Title: Estimation of Smooth Hazard Models for Interval-Censored Data
Version: 2024.04.10
Description: Estimation of two-state (survival) models and irreversible illness- death models with possibly interval-censored, left-truncated and right-censored data. Proportional intensities regression models can be specified to allow for covariates effects separately for each transition. We use either a parametric approach with Weibull baseline intensities or a semi-parametric approach with M-splines approximation of baseline intensities in order to obtain smooth estimates of the hazard functions. Parameter estimates are obtained by maximum likelihood in the parametric approach and by penalized maximum likelihood in the semi-parametric approach.
Encoding: UTF-8
Copyright: See inst/COPYRIGHTS
Depends: R (≥ 1.9.1), prodlim (≥ 1.4.9)
Imports: lava (≥ 1.4.1), mvtnorm (≥ 1.0-3)
Maintainer: Thomas Alexander Gerds <tag@biostat.ku.dk>
License: GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Packaged: 2024-04-10 14:10:36 UTC; tag
Suggests: testthat (≥ 3.0.0)
Config/testthat/edition: 3
RoxygenNote: 7.3.1
NeedsCompilation: yes
Author: Celia Touraine [aut], Thomas Alexander Gerds [aut, cre], Pierre Joly [aut] (Author and maintainer of the Fortran code), Cecile Proust-Lima [aut] (Author of the Fortran code), Helene Jacqmin-Gadda [aut] (Author of the Fortran code), Amadou Diakite [aut] (Author of the Fortran code), W.D. Cody [aut] (Author of the Fortran code), A.H. Morris [aut] (Author of the Fortran code), B.W. Brown [aut] (Author of the Fortran code), Robin Genuer [ctb]
Repository: CRAN
Date/Publication: 2024-04-10 20:00:08 UTC

Paquid data set

Description

Paquid data set composed of 1000 subjects selected randomly from the Paquid data set of 3675 subjects.

Format

A data frame with 1000 rows and the following 8 columns.

dementia

dementia status, 0=non-demented, 1=demented

death

death status, 0=alive, 1=dead

e

age at entry in the study

l

for demented subjects: age at the visit before the diagnostic visit; for non-demented subjects: age at the last visit (censoring age)

r

for demented subjects: age at the diagnostic visit; for non-demented subjects: age at the last visit (censoring age)

t

for dead subjects: age at death; for alive subject: age at the latest news

certif

primary school certificate:0=without certificate, 1=with certificate

gender

gender: 0=female, 1=male

Examples


data(Paq1000)

Fit an illness-death model

Description

Fit an illness-death model using either a semi-parametric approach (penalized likelihood with an approximation of the transition intensity functions by linear combination of M-splines) or a parametric approach (specifying Weibull distributions on the transition intensities). Left-truncated, right-censored, and interval-censored data are allowed. State 0 corresponds to the initial state, state 1 to the transient one, state 2 to the absorbant one. The allowed transitions are: 0 –> 1, 0 –> 2 and 1 –> 2.

Usage

idm(
  formula01,
  formula02,
  formula12,
  data,
  maxiter = 200,
  eps = c(5, 5, 3),
  n.knots = c(7, 7, 7),
  knots = "equidistant",
  CV = FALSE,
  kappa = c(1000000, 500000, 20000),
  method = "Weib",
  conf.int = 0.95,
  print.iter = FALSE,
  subset = NULL,
  na.action = na.fail
)

Arguments

formula01

A formula specifying a regression model for the 0 --> 1 transition from the initial state to the transient state of the illness-death model. The right hand side of the formula specifies the covariate terms, and the left hand side must be an event history object as returned by the function Hist.

formula02

A formula specifying a regression model for the 0 --> 2 transition from the initial state to the absorbing state. The left hand side must be equal to the left hand side of formula01. If missing it is set to formula01.

formula12

A formula specifying a regression model for the 1 --> 2 transition from the transient state to the absorbing state. operator is not required. If missing it is set to formula01.

data

A data frame in which to interpret the variables of formula01, formula02 and formula12.

maxiter

Maximum number of iterations. The default is 200.

eps

A vector of 3 integers >0 used to define the power of three convergence criteria: 1. for the regression parameters, 2. for the likelihood, 3. for the second derivatives. The default is c(5,5,3) which is translated into convergence if the respective values change less then 10^{-5} (for regression parameters and likelihood) and 10^{-3} for the second derivatives between two iterations.

