is NA, indicating that no covariates are included. The number of vectors in x must match the number of vectors in beta. Each vector in x must contain the name of the distribution and the parameter(s), which are: the probability of success in the case of a Bernoulli distribution; the mean and the variance in the case of a normal distribution; and the minimum and maximum in the case of a uniform distribution.

lambda

real number indicating the mean duration of each event or discontinous risk time, assumed to follow a zero-truncated Poisson distribution. Its default value is NA, corresponding to the case where the duration of each event or discontinous risk time is unnecessary information for the user.

max.ep

integer value that matches the maximum permitted number of episodes per subject. Its default value is Inf, i.e. the number of episodes per subject is no limited.

priskb

proportion of subjects at risk prior to the start of follow-up, defaults to 0.

max.old

maximum time at risk prior to the start of follow-up.

Details

In order to get the function to work properly, the length of the vectors containing the parameters of the time to event and time to censure distributions and the number of distributions indicated in the parameter dist must be the same. Finally, priskb and max.old must be positive numbers, with priskb being between 0 and 1. Notice that large values of max.old can result in the routine taking a long time to simulate a cohort with the specified size.

Value

An object of class rec.ev.data.sim. It is a data frame containing the episodes suffered by the corresponding subjects. The columns of the data frame are detailed below

nid

an integer number that identifies the subject.

real.episode

number of the episode corresponding to the real history of the individual.

obs.episode

number of the episode corresponding to the follow-up time of the individual.

time

time until the corresponding event happens (or time to subject drop-out), regarding the beginning of the follow-up time.

status

logical value indicating if the episode corresponds to an event or a drop-out.

start

time at which an episode starts, taking the beginning of follow-up as the origin of the time scale.

stop

time at which an episode ends, taking the beginning of follow-up as the origin of the time scale.

time2

time until the corresponding event happens (or time to subject drop-out), in calendar time.

start2

time at which an episode starts, where the time scale is calendar time.

stop2

time at which an episode ends, where the time scale is calendar time.

old

real value indicating the time that the individual was at risk before the beginning of follow-up.

risk.bef

factor that indicates if an individual was at risk before the beginning of follow-up or not.

long

time not at risk immediately after an episode.

z

Individual heterogeneity generated according to the specified distribution.

x

value of each covariate randomly generated for each subject in the cohort.

Author(s)

David Moriña, Universitat de Barcelona and Albert Navarro, Universitat Autònoma de Barcelona

References

Kelly PJ, Lim LL. Survival analysis for recurrent event data: an application to childhood infectious diseases. Stat Med 2000 Jan 15;19(1):13-33.

Bender R, Augustin T, Blettner M. Generating survival times to simulate Cox proportional hazards models. Stat Med 2005 Jun 15;24(11):1713-1723.

Metcalfe C, Thompson SG. The importance of varying the event generation process in simulation studies of statistical methods for recurrent events. Stat Med 2006 Jan 15;25(1):165-179.

Reis RJ, Utzet M, La Rocca PF, Nedel FB, Martin M, Navarro A. Previous sick leaves as predictor of subsequent ones. Int Arch Occup Environ Health 2011 Jun;84(5):491-499.

Navarro A, Moriña D, Reis R, Nedel FB, Martin M, Alvarado S. Hazard functions to describe patterns of new and recurrent sick leave episodes for different diagnoses. Scand J Work Environ Health 2012 Jan 27.

Moriña D, Navarro A. The R package survsim for the simulation of simple and complex survival data. Journal of Statistical Software 2014 Jul; 59(2):1-20.

See Also

survsim-package, accum, mult.ev.sim, simple.surv.sim, crisk.sim

Examples

### A cohort with 500 subjects, with a maximum follow-up time of 1825 days and 
### just a covariate, following a Bernoulli distribution, and a corresponding 
### beta of -0.4, -0.5, -0.6 and -0.7 for each episode. Note that random effect is
### the same for all events.

sim.data <- rec.ev.sim(n=500, foltime=1825, dist.ev=c('lnorm','llogistic', 
'weibull','weibull'),anc.ev=c(1.498, 0.924, 0.923, 1.051),beta0.ev=c(7.195, 
6.583, 6.678, 6.430),,anc.cens=c(1.272, 1.218, 1.341, 1.484),
beta0.cens=c(7.315, 6.975, 6.712, 6.399), z=list(c("unif", 0.8,1.2)), 
beta=list(c(-0.4,-0.5,-0.6,-0.7)), x=list(c("bern", 0.5)),
lambda=c(2.18,2.33,2.40,3.46), priskb=0.5, max.old=730)

summary(sim.data)