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The goal of FlexVarJM is to estimate joint model with subject-specific time-dependent variability.
The global function is ‘lsjm’. It handles to estimate joint model with a marker which has a subject-specific time-dependent variability and competing events with the possibility to take into account the left truncation. For more information you can read the corresponding article : https://arxiv.org/abs/2306.16785
You can install the development version of FlexVarJM from GitHub with:
This is an example in a simulated dataset where is a binary variable.
\[y_i(t_{ij}) = \color{blue}\tilde{y}_i(t_{ij}) \color{black} + \epsilon_{ij} = \beta_0 + b_{0i} + (\beta_1 + b_{1i})t_{ij} + \beta_2 * binary_i + \epsilon_{ij} \]
For the first risk, k = 1, we estimate the following risk function :
\[ \lambda_{i1}(t) = \lambda_{01}(t)\exp(\gamma_{11}*binary_i + \color{blue}\alpha_{11}\tilde{y}_i(t) + \color{red}\alpha_{\sigma 1} \sigma_i(t) \color{black}) \] And for the second risk, k = 2 : \[ \lambda_{i2}(t) = \lambda_{02}(t)\exp(\color{blue}\alpha_{21}\tilde{y_i}(t) + \color{blue}\alpha_{22}\tilde{y}'_i(t) + \color{red}\alpha_{\sigma 2} \sigma_i(t) \color{black}) \]
where :
\(\epsilon_{i}(t_{ij}) \sim \mathcal{N}(0, \color{red}\sigma_i^2\color{black})\) with \(\color{red}\log(\sigma_i(t_{ij})) = \mu_0 + \tau_{0i} + (\mu_1 + \tau_{1i})\times t_{ij} + \mu_2 * binary_i\)
with \(b_i=\left(b_{0i},b_{1i}\right)^{\top}\) and \(\tau_i=\left(\tau_{0i},\tau_{1i}\right)^{\top}\) assuming that the two sets of random effects \(b_i\) and \(\tau_i\) are not independent: \[(b_i, \tau_i)^\top \sim N(0, \Sigma)\]
\(\lambda_{0k}(t) = \kappa_k^2 t^{\kappa_k^2-1}e^{\zeta_{0k}}\) : Weibull function
\(\tilde{y}'_i(t)\) is the current slope of the marker \(y\)
example <- lsjm(formFixed = y~visit+binary,
formRandom = ~ visit,
formGroup = ~ID,
formSurv = Surv(time, event ==1 ) ~ binary,
timeVar = "visit",
data.long = Data_toy,
variability_hetero = TRUE,
formFixedVar =~visit+binary,
formRandomVar =~visit,
correlated_re = TRUE,
sharedtype = c("current value", "variability"),
hazard_baseline = "Weibull",
competing_risk = TRUE,
formSurv_CR = Surv(time, event ==2 ) ~ 1,
hazard_baseline_CR = "Weibull",
sharedtype_CR = c("slope", "variability"),
formSlopeFixed =~1,
formSlopeRandom = ~1,
indices_beta_slope = c(2),
S1 = 500,
S2 = 1000,
nproc = 5,
Comp.Rcpp = TRUE
)
summary(example)You can access to the table of estimations and standard deviation with :
The computing time is given by :
The output of the marqLevAlg algorithm is in :
Finally, some elements of control are in :
You can check the goodness-of-fit of the longitudinal submodel and of the survival submodel by computing the predicted random effects :
You can compute the probability for (new) individual(s) to have event 1 or 2 between time s and time s+t years given that he did not experience any event before time s, its trajectory of marker until time s ans the set of estimated parameters. To have a ‘IC%’ confidence interval, the predictions are computed ‘nb.draws’ time and the percentiles of the predictions are computed. For example, for individuals 1 and 3 to experiment the event 1 at time 1.5, 2, and 3, given their measurements until time 1 :
newdata <- Data_toy[which(Data_toy$ID %in% c(1,3)),]
predyn(newdata,example,1, c(1.5,2,3), event = 1, IC = 95, nb.draws = 500, graph = TRUE)These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.