n.knots

For method="Splines" only, a vector of length 3 specifing the number of knots, one for each transition, for the M-splines estimate of the baseline intensities in the order 0 --> 1, 0 --> 2, 1 --> 2. The default is c(7,7,7). When knots are specified as a list this argument is ignored. The algorithm needs least 5 knots and at most 20 knots.

knots

Argument only active for the penalized likelihood approach method="Splines". There are three ways to control the placement of the knots between the smallest and the largest of all time points:

knots="equidistant"

Knots are placed with same distance on the time scale.

knots="quantiles"

Knots are placed such that the number of observations is roughly the same between knots.

knots=list()

List of 1 or 2 or three vectors. The list elements are the actual placements (timepoints) of the knots for the M-spline. The list may contain one vector of placements for each transition in the order 0 --> 1, 0 --> 2, 1 --> 2. If only vector is specifified the knots are used for all transitions. If only 2 vectors are specifified, the knots for the 0 --> 1 transition are also used for the 1 --> 2 transition.

The algorithm needs at least 5 knots and allows no more than 20 knots.

CV

Binary variable equals to 1 when search (by approximated cross validation) of the smoothing parameters kappa and 0 otherwise. Argument for the penalized likelihood approach. The default is 0.

kappa

Argument only active for the penalized likelihood approach method="Splines". A vector with 3 positive values (smoothing parameters), one for each transition, in the order 0 –> 1, 0 –> 2 and 1 –> 2.. If CV=1 these are used as starting values for a cross validation search to optimize kappa.

method

type of estimation method: "Splines" for a penalized likelihood approach with approximation of the transition intensities by M-splines, "Weib" for a parametric approach with a Weibull distribution on the transition intensities. Default is "Weib".

conf.int

Level of confidence pointwise confidence intervals of the transition intensities, i.e., a value between 0 and 1, the default is 0.95. The default is also used when conf.int=TRUE. To avoid computation of confidence intervals, set conf.int to FALSE or NULL.

print.iter

boolean parameter. Equals to TRUE to print the likelihood during the iteration process, FALSE otherwise. Default is FALSE. This option is not running on Windows.

subset

expression indicating the subset of the rows of data to be used in the fit. All observations are included by default.

na.action

how NAs are treated. The default is first, any na.action attribute of data, second a na.action setting of options, and third 'na.fail' if that is unset. The 'factory-fresh' default is na.omit. Another possible value is NULL.

Details

The estimated parameters are obtained using the robust Marquardt algorithm (Marquardt, 1963) which is a combination between a Newton-Raphson algorithm and a steepest descent algorithm.

Value

call

the call that produced the result.

coef

regression parameters.

loglik

vector containing the log-likelihood without and with covariate.

cv

vector containing the convergence criteria.

niter

number of iterations.

converged

integer equal to 1 when the model converged, 2, 3 or 4 otherwise.

modelPar

Weibull parameters.

N

number of subjects.

events1

number of events 0 –> 1.

events2

number of events 0 –> 2 or 0 –> 1 –> 2.

NC

vector containing the number of covariates on transitions 0 –> 1, 0 –> 2, 1 –> 2.

responseTrans

model response for the 0 –> 1 transition. Hist or Surv object.

responseAbs

model response for the 0 –> 2 transition. Hist or Surv object.

time

times for which transition intensities have been evaluated for plotting. Vector in the Weibull approach. Matrix in the penalized likelihhod approach for which the colums corresponds to the transitions 0 –> 1, 1 –> 2, 0 –> 2.

intensity01

matched values of the intensities for transition 0 –> 1.

lowerIntensity01

lower confidence intervals for the values of the intensities for transition 0 –> 1.

upperIntensity01

upper confidence intervals for the values of the intensities for transition 0 –> 1.

intensity02

matched values of the intensities for transition 0 –> 2.

lowerIntensity02

lower confidence intervals for the values of the intensities for transition 0 –> 2.

upperIntensity02

upper confidence intervals for the values of the intensities for transition 0 –> 2.

intensity12

matched values of the intensities for transition 1 –> 2.

lowerIntensity12

lower confidence intervals for the values of the intensities for transition 1 –> 2.

upperIntensity12

upper confidence intervals for the values of the intensities for transition 1 –> 2.

RR

vector of relative risks.

V

variance-covariance matrix derived from the Hessian of the log-likelihood if using method="Weib" or, from the Hessian of the penalized log-likelihood if using method="Splines".

se

standart errors of the regression parameters.

