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=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.
Examples
# Right censored survival data without covariates
m0 <- lvm()
distribution(m0,"eventtime") <- dist_cox_weibull(scale=1/100,shape=2)
distribution(m0,"censtime") <- dist_cox_exponential(rate=1/10)
m0 <- eventTime(m0,time~min(eventtime=1,censtime=0),"status")
sim(m0,10)
#> eventtime censtime time status
#> 1 2.926271 6.33789847 2.92627069 1
#> 2 8.344222 4.74652821 4.74652821 0
#> 3 8.709571 1.01521669 1.01521669 0
#> 4 12.123156 14.29913849 12.12315585 1
#> 5 3.335345 7.66880380 3.33534488 1
#> 6 9.752270 5.25456422 5.25456422 0
#> 7 10.100591 19.88940715 10.10059052 1
#> 8 4.975192 0.03572453 0.03572453 0
#> 9 11.969996 5.13460709 5.13460709 0
#> 10 9.969863 13.64265677 9.96986289 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") <- dist_cox_weibull(scale=1/100,shape=2)
distribution(m,"censtime") <- dist_cox_weibull(scale=1/100,shape=2)
m <- eventTime(m,time~min(eventtime=1,censtime=0),"status")
distribution(m,"sex") <- dist_bernoulli(p=0.4)
distribution(m,"sbp") <- dist_gaussian(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 20.667384 1.579332 1.579332 0 0 95.12589
#> 2 35.413402 8.648746 8.648746 0 0 144.87930
#> 3 4.949838 7.240880 4.949838 1 1 99.03852
#> 4 3.392850 10.831823 3.392850 1 0 134.11068
#> 5 27.614563 14.377394 14.377394 0 1 146.78043
#> 6 16.132868 6.859990 6.859990 0 0 131.89052
# The parameters can be recovered using a Cox regression
# routine or a Weibull regression model. E.g.,
if (FALSE) { # \dontrun{
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 dist_weibull instead
# of dist_cox_weibull to specify the event time distributions.
# Here is an example:
ma <- lvm()
distribution(ma,"eventtime") <- dist_weibull(scale=3,shape=1/0.7)
distribution(ma,"censtime") <- dist_weibull(scale=2,shape=1/0.7)
ma <- eventTime(ma,time~min(eventtime=1,censtime=0),"status")
distribution(ma,"sex") <- dist_bernoulli(p=0.4)
distribution(ma,"sbp") <- dist_gaussian(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) { # \dontrun{
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") <-
dist_weibull(intercept=-log(1/100)/2,sigma=1/2)
distribution(model.aft,"censtime") <-
dist_weibull(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") <- dist_weibull(scale=100^(1/2), shape=2)
distribution(model.aft,"censtime") <- dist_weibull(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") <- dist_cox_weibull(scale=1/100,shape=2)
distribution(model.cox,"censtime") <- dist_cox_weibull(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) <- dist_bernoulli()
regression(mc) <- T1~f(X1,-.5)+f(X2,0.3)
regression(mc) <- T2~f(X2,0.6)
distribution(mc,~T1) <- dist_cox_weibull(scale=1/100)
distribution(mc,~T2) <- dist_cox_weibull(scale=1/100)
distribution(mc,~C) <- dist_cox_weibull(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