idmModel: Generate illness-death model objects
In SmoothHazard: Smooth models for interval-censored data with applications to survival and illness-death models
Description
Usage
Arguments
Details
Value
Author(s)
Examples
Description
Function to generate an illness-death model for simulation.
Usage
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idmModel(scale.illtime = 1/100, shape.illtime = 1, scale.lifetime = 1/100,
shape.lifetime = 1, scale.waittime = 1/100, shape.waittime = 1,
scale.censtime = 1/100, shape.censtime = 1, n.inspections = 5,
schedule = 10, punctuality = 5)
Arguments
scale.illtime
Weilbull scale for latent illness time
shape.illtime
Weilbull shape for latent illness time
scale.lifetime
Weilbull scale for latent life time
shape.lifetime
Weilbull shape for latent life time
scale.waittime
Weilbull scale for latent life time
shape.waittime
Weilbull shape for latent life time
scale.censtime
Weilbull scale for censoring time
shape.censtime
Weilbull shape for censoring time
n.inspections
Number of inspection times
schedule
Mean of the waiting time between adjacent
inspections.
punctuality
Standard deviation of waiting time between
inspections.
Details
Based on the functionality of the lava PACKAGE the function generates
a latent variable model (latent illtime, waittime and lifetime)
and censoring mechanism (censtime, inspection1,inspection2,...,inspectionK).
The function sim.idmModel then simulates
right censored lifetimes and interval censored illness times.
Value
A latent variable model object lvm
Author(s)
Thomas Alexander Gerds
Examples
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## Not run:
library(lava)
library(prodlim)
# generate illness-death model based on exponentially
# distributed times
m <- idmModel(scale.illtime=1/70,
shape.illtime=1.8,
scale.lifetime=1/50,
shape.lifetime=0.7,
scale.waittime=1/30,
shape.waittime=0.7)
round(sim(m,6),1)
# Estimate the parameters of the Weibull models
# based on the uncensored exact event times
# and the uncensored illstatus.
set.seed(18)
d <- sim(m,100,latent=FALSE)
d$uncensored.status <- 1
f <- idm(formula01=Hist(time=illtime,event=illstatus)~1,
formula02=Hist(time=lifetime,event=uncensored.status)~1,
data=d,
conf.int=FALSE)
print(f)
# Change the rate of the 0->2 and 0->1 transitions
# also the rate of the 1->2 transition
# and also lower the censoring rate
m <- idmModel(scale.lifetime=1/2000,
scale.waittime=1/30,
scale.illtime=1/1000,
scale.censtime=1/1000)
set.seed(18)
d <- sim(m,50,latent=TRUE)
d$uncensored.status <- 1
f <- idm(formula01=Hist(time=observed.illtime,event=illstatus)~1,
formula02=Hist(time=observed.lifetime,event=uncensored.status)~1,
data=d,
conf.int=FALSE)
print(f)
# Estimate based on the right censored observations
fc <- idm(formula01=Hist(time=illtime,event=seen.ill)~1,
formula02=Hist(time=observed.lifetime,event=seen.exit)~1,
data=d,
conf.int=FALSE)
print(fc)
# Estimate based on interval censored and right censored observations
fi <- idm(formula01=Hist(time=list(L,R),event=seen.ill)~1,
formula02=Hist(time=observed.lifetime,event=seen.exit)~1,
data=d,
conf.int=FALSE)
print(fi)
# Estimation of covariate effects:
# X1, X2, X3
m <- idmModel(shape.waittime=2,
scale.lifetime=1/2000,
scale.waittime=1/300,
scale.illtime=1/10000,
scale.censtime=1/10000)
distribution(m,"X1") <- binomial.lvm(p=0.3)
distribution(m,"X2") <- normal.lvm(mean=120,sd=20)
distribution(m,"X3") <- normal.lvm(mean=50,sd=20)
regression(m,to="latent.illtime",from="X1") <- 1.7
regression(m,to="latent.illtime",from="X2") <- 0.07
regression(m,to="latent.illtime",from="X3") <- -0.1
regression(m,to="latent.waittime",from="X1") <- 1.8
regression(m,to="latent.lifetime",from="X1") <- 0.7
set.seed(28)
d <- sim(m,100,latent=TRUE)
head(d)
table(ill=d$seen.ill,death=d$seen.exit)