Xnames01

names of covariates on 0 –> 1.

Xnames02

names of covariates on 0 –> 2.

Xnames12

names of covariates on 1 –> 2.

knots01

knots to approximate by M-splines the intensity of the 0 –> 1 transition.

knots02

knots to approximate by M-splines the intensity of the 0 –> 2 transition.

knots12

knots to approximate by M-splines the intensity of the 1 –> 2 transition.

nknots01

number of knots on transition 0 –> 1.

nknots02

number of knots on transition 0 –> 2.

nknots12

number of knots on transition 1 –> 2.

theta01

square root of splines coefficients for transition 0 –> 1.

theta02

square root of splines coefficients for transition 0 –> 2.

theta12

square root of splines coefficients for transition 1 –> 2.

CV

a binary variable equals to 1 when search of the smoothing parameters kappa by approximated cross-validation, 1 otherwise. The default is 0.

kappa

vector containing the smoothing parameters for transition 0 –> 1, 0 –> 2, 1 –> 2 used to estimate the model by the penalized likelihood approach.

CVcrit

cross validation criteria.

DoF

degrees of freedom of the model.

na.action

observations deleted if missing values.

Author(s)

R: Celia Touraine <Celia.Touraine@isped.u-bordeaux2.fr> Fortran: Pierre Joly <Pierre.Joly@isped.u-bordeaux2.fr>

References

D. Marquardt (1963). An algorithm for least-squares estimation of nonlinear parameters. SIAM Journal of Applied Mathematics, 431-441.

See Also

print.idm summary.idm predict.idm

Examples

library(lava)
library(prodlim)
set.seed(17)
d <- simulateIDM(100)
# right censored data
fitRC <- idm(formula01=Hist(time=observed.illtime,event=seen.ill)~X1+X2,
             formula02=Hist(time=observed.lifetime,event=seen.exit)~X1+X2,
             formula12=Hist(time=observed.lifetime,event=seen.exit)~X1+X2,data=d,
             conf.int=FALSE)
fitRC


set.seed(17)
d <- simulateIDM(300)
fitRC.splines <- idm(formula01=Hist(time=observed.illtime,event=seen.ill)~X1+X2,
             formula02=Hist(time=observed.lifetime,event=seen.exit)~X1+X2,
             formula12=Hist(time=observed.lifetime,event=seen.exit)~1,data=d,
             conf.int=FALSE,method="splines")

# interval censored data
fitIC <- idm(formula01=Hist(time=list(L,R),event=seen.ill)~X1+X2,
             formula02=Hist(time=observed.lifetime,event=seen.exit)~X1+X2,
             formula12=Hist(time=observed.lifetime,event=seen.exit)~X1+X2,data=d,
             conf.int=FALSE)
fitIC



    data(Paq1000)

    # Illness-death model with certif on the 3 transitions
    # Weibull parametrization and likelihood maximization

    fit.weib <- idm(formula02=Hist(time=t,event=death,entry=e)~certif,
                    formula01=Hist(time=list(l,r),event=dementia)~certif,
                    data=Paq1000)

    # Illness-death model with certif on transitions 01 and 02
    # Splines parametrization and penalized likelihood maximization
    fit.splines <-  idm(formula02=Hist(time=t,event=death,entry=e)~certif,
                        formula01=Hist(time=list(l,r),event=dementia)~certif,
                        formula12=~1,
                        method="Splines",
                        data=Paq1000)
    fit.weib
    summary(fit.splines)

Generate illness-death model objects

Description

Function to generate an illness-death model for simulation.

Usage

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


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)

M-spline estimate of the transition intensity function

Description

M-spline estimate of the transition intensity function and the cumulative transition intensity function for survival and illness-death models

Usage

intensity(times, knots, number.knots, theta, linear.predictor = 0)

Arguments

times

Time points at which to estimate the intensity function

knots

Knots for the M-spline

number.knots

Number of knots for the M-splines (and I-splines see details)

theta

The coefficients for the linear combination of M-splines (and I-splines see details)

linear.predictor

Linear predictor beta*Z. When it is non-zero, transition and cumulative transition are multiplied by exp(linear.predictor). Default is zero.

Details

The estimate of the transition intensity function is a linear combination of M-splines and the estimate of the cumulative transition intensity function is a linear combination of I-splines (the integral of a M-spline is called I-spline). The coefficients theta are the same for the M-splines and I-splines.

