idmModel: Generate illness-death model objects

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

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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 1, 2019, 8 p.m.