For example, if the model 'm' includes latent event time variables are called 'T1' and 'T2' and 'C' is the end of follow-up (right censored), then one can specify

eventTime(object, formula, eventName = "status", ...)

Arguments

object

Model object

formula

Formula (see details)

eventName

Event names

...

Additional arguments to lower levels functions

Details

eventTime(object=m,formula=ObsTime~min(T1=a,T2=b,C=0,"ObsEvent"))

when data are simulated from the model one gets 2 new columns:

- "ObsTime": the smallest of T1, T2 and C - "ObsEvent": 'a' if T1 is smallest, 'b' if T2 is smallest and '0' if C is smallest

Note that "ObsEvent" and "ObsTime" are names specified by the user.

Author

Thomas A. Gerds, Klaus K. Holst

Examples


# Right censored survival data without covariates
m0 <- lvm()
distribution(m0,"eventtime") <- coxWeibull.lvm(scale=1/100,shape=2)
distribution(m0,"censtime") <- coxExponential.lvm(rate=10)
m0 <- eventTime(m0,time~min(eventtime=1,censtime=0),"status")
sim(m0,10)
#>    eventtime  censtime      time status
#> 1   2.411880  4.533928  2.411880      1
#> 2  12.611888 23.252592 12.611888      1
#> 3  10.065578 17.943372 10.065578      1
#> 4  12.901187  6.581174  6.581174      0
#> 5   2.272443 25.195749  2.272443      1
#> 6   9.514347  3.575997  3.575997      0
#> 7   6.423498  2.912756  2.912756      0
#> 8   2.439480  4.756341  2.439480      1
#> 9  11.931257  4.708455  4.708455      0
#> 10  2.167252 10.303195  2.167252      1

# Alternative specification of the right censored survival outcome
## eventTime(m,"Status") <- ~min(eventtime=1,censtime=0)

# Cox regression:
# lava implements two different parametrizations of the same
# Weibull regression model. The first specifies
# the effects of covariates as proportional hazard ratios
# and works as follows:
m <- lvm()
distribution(m,"eventtime") <- coxWeibull.lvm(scale=1/100,shape=2)
distribution(m,"censtime") <- coxWeibull.lvm(scale=1/100,shape=2)
m <- eventTime(m,time~min(eventtime=1,censtime=0),"status")
distribution(m,"sex") <- binomial.lvm(p=0.4)
distribution(m,"sbp") <- normal.lvm(mean=120,sd=20)
regression(m,from="sex",to="eventtime") <- 0.4
regression(m,from="sbp",to="eventtime") <- -0.01
sim(m,6)
#>   eventtime  censtime      time status sex       sbp
#> 1  8.545196 13.206909  8.545196      1   0  99.50431
#> 2 16.881250 14.468739 14.468739      0   0 126.00263
#> 3 19.312301 11.738692 11.738692      0   0 102.51833
#> 4  7.557589  8.422240  7.557589      1   0 109.83046
#> 5 18.069883 12.497991 12.497991      0   0 120.36231
#> 6  4.874140  6.903913  4.874140      1   0 117.84913
# The parameters can be recovered using a Cox regression
# routine or a Weibull regression model. E.g.,
if (FALSE) {
    set.seed(18)
    d <- sim(m,1000)
    library(survival)
    coxph(Surv(time,status)~sex+sbp,data=d)

    sr <- survreg(Surv(time,status)~sex+sbp,data=d)
    library(SurvRegCensCov)
    ConvertWeibull(sr)