Important: the theta parameters returned by idm and shr are in fact the square root of the splines coefficients. See examples.

This function is a R-translation of a corresponding Fortran function called susp. susp is used internally by idm and shr.

Value

times

The time points at which the following estimates are evaluated.

intensity

The transition intensity function evaluated at times.

cumulative.intensity

The cumulative transition intensity function evaluated at times

survival

The "survival" function, i.e., exp(-cumulative.intensity)

Author(s)

R: Celia Touraine <Celia.Touraine@isped.u-bordeaux2.fr> and Thomas Alexander Gerds <tag@biostat.ku.dk> Fortran: Pierre Joly <Pierre.Joly@isped.u-bordeaux2.fr>

See Also

shr, idm

Examples

data(testdata)
fit.su <- shr(Hist(time=list(l, r), id) ~ cov,
              data = testdata,method = "Splines",CV = TRUE)
intensity(times = fit.su$time, knots = fit.su$knots,
           number.knots = fit.su$nknots, theta = fit.su$theta^2)


  data(Paq1000)
  fit.idm <-  idm(formula02 = Hist(time = t, event = death, entry = e) ~ certif,
                  formula01 = Hist(time = list(l,r), event = dementia) ~ certif,
                  formula12 = ~ certif, method = "Splines", data = Paq1000)
  # Probability of survival in state 0 at age 80 for a subject with no cep given
  # that he is in state 0 at 70
  su0 <- (intensity(times = 80, knots = fit.idm$knots01, 
                   number.knots = fit.idm$nknots01, 
                   theta = fit.idm$theta01^2)$survival
         *intensity(times = 80, knots = fit.idm$knots02, 
                   number.knots = fit.idm$nknots02, 
                   theta = fit.idm$theta02^2)$survival)/
        (intensity(times = 70, knots = fit.idm$knots01, 
                   number.knots = fit.idm$nknots01, 
                   theta = fit.idm$theta01^2)$survival
        *intensity(times = 70, knots = fit.idm$knots02, 
                   number.knots = fit.idm$nknots02, 
                   theta = fit.idm$theta02^2)$survival)
  # Same result as:  
  predict(fit.idm, s = 70, t = 80, conf.int = FALSE) # see first element

Plot method for an illness-death model

Description

Plot estimated baseline transition intensities from an object of class idm optionally with confidence limits.

Usage

## S3 method for class 'idm'
plot(
  x,
  conf.int = FALSE,
  citype = "shadow",
  add = FALSE,
  axes = TRUE,
  col,
  lwd,
  lty,
  xlim,
  ylim,
  xlab,
  ylab,
  legend = TRUE,
  transition = c("01", "02", "12"),
  ...
)

Arguments

x

a idmWeib class object (output from calling idm with the (default) option intensities="Weib".

conf.int

If TRUE show confidence limits

citype

Type of confidence limits, can be "shadow" or "bars"

add

If TRUE add to existing plot

axes

If TRUE axes are drawn

col

Color of the lines

lwd

Width of the lines

lty

Type of the lines

xlim

Limits for x-axis

ylim

Limits for y-axis

xlab

Label for x-axis

ylab

Label for y-axis

legend

If TRUE a legend is drawn, which can be further controlled via SmartControl.

transition

Choose one of the transition intensities: c("01","02","12").

...

Passed to SmartControl

Value

Print a plot of the baseline transition intensities of an illness-death model estimated using a Weibull approach.

See Also

print.idm,summary.idm,idm,

idm

Examples


library(lava)
library(prodlim)
m <- idmModel(scale.lifetime=1/10,scale.illtime=1/8)
distribution(m,"X") <- binomial.lvm()
regression(m,latent.lifetime~X) <- 0.7
set.seed(30)
d <- sim(m,100)
fit.weib <- idm(formula02=Hist(observed.lifetime,event=seen.exit)~1,
formula01=Hist(time=list(L,R),event=seen.ill)~1,data=d,conf.int=FALSE)
plot(fit.weib)


## FIXME: the limits for the 01 transition are a bit wide!?
## with bootstrap confidence limits
fit.weib <- idm(formula02=Hist(observed.lifetime,event=seen.exit)~1,
formula01=Hist(time=list(L,R),event=seen.ill)~1,data=d,conf.int=TRUE)
plot(fit.weib)

Plot method for a survival model.

Description

Plot estimated baseline survival function from an object of class shr. Pointwise confidence limits are available.