# Estimation based on uncensored data
d$uncensored.status <- 1
# uncensored data
F1 <- idm(formula01=Hist(time=illtime,event=illstatus)~X1+X2+X3,
formula02=Hist(time=lifetime,event=uncensored.status)~X1+X2+X3,
data=d,conf.int=FALSE)
print(F1)
# Estimation based on right censored data
F2 <- idm(formula01=Hist(time=illtime,event=seen.ill)~X1+X2+X3,
formula02=Hist(time=observed.lifetime,event=seen.exit)~X1+X2+X3,
data=d,conf.int=FALSE)
print(F2)
# Estimation based on interval censored and right censored data
F3 <- idm(formula01=Hist(time=list(L,R),event=seen.ill)~X1+X2+X3,
formula02=Hist(time=observed.lifetime,event=seen.exit)~X1+X2+X3,
data=d,conf.int=FALSE)
print(F3)
cbind(uncensored=F1$coef,right.censored=F2$coef,interval.censored=F3$coef)
## End(Not run)
Example output
Loading required package: prodlim
censtime illtime illstatus lifetime L R seen.ill seen.exit
1 87.3 9.8 1 21.5 6.9 19.1 1 1
2 116.2 12.4 1 114.9 0.0 13.2 1 1
3 68.8 6.6 1 84.6 0.0 13.4 1 0
4 34.1 14.4 1 38.7 13.5 18.4 1 0
5 37.2 8.4 1 121.7 0.0 10.8 1 0
6 73.0 4.6 1 67.3 0.0 5.4 1 1
observed.lifetime observed.illtime
1 21.5 9.8
2 114.9 12.4
3 68.8 6.6
4 34.1 14.4
5 37.2 8.4
6 67.3 4.6
Call:
idm(formula01 = Hist(time = illtime, event = illstatus) ~ 1,
formula02 = Hist(time = lifetime, event = uncensored.status) ~
1, data = d, conf.int = FALSE)
Illness-death regression model using Weibull parametrization
to estimate the baseline transition intensities.
number of subjects: 100
number of events '0 -> 1': 94
number of events '0 -> 2' or '0 -> 1 -> 2': 100
number of covariates: 0 0 0
----
Model converged.
number of iterations: 7
convergence criteria: parameters= 4.5e-11
: likelihood= 8.9e-09
: second derivatives= 6.2e-16
Without covariates With covariates
log-likelihood -876.4219 0
Parameters of the Weibull distributions: 'S(t) = exp(-(b*t)^a)'
transition 0 -> 1 transition 0 -> 2 transition 1 -> 2
shape (a) 1.8852734 0.819140818 0.5239669
scale (b) 0.1026855 0.004036428 0.0126208
Call:
idm(formula01 = Hist(time = observed.illtime, event = illstatus) ~
1, formula02 = Hist(time = observed.lifetime, event = uncensored.status) ~
1, data = d, conf.int = FALSE)
Illness-death regression model using Weibull parametrization
to estimate the baseline transition intensities.
number of subjects: 50
number of events '0 -> 1': 34
number of events '0 -> 2' or '0 -> 1 -> 2': 50
number of covariates: 0 0 0
----
Model converged.
number of iterations: 11
convergence criteria: parameters= 1.2e-11
: likelihood= 2e-09
: second derivatives= 2.5e-14
Without covariates With covariates
log-likelihood -500.183 0
Parameters of the Weibull distributions: 'S(t) = exp(-(b*t)^a)'
transition 0 -> 1 transition 0 -> 2 transition 1 -> 2
shape (a) 1.324300827 1.241391811 1.17527272
scale (b) 0.001928705 0.001052337 0.03612296
Call:
idm(formula01 = Hist(time = illtime, event = seen.ill) ~ 1, formula02 = Hist(time = observed.lifetime,
event = seen.exit) ~ 1, data = d, conf.int = FALSE)
Illness-death regression model using Weibull parametrization
to estimate the baseline transition intensities.
number of subjects: 50
number of events '0 -> 1': 18
number of events '0 -> 2' or '0 -> 1 -> 2': 24
number of covariates: 0 0 0
----
Model converged.
number of iterations: 11
convergence criteria: parameters= 1.2e-09
: likelihood= 4.7e-08
: second derivatives= 5.6e-13
Without covariates With covariates
log-likelihood -274.9932 0
Parameters of the Weibull distributions: 'S(t) = exp(-(b*t)^a)'
transition 0 -> 1 transition 0 -> 2 transition 1 -> 2
shape (a) 1.07423525 1.2515356328 0.95656563
scale (b) 0.00106407 0.0004829543 0.03842021
Warning message:
In idm(formula01 = Hist(time = list(L, R), event = seen.ill) ~ 1, :
Model did not converge. You could try to increase the 'maxit' parameter and set 'CV=1'.
