Description Usage Arguments Details Value Author(s) References Examples
The 2-state mixture model which includes an initial state (X=1) and two absorbing states in competition (X=2 and X=3). Parameters are estimated by (weighted) Likelihood maximization.
1 2 3 4 5 | mm2(t, sequence, weights=NULL, dist, cuts.12=NULL, cuts.13=NULL,
ini.dist.12=NULL, ini.dist.13=NULL, cov.12=NULL, init.cov.12=NULL,
names.12=NULL, cov.13=NULL, init.cov.13=NULL, names.13=NULL,
cov.p=NULL, init.cov.p=NULL, names.p=NULL, init.intercept.p=NULL,
conf.int=TRUE, silent=TRUE, precision=10^(-6))
|
t |
A numeric vector with the observed times in days from baseline to the last observation. |
sequence |
A numeric vector with the sequence of observed states. Three possible values are allowed: 1 (the individual is right-censored in X=1), 12 (the individual transits to X=2) and 13 (the individual transits to X=3). |
weights |
A numeric vector with the weights for correcting the contribution of each individual. When the vector is completed, the IPW estimator is implemented. Default is |
dist |
A character vector with two arguments describing respectively the distributions of duration time for transitions 1->2 and 1->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 |
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. |
cov.12 |
A matrix (or data frame) with the explicative time-fixed 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 cause-specific 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 time-fixed 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 cause-specific hazards ratios) associated to |
names.13 |
An optional character vector with name of explicative variables associated to |
cov.p |
A matrix (or data frame) with the explicative time-fixed variable(s) related to the probability P(X=2), which is regressing according to a logistic function. |
init.cov.p |
A numeric vector of initial values for regression coefficients (logarithm of the cause-specific hazards ratios) associated to |
names.p |
An optional character vector with name of explicative variables associated to |
init.intercept.p |
A numeric value to iniate the intercept of the logit of P(X=2). Default value is 0. |
conf.int |
A logical value specifying if the pointwise confidence intervals for parameters and the variance-covariance matrix should be returned. Default is |
silent |
A logical value specifying if the log-likelihood value should be returned at each iteration. Default is |
precision |
A numeric positive value indicating the required precision for the log-likelihood 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^{ν-1} |
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^{ν-1} |
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 |
The character string indicating the estimated model: "mm2 (mixture model with two competing events)". |
dist |
A character vector with two arguments describing respectively the distributions of duration time for transitions 1->2 and 1->3. |
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. |
covariates |
A numeric vector indicating the numbers of covariates respectively related to the time to the event X=2, the time to the event X=3, the long-term probability P(X=2). |
table |
A data frame containing the estimated parameters of the model ( |
cov.matrix |
A data frame corresponding to variance-covariance matrix of the parameters. |
LogLik |
A numeric value corresponding to the (weighted) log-likelihood of the model. |
AIC |
A numeric value corresponding to the Akaike Information Criterion of the model. |
Yohann Foucher <Yohann.Foucher@univ-nantes.fr>
Trebern-Launay K, KesslerM, Bayat-Makoei S, Querard AH, Briancon S, Giral M, Foucher Y. Horizontal mixture model for competing risks: a method to obtain easily interpretable results by both physicians and patients-illustration for waitlisted renal transplant candidates in a perspective of patient-centered decision making. Manuscript submitted. 2017.
Austin PC. An Introduction to Propensity Score Methods for Reducing the Effects of Confounding in Observational Studies. Multivariate Behav Res May 2011; 46(3): 399-424. <DOI: 10.1080/ 00273171.2011.568786>
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 | # import the observed data
# X=1 corresponds to initial state with a functioning graft,
# X=2 to acute rejection episode (transient state),
# X=3 to return to dialysis, X=4 to death with a functioning graft
data(dataDIVAT)
dim(dataDIVAT)
# A subgroup analysis to reduce the time needed for this example
dataDIVAT$id<-c(1:nrow(dataDIVAT))
set.seed(2)
d2<-dataDIVAT[dataDIVAT$id %in% sample(dataDIVAT$id, 300, replace = FALSE),]
# Data-management: two competing events
# the patient death is now X=2
# the return in dialysis is now X=3
d2$time<-NA
d2$time[d2$trajectory==1]<-d2$time1[d2$trajectory==1]
d2$time[d2$trajectory==12]<-d2$time2[d2$trajectory==12]
d2$trajectory[d2$trajectory==12]<-1
d2$time[d2$trajectory==13]<-d2$time1[d2$trajectory==13]
d2$time[d2$trajectory==123]<-d2$time2[d2$trajectory==123]
d2$trajectory[d2$trajectory==123]<-13
d2$time[d2$trajectory==14]<-d2$time1[d2$trajectory==14]
d2$time[d2$trajectory==124]<-d2$time2[d2$trajectory==124]
d2$trajectory[d2$trajectory==124]<-14
d2$trajectory[d2$trajectory==14]<-12
table(d2$trajectory)
# Univariable horizontal mixture model one binary explicative variable
# z is 1 if delayed graft function and 0 otherwise
mm2.test <- mm2(t=d2$time, sequence=d2$trajectory, weights=NULL,
dist=c("E","W"), cuts.12=NULL, cuts.13=NULL,
ini.dist.12=c(9.28), ini.dist.13=c(9.92, -0.23),
cov.12=d2$z, init.cov.12=0.84, names.12="beta_12",
cov.13=d2$z, init.cov.13=0.76, names.13="beta_13",
cov.p=NULL, init.cov.p=NULL, names.p=NULL, init.intercept.p=-0.75,
conf.int=TRUE, silent=FALSE)
mm2.test$table
|
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.