Usage

## S3 method for class 'shr'
plot(
  x,
  type = "shr",
  add = FALSE,
  newdata = NULL,
  cause = NULL,
  col,
  lty,
  lwd,
  ylim,
  xlim,
  xlab = "Time",
  ylab,
  legend = TRUE,
  confint = TRUE,
  timeOrigin = 0,
  axes = TRUE,
  percent = TRUE,
  ...
)

Arguments

x

a shrWeib or a shrSplines class object (output from calling shr function).

type

type of function to plot. The default is "shr".

add

boolean.

newdata

newdata.

cause

cause.

col

col.

lty

lty.

lwd

lwd.

ylim

ylim.

xlim

xlim.

xlab

xlab.

ylab

ylab.

legend

legend.

confint

confint.

timeOrigin

timeOrigin.

axes

axes.

percent

percent.

...

other graphical parameters.

Value

Print a plot of a suvival model.

Author(s)

R: Celia Touraine <Celia.Touraine@isped.u-bordeaux2.fr> Fortran: Pierre Joly <Pierre.Joly@isped.u-bordeaux2.fr>

See Also

plot.shr

Examples


# Weibull survival model
library(prodlim)
data(testdata)
fit.su <- shr(Hist(time=list(l,r),id)~cov,data=testdata) 

# pointwise confidence limits
plot(fit.su)

# no pointwise confidence limits
plot(fit.su,confint=FALSE)

Predictions for an illness-death model using either a penalized likelihood approach or a Weibull parametrization.

Description

Predict transition probabilities and cumulative probabilities from an object of class idmSplines with confidence intervals are calculated.

Usage

## S3 method for class 'idm'
predict(
  object,
  s,
  t,
  newdata,
  nsim = 200,
  seed = 21,
  conf.int = 0.95,
  lifeExpect = FALSE,
  maxtime,
  ...
)

Arguments

object

an idm class objects returned by a call to the idm function

s

time point at which prediction is made.

t

time horizon for prediction.

newdata

A data frame with covariate values for prediction.

nsim

number of simulations for the confidence intervals calculations. The default is 200.

seed

Seed passed to set.seed for Monte Carlo simulation of confidence intervals.

conf.int

Level of confidence, i.e., a value between 0 and 1, the default is 0.95. The default is also used when conf.int=TRUE. To avoid computation of confidence intervals, set conf.int to FALSE or NULL.

lifeExpect

Logical. If TRUE compute life expectancies, i.e., t=Inf.

maxtime

The upper limit of integration for calculations of life expectancies from Weibull parametrizations.

...

other parameters.

Value

a list containing the following predictions with pointwise confidence intervals:

p00

the transition probability p_{00}.

p01

the transition probability p_{01}.

p11

the transition probability p_{11}.

p12

the transition probability p_{12}.

p02_0

the probability of direct transition from state 0 to state 2.

p02_1

the probability of transition from state 0 to state 2 via state 1.

p02

transition probability p_{02}. Note that p02=p_02_0+p02_1.

F01

the lifetime risk of disease. F01=p01+p02_1.

F0.

the probability of exit from state 0. F0.=p02_0+p01+p02_1.

Author(s)

R: Celia Touraine <Celia.Touraine@isped.u-bordeaux2.fr> and Thomas Alexander Gerds <tag@biostat.ku.dk> Fortran: Pierre Joly <Pierre.Joly@isped.u-bordeaux2.fr>

See Also

idm

Examples



set.seed(100)
d=simulateIDM(n = 200)
fit <- 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)
predict(fit,s=0,t=80,conf.int=FALSE,lifeExpect=FALSE)
predict(fit,s=0,t=80,nsim=4,conf.int=TRUE,lifeExpect=FALSE)
predict(fit,s=0,t=80,nsim=4,conf.int=FALSE,lifeExpect=TRUE)

data(Paq1000)
library(prodlim)
fit.paq <- idm(formula02=Hist(time=t,event=death,entry=e)~certif,
formula01=Hist(time=list(l,r),event=dementia)~certif,data=Paq1000)

predict(fit.paq,s=70,t=80,newdata=data.frame(certif=1))
predict(fit.paq,s=70,lifeExpect=TRUE,newdata=data.frame(certif=1))

fit.splines <-  idm(formula02=Hist(time=t,event=death,entry=e)~certif,
		formula01=Hist(time=list(l,r),event=dementia)~certif,
                formula12=~1,
                method="Splines",
		data=Paq1000)

predict(fit.splines,s=70,t=80,newdata=data.frame(certif=1))
predict(fit.splines,s=70,t=80,lifeExpect=TRUE,newdata=data.frame(certif=1),nsim=20)