Call:
idm(formula01 = Hist(time = list(L, R), event = seen.ill) ~ 1,
formula02 = Hist(time = observed.lifetime, event = seen.exit) ~
1, data = d, conf.int = FALSE)
Illness-death regression model using Weibull parametrization
to estimate the baseline transition intensities.
number of subjects: 50
number of events '0 -> 1': 18
number of events '0 -> 2' or '0 -> 1 -> 2': 24
number of covariates: 0 0 0
Parameters of the Weibull distributions: 'S(t) = exp(-(b*t)^a)'
transition 0 -> 1 transition 0 -> 2 transition 1 -> 2
shape (a) 1.000000000 1.000000000 1.000000000
scale (b) 0.000982495 0.001309993 0.001309993
Warning messages:
1: In print.idm(fi) : The model did not converge.
2: Maximum number of iterations reached.
latent.illtime latent.lifetime latent.waittime censtime X1 X2 X3
1 1.217973 2804.9085 14.518521 33713.559 0 134.6338 11.95686
2 280.525594 748.9620 7.263955 3508.494 0 132.2453 48.71410
3 1.162656 592.3499 23.795270 8732.422 0 128.7554 23.37666
4 2.341798 5638.3843 9.969513 17502.474 1 110.3836 13.60017
5 245.194273 781.3930 6.962619 19363.433 1 109.8695 53.25339
6 510.382597 955.4774 12.837700 1265.768 0 121.8592 60.62793
illtime illstatus lifetime L R seen.ill seen.exit
1 1.217973 1 15.73649 0.00000 9.574974 1 1
2 280.525594 1 287.78955 49.81715 287.789549 1 1
3 1.162656 1 24.95793 0.00000 17.479958 1 1
4 2.341798 1 12.31131 0.00000 3.979647 1 1
5 245.194273 1 252.15689 43.89710 252.156891 1 1
6 510.382597 1 523.22030 44.38116 523.220297 1 1
observed.lifetime observed.illtime
1 15.73649 1.217973
2 287.78955 280.525594
3 24.95793 1.162656
4 12.31131 2.341798
5 252.15689 245.194273
6 523.22030 510.382597
death
ill 0 1
0 4 22
1 0 74
Call:
idm(formula01 = Hist(time = illtime, event = illstatus) ~ X1 +
X2 + X3, formula02 = Hist(time = lifetime, event = uncensored.status) ~
X1 + X2 + X3, data = d, conf.int = FALSE)
Illness-death regression model using Weibull parametrization
to estimate the baseline transition intensities.
number of subjects: 100
number of events '0 -> 1': 77
number of events '0 -> 2' or '0 -> 1 -> 2': 100
number of covariates: 3 3 3
----
Model converged.
number of iterations: 12
convergence criteria: parameters= 9.2e-10
: likelihood= 1.7e-09
: second derivatives= 3.3e-14
Without covariates With covariates
log-likelihood -986.0347 -890.4222
Parameters of the Weibull distributions: 'S(t) = exp(-(b*t)^a)'
transition 0 -> 1 transition 0 -> 2 transition 1 -> 2
shape (a) 1.0871865355 1.481407274 1.25719831
scale (b) 0.0002190188 0.000168841 0.01308373
Regression coefficients:
$`transition 0 -> 1`
Factor coef SE coef exp(coef) CI p-value
1 X1 1.5978 0.3099 4.9421 [2.69; 9.07] < 1e-04
2 X2 0.0743 0.0086 1.0771 [1.06; 1.10] < 1e-04
3 X3 -0.1199 0.0124 0.8870 [0.87; 0.91] < 1e-04
$`transition 0 -> 2`
Factor coef SE coef exp(coef) CI p-value
4 X1 1.4709 0.5353 4.3530 [1.52;12.43] 0.005997
5 X2 0.0127 0.0120 1.0128 [0.99; 1.04] 0.290496
6 X3 0.0003 0.0170 1.0003 [0.97; 1.03] 0.985167
$`transition 1 -> 2`
Factor coef SE coef exp(coef) CI p-value
7 X1 1.2514 0.3150 3.4951 [1.89; 6.48] < 1e-04
8 X2 0.0150 0.0081 1.0151 [1.00; 1.03] 0.063200
9 X3 -0.0118 0.0107 0.9883 [0.97; 1.01] 0.269752
Call:
idm(formula01 = Hist(time = illtime, event = seen.ill) ~ X1 +
X2 + X3, formula02 = Hist(time = observed.lifetime, event = seen.exit) ~
X1 + X2 + X3, data = d, conf.int = FALSE)
Illness-death regression model using Weibull parametrization
to estimate the baseline transition intensities.
