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", ...)Model object
Formula (see details)
Event names
Additional arguments to lower levels functions
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.
# Right censored survival data without covariates
m0 <- lvm()
distribution(m0,"eventtime") <- coxWeibull.lvm(scale=1/100,shape=2)
distribution(m0,"censtime") <- coxExponential.lvm(rate=1/10)
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=1/0.7)
distribution(ma,"censtime") <- weibull.lvm(scale=2,shape=1/0.7)
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 following are equivalent parametrizations
# which produce exactly the same random numbers:
model.aft <- lvm()
distribution(model.aft,"eventtime") <- weibull.lvm(intercept=-log(1/100)/2,sigma=1/2)
distribution(model.aft,"censtime") <- weibull.lvm(intercept=-log(1/100)/2,sigma=1/2)
sim(model.aft,6,seed=17)
#> 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
model.aft <- lvm()
distribution(model.aft,"eventtime") <- weibull.lvm(scale=100^(1/2), shape=2)
distribution(model.aft,"censtime") <- weibull.lvm(scale=100^(1/2), shape=2)
sim(model.aft,6,seed=17)
#> 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
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)
sim(model.cox,6,seed=17)
#> 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 7.023211 -0.05517906 14.575911 11.814841 7.023211 1
#> 2 1 6.179319 0.83847112 5.138275 7.716248 5.138275 2
#> 3 1 5.890305 0.15937013 9.886258 12.038218 5.890305 1
#> 4 0 15.128422 0.62595440 13.871923 11.629342 11.629342 0
#> 5 1 12.075247 0.63358473 9.551212 2.196766 2.196766 0
#> 6 0 19.313957 0.68102765 7.433206 3.930187 3.930187 0