Print method for idm objects

Description

Print a summary of a fitted illness-death model

Usage

## S3 method for class 'idm'
print(x, conf.int = 0.95, digits = 4, pvalDigits = 4, eps = 0.0001, ...)

Arguments

x

Class idm object, i.e. the result of a call to the idm function with intensities="Weib".

conf.int

The level of confidence for the hazard ratios. The default is 0.95.

digits

Number of digits to print.

pvalDigits

Number of digits to print for p-values.

eps

Passed to format.pval.

...

Not used.

Value

No return value.

Author(s)

Celia Touraine <Celia.Touraine@isped.u-bordeaux2.fr>, Thomas A. Gerds <tag@biostat.ku.dk>

See Also

summary.idm, plot.idm

Examples


data(Paq1000)
library(prodlim)
fit.splines <-  idm(formula02=Hist(time=t,event=death,entry=e)~certif,
		formula01=Hist(time=list(l,r),event=dementia)~certif,
                formula12=~1,
                method="Splines",
		data=Paq1000)
print(fit.splines)

Print method for shrSplines objects

Description

Print a summary of a fitted illness-death model using the penalized likelihood approach.

Usage

## S3 method for class 'shr'
print(x, conf.int = 0.95, digits = 4, pvalDigits = 4, eps = 0.0001, ...)

Arguments

x

a shr object, i.e., the result of a call to the shr function with hazard="Splines".

conf.int

The level of confidence for the hazard ratios. The default is 0.95.

digits

number of digits to print.

pvalDigits

number of digits to print for p-values.

eps

convergence criterion used for p-values.

...

other unusued arguments.

Value

No return value.

Author(s)

R: Celia Touraine <Celia.Touraine@isped.u-bordeaux2.fr> Fortran: Pierre Joly <Pierre.Joly@isped.u-bordeaux2.fr>

See Also

summary.shr, plot.shr

Examples



# a penalized survival model 
library(prodlim)
data(testdata)
fit.su <- shr(Hist(time=list(l,r),id)~cov,data=testdata,method="Splines") 
print(fit.su)

Fit a survival model

Description

Fit a survival model using either a semi-parametric approach (penalized likelihood with an approximation of the hazard function by linear combination of M-splines) or a parametric approach (specifying a Weibull distribution on the hazard function). Left-truncated, right-censored, and interval-censored data are allowed.

Usage

shr(
  formula,
  data,
  eps = c(5, 5, 3),
  n.knots = 7,
  knots = "equidistant",
  CV = FALSE,
  kappa = 10000,
  conf.int = 0.95,
  maxiter = 200,
  method = "Weib",
  print.iter = FALSE,
  na.action = na.omit
)

Arguments

formula

a formula object with the response on the left hand side and the terms on the right hand side. The response must be a survival object or Hist object as returned by the 'Surv' or 'Hist' function.

data

a data frame in which to interpret the variables named in the formula.

eps

a vector of length 3 for the convergence criteria (criterion for parameters, criterion for likelihood, criterion for second derivatives). The default is c(5,5,3) and corresponds to criteria equals to 10^{-5}, 10^{-5} and 10^{-3}.

n.knots

Argument only active for the penalized likelihood approach method="splines". Number of knots for the splines to use to approximate the hazard function. The default is 7. If knots are given as a vector this argument is ignored. The algorithm needs least 5 knots and at most 20 knots.

knots

Argument only active for the penalized likelihood approach method="splines". There are three ways to control the placement of the knots between the smallest and the largest of all time points:

knots="equidistant"

Knots are placed with same distance on the time scale.

knots="quantiles"

Knots are placed such that the number of observations is roughly the same between knots.

knots=list()

List of length 3. The list elements are the actual placements (timepoints) of the knots for the M-spline.

The algorithm reuqires at least 5 knots and allows no more than 20 knots.