number of subjects: 100
number of events '0 -> 1': 74
number of events '0 -> 2' or '0 -> 1 -> 2': 96
number of covariates: 3 3 3
----
Model converged.
number of iterations: 13
convergence criteria: parameters= 3.3e-09
: likelihood= 1.1e-07
: second derivatives= 1.6e-13
Without covariates With covariates
log-likelihood -942.8116 -847.0686
Parameters of the Weibull distributions: 'S(t) = exp(-(b*t)^a)'
transition 0 -> 1 transition 0 -> 2 transition 1 -> 2
shape (a) 1.0959001727 1.4474687373 1.25941541
scale (b) 0.0001848469 0.0001183147 0.01132937
Regression coefficients:
$`transition 0 -> 1`
Factor coef SE coef exp(coef) CI p-value
1 X1 1.6380 0.3125 5.1448 [2.79; 9.49] < 1e-04
2 X2 0.0767 0.0089 1.0797 [1.06; 1.10] < 1e-04
3 X3 -0.1221 0.0128 0.8850 [0.86; 0.91] < 1e-04
$`transition 0 -> 2`
Factor coef SE coef exp(coef) CI p-value
4 X1 1.2724 0.5566 3.5695 [1.20;10.63] 0.02224
5 X2 0.0154 0.0119 1.0155 [0.99; 1.04] 0.19701
6 X3 0.0043 0.0175 1.0043 [0.97; 1.04] 0.80739
$`transition 1 -> 2`
Factor coef SE coef exp(coef) CI p-value
7 X1 1.2607 0.3188 3.5277 [1.89; 6.59] < 1e-04
8 X2 0.0156 0.0086 1.0157 [1.00; 1.03] 0.06895
9 X3 -0.0090 0.0111 0.9910 [0.97; 1.01] 0.41700
Call:
idm(formula01 = Hist(time = list(L, R), event = seen.ill) ~ X1 +
X2 + X3, formula02 = Hist(time = observed.lifetime, event = seen.exit) ~
X1 + X2 + X3, data = d, conf.int = FALSE)
Illness-death regression model using Weibull parametrization
to estimate the baseline transition intensities.
number of subjects: 100
number of events '0 -> 1': 74
number of events '0 -> 2' or '0 -> 1 -> 2': 96
number of covariates: 3 3 3
----
Model converged.
number of iterations: 15
convergence criteria: parameters= 1.1e-09
: likelihood= 1.8e-08
: second derivatives= 1.8e-13
Without covariates With covariates
log-likelihood -729.9178 -645.8426
Parameters of the Weibull distributions: 'S(t) = exp(-(b*t)^a)'
transition 0 -> 1 transition 0 -> 2 transition 1 -> 2
shape (a) 1.0967495268 1.4480228688 1.28707317
scale (b) 0.0002480193 0.0001182723 0.00872902
Regression coefficients:
$`transition 0 -> 1`
Factor coef SE coef exp(coef) CI p-value
1 X1 1.6195 0.3391 5.0504 [2.60; 9.82] < 1e-04
2 X2 0.0713 0.0097 1.0739 [1.05; 1.09] < 1e-04
3 X3 -0.1166 0.0139 0.8899 [0.87; 0.91] < 1e-04
$`transition 0 -> 2`
Factor coef SE coef exp(coef) CI p-value
4 X1 1.2717 0.5565 3.5668 [1.20;10.62] 0.022306
5 X2 0.0153 0.0119 1.0154 [0.99; 1.04] 0.196893
6 X3 0.0044 0.0174 1.0044 [0.97; 1.04] 0.802736
$`transition 1 -> 2`
Factor coef SE coef exp(coef) CI p-value
7 X1 1.3730 0.4669 3.9471 [1.58; 9.86] 0.003273
8 X2 0.0194 0.0109 1.0196 [1.00; 1.04] 0.075078
9 X3 -0.0108 0.0149 0.9893 [0.96; 1.02] 0.468960
uncensored right.censored interval.censored
X1 1.5977853755 1.637979393 1.619471967
X2 0.0742504069 0.076655201 0.071275469
X3 -0.1199068963 -0.122127934 -0.116631554
X1 1.4708637246 1.272435012 1.271655708
X2 0.0126847580 0.015367886 0.015314126
X3 0.0003152041 0.004260136 0.004354287
X1 1.2513711588 1.260652896 1.372976038
X2 0.0150219691 0.015624757 0.019446165
X3 -0.0117993289 -0.009032945 -0.010769769
SmoothHazard documentation built on May 2, 2019, 4:43 p.m.
