Description Usage Arguments Details Value Author(s) References Examples
View source: R/markov.4states.rsadd.R
The 4state Markov relative survival model includes an initial state (X=1), a transient state (X=2), and two absorbing states including death (X=3, and X=4 for death). The possible transitions are: 1>2, 1>3, 1>4, 2>3 and 2>4. Assuming additive risks, the observed mortality hazard (X=4) is the sum of two components: the expected population mortality (X=P) and the excess mortality related to the disease under study (X=E). The expected population mortality hazard (X=P) can be obtained from the death rates provided by life tables of statistical national institutes. These tables indicate the proportion of people dead in a calendar year stratified by birthdate and gender.
1 2 3 4 5 6 7 8 9 10 11  markov.4states.rsadd(times1, times2, sequences, weights=NULL, dist,
cuts.12=NULL, cuts.13=NULL, cuts.14=NULL, cuts.23=NULL,
cuts.24=NULL, ini.dist.12=NULL, ini.dist.13=NULL,
ini.dist.14=NULL, ini.dist.23=NULL, ini.dist.24=NULL,
cov.12=NULL, init.cov.12=NULL, names.12=NULL,
cov.13=NULL, init.cov.13=NULL, names.13=NULL,
cov.14=NULL, init.cov.14=NULL, names.14=NULL,
cov.23=NULL, init.cov.23=NULL, names.23=NULL,
cov.24=NULL, init.cov.24=NULL, names.24=NULL,
p.age, p.sex, p.year, p.rate.table,
conf.int=TRUE, silent=TRUE, precision=10^(6))

times1 
A numeric vector with the observed times in days from baseline to the first transition (X=2, X=3 or X=4) or to the rightcensoring (in X=1 at the last followup). 
times2 
A numeric vector with the observed times in days from baseline to the second transition or to the right censoring (in X=2 at the last followup). 
sequences 
A numeric vector with the sequences of observed states. Six possible values are allowed: 1 (individual rightcensored in X=1), 12 (individual rightcensored in X=2), 13 (individual who directly transited from X=1 to X=3), 14 (individual who directly transited from X=1 to X=4), 123 (individual who transited from X=1 to X=3 through X=2), 124 (individual who transited from X=1 to X=4 through X=2). 
weights 
a numeric vector with the weights for correcting the contribution of each individual. Default is 
dist 
A character vector with three arguments describing respectively the distributions of duration time for transitions 1>2, 1>3 and 2>3. Arguments allowed are 
cuts.12 
A numeric vector indicating the timepoints in days for the piecewise exponential distribution related to the time from X=1 to X=2. Only internal timepoints are allowed: timepoints cannot be 
cuts.13 
A numeric vector indicating the timepoints in days for the piecewise exponential distribution related to the time from X=1 to X=3. Only internal timepoints are allowed: timepoints cannot be 
cuts.14 
A numeric vector indicating the timepoints in days for the piecewise exponential distribution related to the time from X=1 to X=4. Only internal timepoints are allowed: timepoints cannot be 
cuts.23 
A numeric vector indicating the timepoints in days for the piecewise exponential distribution related to the time from X=2 to X=3. Only internal timepoints are allowed: timepoints cannot be 
cuts.24 
A numeric vector indicating the timepoints in days for the piecewise exponential distribution related to the time from X=2 to X=4. Only internal timepoints are allowed: timepoints cannot be 
ini.dist.12 
A numeric vector of initial values for the distribution from X=1 to X=2. The logarithm of the parameters have to be declared. Default value is 1. 
ini.dist.13 
A numeric vector of initial values for the distribution from X=1 to X=3. The logarithm of the parameters have to be declared. Default value is 1. 
ini.dist.14 
A numeric vector of initial values for the distribution from X=1 to X=4. The logarithm of the parameters have to be declared. Default value is 1. 
ini.dist.23 
A numeric vector of initial values for the distribution from X=2 to X=3. The logarithm of the parameters have to be declared. Default value is 1. 
ini.dist.24 
A numeric vector of initial values for the distribution from X=2 to X=4. The logarithm of the parameters have to be declared. Default value is 1. 
cov.12 
A matrix (or data frame) with the explicative timefixed variable(s) related to the time from X=1 to X=2. 
init.cov.12 
A numeric vector of initial values for regression coefficients (logarithm of the causespecific hazards ratios) associated to 
names.12 
An optional character vector with name of explicative variables associated to 
cov.13 
A numeric matrix (or data frame) with the explicative timefixed variable(s) related to the time from X=1 to X=3. 
init.cov.13 
A numeric vector of initial values for regression coefficients (logarithm of the causespecific hazards ratios) associated to 
names.13 
An optional character vector with name of explicative variables associated to 
cov.14 
A numeric matrix (or data frame) with the explicative timefixed variable(s) related to the time from X=1 to X=4. 
init.cov.14 
A numeric vector of initial values for regression coefficients (logarithm of the causespecific hazards ratios) associated to 
names.14 
An optional character vector with name of explicative variables associated to 
cov.23 
A numeric matrix (or data frame) with the explicative timefixed variable(s) related to the time from X=2 to X=3. 
init.cov.23 
A numeric vector of initial values for regression coefficients (logarithm of the causespecific hazards ratios) associated to 
names.23 
An optional character vector with name of explicative variables associated to 
cov.24 
A numeric matrix (or data frame) with the explicative timefixed variable(s) related to the time from X=2 to X=4. 