CV

binary variable equals to 1 when search (by approximated cross validation) of the smoothing parameter kappa and 0 otherwise. Argument for the penalized likelihood approach. The default is 0.

kappa

Argument only active for the penalized likelihood approach method="splines". A positive number (smoothing parameter) If CV=1 the value is used as a starting value for a cross validation search to optimize kappa.

conf.int

Level of confidence pointwise confidence intervals of the survival and hazard functions, i.e., a value between 0 and 1, the default is 0.95. The default is also used when conf.int=TRUE. To avoid computation of confidence intervals, set conf.int to FALSE or NULL.

maxiter

maximum number of iterations. The default is 200.

method

type of estimation method: "Splines" for a penalized likelihood approach with approximation of the hazard function by M-splines, "Weib" for a parametric approach with a Weibull distribution on the hazard function. Default is "Weib".

print.iter

boolean parameter. Equals to TRUE to print the likelihood during the iteration process, FALSE otherwise. Default is FALSE. This option is not running on Windows.

na.action

how NAs are treated. The default is first, any na.action attribute of data, second a na.action setting of options, and third 'na.fail' if that is unset. The 'factory-fresh' default is na.omit. Another possible value is NULL.

Details

The estimated parameters are obtained using the robust Marquardt algorithm (Marquardt, 1963) which is a combination between a Newton-Raphson algorithm and a steepest descent algorithm.

Value

call
coef

regression parameters.

loglik

vector containing the log-likelihood without and with covariate.

modelPar

Weibull parameters.

N

number of subjects.

NC

number of covariates.

nevents

number of events.

modelResponse

model response: Hist or Surv object.

converged

integer equal to 1 when the model converged, 2, 3 or 4 otherwise.

time

times for which survival and hazard functions have been evaluated for plotting.

hazard

matched values of the hazard function.

lowerHazard

lower confidence limits for hazard function.

upperHazard

upper confidence limits for hazard function.

surv

matched values of the survival function.

lowerSurv

lower confidence limits for survival function.

upperSurv

upper confidence limits for survival function.

RR

vector of relative risks.

V

variance-covariance matrix.

se

standard errors.

knots

knots of the M-splines estimate of the hazard function.

nknots

number of knots.

CV

a binary variable equals to 1 when search of the smoothing parameter kappa by approximated cross-validation, 1 otherwise. The default is 0.

niter

number of iterations.

cv

vector containing the convergence criteria.

na.action

observations deleted if missing values.

Author(s)

R: Celia Touraine celia.touraine@icm.unicancer.fr Fortran: Pierre Joly Pierre.Joly@isped.u-bordeaux2.fr

References

D. Marquardt (1963). An algorithm for least-squares estimation of nonlinear parameters. SIAM Journal of Applied Mathematics, 431-441.

See Also

shr, print.shr, summary.shr, print.shr,

Examples


# Weibull survival model
library(prodlim)
data(testdata)
fit.su <- shr(Hist(time=list(l,r),id)~cov,data=testdata) 
fit.su
summary(fit.su)

shr.spline <- shr(Hist(time=list(l,r),id)~cov,data=testdata,method="splines",n.knots=6)
shr.spline
shr.spline.q <- shr(Hist(time=list(l,r),id)~cov,data=testdata,
                    method="splines",n.knots=6,knots="quantiles")
plot(shr.spline.q)

## manual placement of knots
shr.spline.man <- shr(Hist(time=list(l,r),id)~cov,data=testdata,method="splines",knots=seq(0,7,1))

Simulate illness-death model data

Description

Function to simulate illness-death model data

Usage

## S3 method for class 'idmModel'
sim(
  x,
  n,
  illness.known.at.death = TRUE,
  compliance = 1,
  latent = FALSE,
  keep.inspectiontimes = FALSE,
  ...
)

Arguments

x

An idmModel object as obtained with idmModel

n

Number of observations

illness.known.at.death

Affects the value of variable seen.ill

compliance

Probability of missing an inspection time.

latent

if TRUE keep the latent event times

keep.inspectiontimes

if TRUE keep the inspection times.

...

Extra arguments given to sim

Details

Based on the functionality of the lava PACKAGE

Value

A data set with interval censored observations from an illness-death model

Author(s)

Thomas Alexander Gerds

Examples

example(idmModel)
help(idmModel)

Simulate interval censored survival data

Description

Function to simulate interval censored survival data

Usage

## S3 method for class 'survIC'
sim(x, n, compliance = 1, latent = TRUE, keep.inspectiontimes = FALSE, ...)

Arguments

x

An survIC object as obtained with survIC

n

Number of observations

compliance

Probability of missing an inspection time.

latent

if TRUE keep the latent event times

keep.inspectiontimes

if TRUE keep the inspection times.