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Description Usage Arguments Details Value Author(s) Examples
Description
Function to generate an illness-death model for simulation.
Usage
1 2 3 4 | idmModel(scale.illtime = 1/100, shape.illtime = 1, scale.lifetime = 1/100,
shape.lifetime = 1, scale.waittime = 1/100, shape.waittime = 1,
scale.censtime = 1/100, shape.censtime = 1, n.inspections = 5,
schedule = 10, punctuality = 5)
|
Arguments
scale.illtime |
Weilbull scale for latent illness time |
shape.illtime |
Weilbull shape for latent illness time |
scale.lifetime |
Weilbull scale for latent life time |
shape.lifetime |
Weilbull shape for latent life time |
scale.waittime |
Weilbull scale for latent life time |
shape.waittime |
Weilbull shape for latent life time |
scale.censtime |
Weilbull scale for censoring time |
shape.censtime |
Weilbull shape for censoring time |
n.inspections |
Number of inspection times |
schedule |
Mean of the waiting time between adjacent inspections. |
punctuality |
Standard deviation of waiting time between inspections. |
Details
Based on the functionality of the lava PACKAGE the function generates a latent variable model (latent illtime, waittime and lifetime) and censoring mechanism (censtime, inspection1,inspection2,...,inspectionK).
The function sim.idmModel then simulates
right censored lifetimes and interval censored illness times.
Value
A latent variable model object lvm
Author(s)
Thomas Alexander Gerds
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 | ## Not run:
library(lava)
library(prodlim)
# generate illness-death model based on exponentially
# distributed times
m <- idmModel(scale.illtime=1/70,
shape.illtime=1.8,
scale.lifetime=1/50,
shape.lifetime=0.7,
scale.waittime=1/30,
shape.waittime=0.7)
round(sim(m,6),1)
# Estimate the parameters of the Weibull models
# based on the uncensored exact event times
# and the uncensored illstatus.
set.seed(18)
d <- sim(m,100,latent=FALSE)
d$uncensored.status <- 1
f <- idm(formula01=Hist(time=illtime,event=illstatus)~1,
formula02=Hist(time=lifetime,event=uncensored.status)~1,
data=d,
conf.int=FALSE)
print(f)
# Change the rate of the 0->2 and 0->1 transitions
# also the rate of the 1->2 transition
# and also lower the censoring rate
m <- idmModel(scale.lifetime=1/2000,
scale.waittime=1/30,
scale.illtime=1/1000,
scale.censtime=1/1000)
set.seed(18)
d <- sim(m,50,latent=TRUE)
d$uncensored.status <- 1
f <- idm(formula01=Hist(time=observed.illtime,event=illstatus)~1,
formula02=Hist(time=observed.lifetime,event=uncensored.status)~1,
data=d,
conf.int=FALSE)
print(f)
# Estimate based on the right censored observations
fc <- idm(formula01=Hist(time=illtime,event=seen.ill)~1,
formula02=Hist(time=observed.lifetime,event=seen.exit)~1,
data=d,
conf.int=FALSE)
print(fc)
# Estimate based on interval censored and right censored observations
fi <- idm(formula01=Hist(time=list(L,R),event=seen.ill)~1,
formula02=Hist(time=observed.lifetime,event=seen.exit)~1,
data=d,
conf.int=FALSE)
print(fi)
# Estimation of covariate effects:
# X1, X2, X3
m <- idmModel(shape.waittime=2,
scale.lifetime=1/2000,
scale.waittime=1/300,
scale.illtime=1/10000,
scale.censtime=1/10000)
distribution(m,"X1") <- binomial.lvm(p=0.3)
distribution(m,"X2") <- normal.lvm(mean=120,sd=20)
distribution(m,"X3") <- normal.lvm(mean=50,sd=20)
regression(m,to="latent.illtime",from="X1") <- 1.7
regression(m,to="latent.illtime",from="X2") <- 0.07
regression(m,to="latent.illtime",from="X3") <- -0.1
regression(m,to="latent.waittime",from="X1") <- 1.8
regression(m,to="latent.lifetime",from="X1") <- 0.7
set.seed(28)
d <- sim(m,100,latent=TRUE)
head(d)
table(ill=d$seen.ill,death=d$seen.exit)
# Estimation based on uncensored data
d$uncensored.status <- 1