}

# The second parametrization is an accelerated failure time
# regression model and uses the function weibull.lvm instead
# of coxWeibull.lvm to specify the event time distributions.
# Here is an example:

ma <- lvm()
distribution(ma,"eventtime") <- weibull.lvm(scale=3,shape=0.7)
distribution(ma,"censtime") <- weibull.lvm(scale=2,shape=0.7)
ma <- eventTime(ma,time~min(eventtime=1,censtime=0),"status")
distribution(ma,"sex") <- binomial.lvm(p=0.4)
distribution(ma,"sbp") <- normal.lvm(mean=120,sd=20)
regression(ma,from="sex",to="eventtime") <- 0.7
regression(ma,from="sbp",to="eventtime") <- -0.008
set.seed(17)
sim(ma,6)
#>   eventtime  censtime      time status sex       sbp
#> 1 0.5531481 1.1285503 0.5531481      1   1  99.69983
#> 2 4.2973225 1.4665922 1.4665922      0   1 118.40727
#> 3 1.5884110 0.4704796 0.4704796      0   1 115.34026
#> 4 1.7404946 1.2284359 1.2284359      0   1 103.65464
#> 5 0.2765550 0.8633771 0.2765550      1   1 135.44182
#> 6 1.5803203 0.6912997 0.6912997      0   0 116.68776
# The regression coefficients of the AFT model
# can be tranformed into log(hazard ratios):
#  coef.coxWeibull = - coef.weibull / shape.weibull
if (FALSE) {
    set.seed(17)
    da <- sim(ma,1000)
    library(survival)
    fa <- coxph(Surv(time,status)~sex+sbp,data=da)
    coef(fa)
    c(0.7,-0.008)/0.7
}


# The Weibull parameters are related as follows:
# shape.coxWeibull = 1/shape.weibull
# scale.coxWeibull = exp(-scale.weibull/shape.weibull)
# scale.AFT = log(scale.coxWeibull) / shape.coxWeibull
# Thus, the following are equivalent parametrizations
# which produce exactly the same random numbers:

model.aft <- lvm()
distribution(model.aft,"eventtime") <- weibull.lvm(scale=-log(1/100)/2,shape=0.5)
distribution(model.aft,"censtime") <- weibull.lvm(scale=-log(1/100)/2,shape=0.5)
set.seed(17)
sim(model.aft,6)
#>   eventtime  censtime
#> 1  2.890253 3.1436842
#> 2  2.981019 0.4127472
#> 3  1.147834 2.0056626
#> 4  2.948915 1.1571425
#> 5  2.103028 2.1804985
#> 6  5.680430 1.8107400

model.cox <- lvm()
distribution(model.cox,"eventtime") <- coxWeibull.lvm(scale=1/100,shape=2)
distribution(model.cox,"censtime") <- coxWeibull.lvm(scale=1/100,shape=2)
set.seed(17)
sim(model.cox,6)
#>   eventtime  censtime
#> 1 12.552208 13.652847
#> 2 12.946401  1.792538
#> 3  4.984980  8.710482
#> 4 12.806975  5.025406
#> 5  9.133336  9.469785
#> 6 24.669793  7.863944

# The minimum of multiple latent times one of them still
# being a censoring time, yield
# right censored competing risks data

mc <- lvm()
distribution(mc,~X2) <- binomial.lvm()
regression(mc) <- T1~f(X1,-.5)+f(X2,0.3)
regression(mc) <- T2~f(X2,0.6)
distribution(mc,~T1) <- coxWeibull.lvm(scale=1/100)
distribution(mc,~T2) <- coxWeibull.lvm(scale=1/100)
distribution(mc,~C) <- coxWeibull.lvm(scale=1/100)
mc <- eventTime(mc,time~min(T1=1,T2=2,C=0),"event")
sim(mc,6)
#>   X2       T1        X1        T2         C     time event
#> 1  0 7.087078 0.9728744 11.814841  3.204723 3.204723     0
#> 2  0 9.105653 1.7165340  7.716248 15.423587 7.716248     2
#> 3  1 5.069985 0.2552370  8.918131  7.444486 5.069985     1
#> 4  0 5.150130 0.3665811 11.629342  7.433594 5.150130     1
#> 5  1 6.171934 1.1807892  1.627404  2.395786 1.627404     2
#> 6  0 7.931261 0.6431921  3.930187 12.323722 3.930187     2