survsim (version 1.1.8)

mult.ev.sim: Generate a cohort with multiple events

Description

Simulation of cohorts in a context of multiple event survival analysis including several covariates, individual heterogeneity and periods at risk prior and after the start of follow-up.

Multiple event data occurs when each subject can have more than one event of entirely different natures (Kelly, 2000). Examples of this type of event are the occurrence of tumours at different sites in the body or multiple sequalae after a surgery.

We can obtain the observation time of the \(k\)-th event in the \(i\)-th subject, \(y_ik\), in the same manner that we can simulate \(k\) simple independent survival data. Notice that, in multiple-type events, \(T_{ik}\) and \(C_{i}\) are mutually independent and, furthermore, the failure in each event is independent of the others (within each subject all \(y_ik\) are independents for all \(k\)).

Usage

mult.ev.sim(n, foltime, dist.ev, anc.ev, beta0.ev, dist.cens="weibull", 
anc.cens, beta0.cens, z=NULL, beta=NA, x=NA, nsit)

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.

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 event, 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 events. 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 needs to introduce in the simulated cohort. The possible distributions are "normal" for normal distribution, "unif" for uniform distribution and "bern" for 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.

nsit

Number of different events that a subject can suffer. It must match the number of distributions specified in dist.ev.

Value

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

nid

an integer number that identifies the subject.

ev.num

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

time

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

status

logical value indicating if the corresponding event has been suffered or not.

start

time at which the follow-up time begins for each event.

stop

time at which the follow-up time ends for each event.

z

Individual heterogeneity generated according to the specified distribution.

x

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

Details

In order to get the function to work properly, the length of the vectors containing the parameters of the time to event and the number of distributions indicated in the parameter dist.ev must be the same.

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.

Mori<U+00F1>a 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, rec.ev.sim, crisk.sim, simple.surv.sim

Examples

# NOT RUN {
### A cohort with 1000 subjects, with a maximum follow-up time of 3600 days and two 
### covariates, following a Bernoulli and uniform distribution respectively, and a 
### corresponding beta of -0.4, -0.5, -0.6 and -0.7 for each event for the first 
### covariate and a corresponding beta of 0, 0, 0 and 1 for each event for the 
### second covariate. Notice that the time to censorship is assumed to follow a 
### Weibull distribution, as no other distribution is stated and random effect is
### the same for all events.

sim.data <- mult.ev.sim(n=1000, foltime=3600, dist.ev=c('llogistic','weibull', 
'weibull','weibull'),anc.ev=c(0.69978200185280, 0.79691659193027, 
0.82218416457321, 0.85817155198598),beta0.ev=c(5.84298525742252, 5.94362650803287,
5.78182528904637, 5.46865223339755),,anc.cens=1.17783687569519,
beta0.cens=7.39773677281100,z=list(c("unif", 0.8,1.2)), beta=list(c(-0.4,-0.5,-0.6,-0.7),
c(0,0,0,1)), x=list(c("bern", 0.5), c("unif", 0.7, 1.3)), nsit=4)

summary(sim.data)
# }