# uncensored data
F1 <- idm(formula01=Hist(time=illtime,event=illstatus)~X1+X2+X3,
formula02=Hist(time=lifetime,event=uncensored.status)~X1+X2+X3,
data=d,conf.int=FALSE)
print(F1)
# Estimation based on right censored data
F2 <- idm(formula01=Hist(time=illtime,event=seen.ill)~X1+X2+X3,
formula02=Hist(time=observed.lifetime,event=seen.exit)~X1+X2+X3,
data=d,conf.int=FALSE)
print(F2)
# Estimation based on interval censored and right censored data
F3 <- idm(formula01=Hist(time=list(L,R),event=seen.ill)~X1+X2+X3,
formula02=Hist(time=observed.lifetime,event=seen.exit)~X1+X2+X3,
data=d,conf.int=FALSE)
print(F3)
cbind(uncensored=F1$coef,right.censored=F2$coef,interval.censored=F3$coef)
## End(Not run)
|
Example output
Loading required package: prodlim
censtime illtime illstatus lifetime L R seen.ill seen.exit
1 87.3 9.8 1 21.5 6.9 19.1 1 1
2 116.2 12.4 1 114.9 0.0 13.2 1 1
3 68.8 6.6 1 84.6 0.0 13.4 1 0
4 34.1 14.4 1 38.7 13.5 18.4 1 0
5 37.2 8.4 1 121.7 0.0 10.8 1 0
6 73.0 4.6 1 67.3 0.0 5.4 1 1
observed.lifetime observed.illtime
1 21.5 9.8
2 114.9 12.4
3 68.8 6.6
4 34.1 14.4
5 37.2 8.4
6 67.3 4.6
Call:
idm(formula01 = Hist(time = illtime, event = illstatus) ~ 1,
formula02 = Hist(time = lifetime, event = uncensored.status) ~
1, data = d, conf.int = FALSE)
Illness-death regression model using Weibull parametrization
to estimate the baseline transition intensities.
number of subjects: 100
number of events '0 -> 1': 94
number of events '0 -> 2' or '0 -> 1 -> 2': 100
number of covariates: 0 0 0
----
Model converged.
number of iterations: 7
convergence criteria: parameters= 4.5e-11
: likelihood= 8.9e-09
: second derivatives= 6.2e-16
Without covariates With covariates
log-likelihood -876.4219 0
Parameters of the Weibull distributions: 'S(t) = exp(-(b*t)^a)'
transition 0 -> 1 transition 0 -> 2 transition 1 -> 2
shape (a) 1.8852734 0.819140818 0.5239669
scale (b) 0.1026855 0.004036428 0.0126208
Call:
idm(formula01 = Hist(time = observed.illtime, event = illstatus) ~
1, formula02 = Hist(time = observed.lifetime, event = uncensored.status) ~
1, data = d, conf.int = FALSE)
Illness-death regression model using Weibull parametrization
to estimate the baseline transition intensities.
number of subjects: 50
number of events '0 -> 1': 34
number of events '0 -> 2' or '0 -> 1 -> 2': 50
number of covariates: 0 0 0
----
Model converged.
number of iterations: 11
convergence criteria: parameters= 1.2e-11
: likelihood= 2e-09
: second derivatives= 2.5e-14
Without covariates With covariates
log-likelihood -500.183 0
Parameters of the Weibull distributions: 'S(t) = exp(-(b*t)^a)'
transition 0 -> 1 transition 0 -> 2 transition 1 -> 2
shape (a) 1.324300827 1.241391811 1.17527272
scale (b) 0.001928705 0.001052337 0.03612296
Call:
idm(formula01 = Hist(time = illtime, event = seen.ill) ~ 1, formula02 = Hist(time = observed.lifetime,
event = seen.exit) ~ 1, data = d, conf.int = FALSE)
Illness-death regression model using Weibull parametrization
to estimate the baseline transition intensities.
number of subjects: 50
number of events '0 -> 1': 18
number of events '0 -> 2' or '0 -> 1 -> 2': 24
number of covariates: 0 0 0
----
Model converged.
number of iterations: 11
convergence criteria: parameters= 1.2e-09
: likelihood= 4.7e-08
: second derivatives= 5.6e-13
Without covariates With covariates
log-likelihood -274.9932 0
Parameters of the Weibull distributions: 'S(t) = exp(-(b*t)^a)'
transition 0 -> 1 transition 0 -> 2 transition 1 -> 2
shape (a) 1.07423525 1.2515356328 0.95656563
scale (b) 0.00106407 0.0004829543 0.03842021
Warning message:
In idm(formula01 = Hist(time = list(L, R), event = seen.ill) ~ 1, :
Model did not converge. You could try to increase the 'maxit' parameter and set 'CV=1'.