...

Extra arguments given to sim

Details

Based on the functionality of the lava PACKAGE

Value

A data set with interval censored observations

Author(s)

Thomas Alexander Gerds

Examples

library(lava)
example(survIC)
help(survIC)
ol <- survIC()
dat.ol <- sim(ol,10)

Sample illness-death model data

Description

Simulate data from an illness-death model with interval censored event times and covariates

Usage

simulateIDM(n = 100)

Arguments

n

number of observations

Details

Simulate data from an illness-death model with interval censored event times and covariates for the purpose of illustrating the help pages of the SmoothHazard package. See the body of the function for details, i.e., evaluate simulateIDM

Value

Object with class data.frame which contains the simulated data.

See Also

idmModel sim.idmModel

Examples

# simulateIDM
simulateIDM(100)

Summary of a fitted illness-death model

Description

Summarize the event history data of an illness-death regression model and show regression coefficients for transition intensities

Usage

## S3 method for class 'idm'
summary(object, conf.int = 0.95, digits = 4, pvalDigits = 4, eps = 0.0001, ...)

Arguments

object

a idmSplines object, i.e., the result of a call to the idm function with intensities="Splines".

conf.int

The level of confidence for the hazard ratios. The default is 0.95.

digits

number of digits to print.

pvalDigits

number of digits to print for p-values.

eps

convergence criterion used for p-values.

...

other unusued arguments.

Value

No return value.

Author(s)

R: Celia Touraine <Celia.Touraine@isped.u-bordeaux2.fr> Fortran: Pierre Joly <Pierre.Joly@isped.u-bordeaux2.fr>

See Also

idm, print.idm, plot.idm

Examples



library(prodlim)
data(Paq1000)
fit.splines <-  idm(formula02=Hist(time=t,event=death,entry=e)~certif,
		formula01=Hist(time=list(l,r),event=dementia)~certif,
                formula12=~1,
                method="Splines",
		data=Paq1000)
summary(fit.splines)

Summary of a fitted survival model using a penalized likelihood approach

Description

Print a short summary of a fitted illness-death model using the penalized likelihood approach.

Usage

## S3 method for class 'shr'
summary(object, conf.int = 0.95, digits = 4, pvalDigits = 4, eps = 0.0001, ...)

Arguments

object

a shr object, i.e., the result of a call to the shr function.

conf.int

The level of confidence for the hazard ratios. The default is 0.95.

digits

number of digits to print.

pvalDigits

number of digits to print for p-values.

eps

convergence criterion used for p-values.

...

other unusued arguments.

Value

No return value.

Author(s)

Celia Touraine <Celia.Touraine@isped.u-bordeaux2.fr>

See Also

shr, print.shr, plot.shr

Examples



# a penalized survival model 
data(testdata)
library(prodlim)
fit.su <- shr(Hist(time=list(l,r),id)~cov,data=testdata,method="Splines") 
summary(fit.su)

# Weibull survival model 
data(testdata)
fit.su <- shr(Hist(time=list(l,r),id)~cov,data=testdata) 
summary(fit.su)

Generate survival model objects

Description

Function to generate a latent variable model for interval censored survival times.

Usage

survIC(
  scale.time = 1/100,
  shape.time = 1,
  n.inspections = 5,
  schedule = 10,
  punctuality = 5
)

Arguments

scale.time

Weilbull scale for latent time

shape.time

Weilbull shape for latent 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 with a latent time and a censoring mechanism (censtime, inspection1,inspection2,...,inspectionK).

The function sim.survIC then simulates interval censored times.

Value

A latent variable model object lvm

Author(s)

Thomas Alexander Gerds

Examples


library(lava)
library(prodlim)
# generate survival model based on exponentially
# distributed times
m <- survIC(scale.time=1/50, shape.time=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 <- shr(Hist(time=list(L,R),event=uncensored.status)~1,
         data=d,
         conf.int=FALSE)
print(f)

Data set for survival models: right-censored and interval-censored data.

Description

A simulated data frame for survival models composed of right-censored and interval-censored data.

Format

A data frame with 936 observations on the following 4 variables.

l

for diseased subjects: left endpoint of censoring interval; for non-diseased subjects: right censoring time

r

for diseased subjects: right endpoint of censoring interval; for non-diseased subjects: right censoring time for the disease event

id

disease status

cov

covariate

Examples


data(testdata)
head(testdata)

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