init.cov.24 
A numeric vector of initial values for regression coefficients (logarithm of the causespecific hazards ratios) associated to 
names.24 
An optional character vector with name of explicative variables associated to 
p.age 
A numeric vector with the patient ages in days at baseline (X=1). 
p.sex 
A character vector with the genders: 
p.year 
A numeric vector with the entry dates in the study respecting the date format, i.e. in number of days since 01.01.1960. 
p.rate.table 
A list containing the information related to the expected rates of mortality. This list is organized as a 
conf.int 
A logical value specifying if the pointwise confidence intervals for parameters and the variancecovariance matrix should be returned. Default is 
silent 
A logical value specifying if the loglikelihood value should be returned at each iteration. Default is 
precision 
A numeric positive value indicating the required precision for the loglikelihood maximization between each iteration. Default is 10^{6}. 
Hazard functions available are:
Exponential distribution  λ(t)=1/σ 
Weibull distribution  λ(t)=ν(\frac{1}{σ})^{ν}t^{ν1} 
Generalized Weibull distribution  λ(t)=\frac{1}{θ}≤ft(1+≤ft(\frac{t}{σ}\right)^{ν}\right)^{\frac{1}{θ}1} ν≤ft(\frac{1}{σ}\right)^{ν} t^{ν1} 
with σ, ν,and θ>0. The parameter σ varies for each interval when the distribution is piecewise Exponential. We advise to initialize the logarithm of these parameters in ini.dist.12
, ini.dist.13
and ini.dist.23
.
To estimate the marginal effect of a binary exposure, the weights
may be equal to 1/p
, where p
is the estimated probability that the individual belongs to his or her own observed group of exposure. The probabilities p
are often estimated by a logistic regression in which the dependent binary variable is the exposure. The possible confounding factors are the explanatory variables of this logistic model.
object 
A character string indicating the estimated model: "markov.4states.rsadd (4state relative survival markov model with additive risks)". 
dist 
A character vector with two arguments describing respectively the distributions of duration time for transitions 1>2, 1>3, 1>4, 2>3, and 2>4. 
cuts.12 
A numeric vector indicating the timepoints in days for the piecewise exponential distribution related to the time from X=1 to X=2. 
cuts.13 
A numeric vector indicating the timepoints in days for the piecewise exponential distribution related to the time from X=1 to X=3. 
cuts.14 
A numeric vector indicating the timepoints in days for the piecewise exponential distribution related to the time from X=1 to X=4. 
cuts.23 
A numeric vector indicating the timepoints in days for the piecewise exponential distribution related to the time from X=2 to X=3. 
cuts.24 
A numeric vector indicating the timepoints in days for the piecewise exponential distribution related to the time from X=2 to X=4. 
covariates 
A numeric vector indicating the numbers of covariates respectively related to the transition 1>2, 1>3, 1>4, 2>3, and 2>4. 
table 
A data frame containing the estimated parameters of the model ( 
cov.matrix 
A data frame corresponding to variancecovariance matrix of the parameters. 
LogLik 
A numeric value corresponding to the loglikelihood of the estimated model. 
AIC 
A numeric value corresponding to the Akaike Information Criterion of the estimated model. 
Yohann Foucher <Yohann.Foucher@univnantes.fr>
Florence Gillaizeau <Florence.Gillaizeau@univnantes.fr>
Huszti et al. Relative survival multistate Markov model. Stat Med. 10;31(3):26986, 2012. <DOI: 10.1002/sim.4392>
Gillaizeau et al. A multistate additive relative survival semiMarkov model. Stat Methods Med Res. 26(4):17001711, 2017. <doi: 10.1177/ 0962280215586456>.
Gillaizeau et al. Inverse Probability Weighting to control confounding in an illnessdeath model for intervalcensored data. Stat Med. 37(8):12451258, 2018. <doi: 10.1002/sim.7550>.
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  # import the observed data
# (X=1 corresponds to initial state with a functioning graft, X=2 to acute rejection episode,
# X=3 to return to dialysis, X=4 to death with a functioning graft)
data(dataDIVAT1)
# A subgroup analysis to reduce the time needed for this example
dataDIVAT1$id<c(1:nrow(dataDIVAT1))
set.seed(2)
d3<dataDIVAT1[dataDIVAT1$id %in% sample(dataDIVAT1$id, 200, replace = FALSE),]
# import the expected mortality rates
data(fr.ratetable)
# 4state parametric additive relative survival Markov model including one
# explicative variable ('z') on the transition 1>2. We only reduced
# the precision and the number of iteration to save time in this example,
# prefer the default values.
markov.4states.rsadd(times1=d3$time1, times2=d3$time2, sequences=d3$trajectory,
dist=c("E","E","E","E","E"),
ini.dist.12=c(8.34), ini.dist.13=c(10.44), ini.dist.14=c(10.70),
ini.dist.23=c(9.43), ini.dist.24=c(11.11),
cov.12=d3$z, init.cov.12=c(0.04), names.12=c("beta12_z"),
p.age=d3$ageR*365.24, p.sex=d3$sexR,
p.year=as.date(paste("01","01",d3$year.tx), order = "mdy"),
p.rate.table=fr.ratetable, conf.int=TRUE,
silent=FALSE, precision=0.001)

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