Call:
idm(formula01 = Hist(time = list(L, R), event = seen.ill) ~ 1,
formula02 = Hist(time = observed.lifetime, event = seen.exit) ~
1, data = d, conf.int = FALSE)
Illness-death regression model using Weibull parametrization
to estimate the baseline transition intensities.
number of subjects: 50
number of events '0 -> 1': 18
number of events '0 -> 2' or '0 -> 1 -> 2': 24
number of covariates: 0 0 0
Parameters of the Weibull distributions: 'S(t) = exp(-(b*t)^a)'
transition 0 -> 1 transition 0 -> 2 transition 1 -> 2
shape (a) 1.000000000 1.000000000 1.000000000
scale (b) 0.000982495 0.001309993 0.001309993
Warning messages:
1: In print.idm(fi) : The model did not converge.
2: Maximum number of iterations reached.
latent.illtime latent.lifetime latent.waittime censtime X1 X2 X3
1 1.217973 2804.9085 14.518521 33713.559 0 134.6338 11.95686
2 280.525594 748.9620 7.263955 3508.494 0 132.2453 48.71410
3 1.162656 592.3499 23.795270 8732.422 0 128.7554 23.37666
4 2.341798 5638.3843 9.969513 17502.474 1 110.3836 13.60017
5 245.194273 781.3930 6.962619 19363.433 1 109.8695 53.25339
6 510.382597 955.4774 12.837700 1265.768 0 121.8592 60.62793
illtime illstatus lifetime L R seen.ill seen.exit
1 1.217973 1 15.73649 0.00000 9.574974 1 1
2 280.525594 1 287.78955 49.81715 287.789549 1 1
3 1.162656 1 24.95793 0.00000 17.479958 1 1
4 2.341798 1 12.31131 0.00000 3.979647 1 1
5 245.194273 1 252.15689 43.89710 252.156891 1 1
6 510.382597 1 523.22030 44.38116 523.220297 1 1
observed.lifetime observed.illtime
1 15.73649 1.217973
2 287.78955 280.525594
3 24.95793 1.162656
4 12.31131 2.341798
5 252.15689 245.194273
6 523.22030 510.382597
death
ill 0 1
0 4 22
1 0 74
Call:
idm(formula01 = Hist(time = illtime, event = illstatus) ~ X1 +
X2 + X3, formula02 = Hist(time = lifetime, event = uncensored.status) ~
X1 + X2 + X3, data = d, conf.int = FALSE)
Illness-death regression model using Weibull parametrization
to estimate the baseline transition intensities.
number of subjects: 100
number of events '0 -> 1': 77
number of events '0 -> 2' or '0 -> 1 -> 2': 100
number of covariates: 3 3 3
----
Model converged.
number of iterations: 12
convergence criteria: parameters= 9.2e-10
: likelihood= 1.7e-09
: second derivatives= 3.3e-14
Without covariates With covariates
log-likelihood -986.0347 -890.4222
Parameters of the Weibull distributions: 'S(t) = exp(-(b*t)^a)'
transition 0 -> 1 transition 0 -> 2 transition 1 -> 2
shape (a) 1.0871865355 1.481407274 1.25719831
scale (b) 0.0002190188 0.000168841 0.01308373
Regression coefficients:
$`transition 0 -> 1`
Factor coef SE coef exp(coef) CI p-value
1 X1 1.5978 0.3099 4.9421 [2.69; 9.07] < 1e-04
2 X2 0.0743 0.0086 1.0771 [1.06; 1.10] < 1e-04
3 X3 -0.1199 0.0124 0.8870 [0.87; 0.91] < 1e-04
$`transition 0 -> 2`
Factor coef SE coef exp(coef) CI p-value
4 X1 1.4709 0.5353 4.3530 [1.52;12.43] 0.005997
5 X2 0.0127 0.0120 1.0128 [0.99; 1.04] 0.290496
6 X3 0.0003 0.0170 1.0003 [0.97; 1.03] 0.985167
$`transition 1 -> 2`
Factor coef SE coef exp(coef) CI p-value
7 X1 1.2514 0.3150 3.4951 [1.89; 6.48] < 1e-04
8 X2 0.0150 0.0081 1.0151 [1.00; 1.03] 0.063200
9 X3 -0.0118 0.0107 0.9883 [0.97; 1.01] 0.269752
Call:
idm(formula01 = Hist(time = illtime, event = seen.ill) ~ X1 +
X2 + X3, formula02 = Hist(time = observed.lifetime, event = seen.exit) ~
X1 + X2 + X3, data = d, conf.int = FALSE)
Illness-death regression model using Weibull parametrization
to estimate the baseline transition intensities.
number of subjects: 100
number of events '0 -> 1': 74
number of events '0 -> 2' or '0 -> 1 -> 2': 96
number of covariates: 3 3 3
----
Model converged.
number of iterations: 13
convergence criteria: parameters= 3.3e-09
: likelihood= 1.1e-07
: second derivatives= 1.6e-13
Without covariates With covariates
log-likelihood -942.8116 -847.0686
Parameters of the Weibull distributions: 'S(t) = exp(-(b*t)^a)'
transition 0 -> 1 transition 0 -> 2 transition 1 -> 2
shape (a) 1.0959001727 1.4474687373 1.25941541
scale (b) 0.0001848469 0.0001183147 0.01132937
Regression coefficients:
$`transition 0 -> 1`
Factor coef SE coef exp(coef) CI p-value
1 X1 1.6380 0.3125 5.1448 [2.79; 9.49] < 1e-04
2 X2 0.0767 0.0089 1.0797 [1.06; 1.10] < 1e-04
3 X3 -0.1221 0.0128 0.8850 [0.86; 0.91] < 1e-04
$`transition 0 -> 2`
Factor coef SE coef exp(coef) CI p-value
4 X1 1.2724 0.5566 3.5695 [1.20;10.63] 0.02224
5 X2 0.0154 0.0119 1.0155 [0.99; 1.04] 0.19701
6 X3 0.0043 0.0175 1.0043 [0.97; 1.04] 0.80739
$`transition 1 -> 2`
Factor coef SE coef exp(coef) CI p-value
7 X1 1.2607 0.3188 3.5277 [1.89; 6.59] < 1e-04
8 X2 0.0156 0.0086 1.0157 [1.00; 1.03] 0.06895
9 X3 -0.0090 0.0111 0.9910 [0.97; 1.01] 0.41700
Call:
idm(formula01 = Hist(time = list(L, R), event = seen.ill) ~ X1 +
X2 + X3, formula02 = Hist(time = observed.lifetime, event = seen.exit) ~
X1 + X2 + X3, data = d, conf.int = FALSE)
Illness-death regression model using Weibull parametrization
to estimate the baseline transition intensities.
number of subjects: 100
number of events '0 -> 1': 74
number of events '0 -> 2' or '0 -> 1 -> 2': 96
number of covariates: 3 3 3
----
Model converged.
number of iterations: 15
convergence criteria: parameters= 1.1e-09
: likelihood= 1.8e-08
: second derivatives= 1.8e-13
Without covariates With covariates
log-likelihood -729.9178 -645.8426
Parameters of the Weibull distributions: 'S(t) = exp(-(b*t)^a)'
transition 0 -> 1 transition 0 -> 2 transition 1 -> 2
shape (a) 1.0967495268 1.4480228688 1.28707317
scale (b) 0.0002480193 0.0001182723 0.00872902
Regression coefficients:
$`transition 0 -> 1`
Factor coef SE coef exp(coef) CI p-value
1 X1 1.6195 0.3391 5.0504 [2.60; 9.82] < 1e-04
2 X2 0.0713 0.0097 1.0739 [1.05; 1.09] < 1e-04
3 X3 -0.1166 0.0139 0.8899 [0.87; 0.91] < 1e-04
$`transition 0 -> 2`
Factor coef SE coef exp(coef) CI p-value
4 X1 1.2717 0.5565 3.5668 [1.20;10.62] 0.022306
5 X2 0.0153 0.0119 1.0154 [0.99; 1.04] 0.196893
6 X3 0.0044 0.0174 1.0044 [0.97; 1.04] 0.802736
$`transition 1 -> 2`
Factor coef SE coef exp(coef) CI p-value
7 X1 1.3730 0.4669 3.9471 [1.58; 9.86] 0.003273
8 X2 0.0194 0.0109 1.0196 [1.00; 1.04] 0.075078
9 X3 -0.0108 0.0149 0.9893 [0.96; 1.02] 0.468960
uncensored right.censored interval.censored
X1 1.5977853755 1.637979393 1.619471967
X2 0.0742504069 0.076655201 0.071275469
X3 -0.1199068963 -0.122127934 -0.116631554
X1 1.4708637246 1.272435012 1.271655708
X2 0.0126847580 0.015367886 0.015314126
X3 0.0003152041 0.004260136 0.004354287
X1 1.2513711588 1.260652896 1.372976038
X2 0.0150219691 0.015624757 0.019446165
X3 -0.0117993289 -0.009032945 -0.010769769
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