qrjm function

qrjm fits quantile regression joint model

Function using 'JAGS' software via jagsUI package to estimate the quantile regression joint model assuming asymmetric Laplace distribution for residual error. Joint modeling concerns longitudinal data and time-to-event

qrjm(
  formFixed,
  formRandom,
  formGroup,
  formSurv,
  survMod = "weibull",
  param = "value",
  timeVar,
  data,
  tau,
  RE_ind = FALSE,
  n.chains = 3,
  n.iter = 10000,
  n.burnin = 5000,
  n.thin = 1,
  n.adapt = 5000,
  precision = 10,
  C = 1000,
  save_jagsUI = TRUE,
  save_va = FALSE,
  parallel = FALSE
)

Arguments

• formFixed: formula for fixed part of longitudinal submodel with response variable
• formRandom: formula for random part of longitudinal submodel without response variable
• formGroup: formula specifying the cluster variable (e.g. = ~ subject)
• formSurv: survival formula as formula in survival package for latency submodel
• survMod: specifying the baseline risk function for Cox proportional hazard model (only "weibull" is available until now)
• param: shared association including in joint modeling: the classical shared random effects or the current value denoting by "sharedRE" (default) or "value", respectively.
• timeVar: string specify the names of time variable (time of repeated measurements)
• data: dataset of observed variables
• tau: the quantile(s) to be estimated. This must be a number between 0 and 1, otherwise the execution is stopped. If more than one quantile is specified, rounding off to the 4th decimal must give non–duplicated values of tau, otherwise the execution is stopped.
• RE_ind: Boolean denoting if the random effects are assumed independent ; default is FALSE
• n.chains: the number of parallel chains for the model; default is 1.
• n.iter: integer specifying the total number of iterations; default is 10000
• n.burnin: integer specifying how many of n.iter to discard as burn-in ; default is 5000
• n.thin: integer specifying the thinning of the chains; default is 1
• n.adapt: integer specifying the number of iterations to use for adaptation; default is 5000
• precision: variance by default for vague prior distribution
• C: value used in the zero trick; default is 1000.
• save_jagsUI: If TRUE (by default), the output of jagsUI package is returned by the function
• save_va: If TRUE (is FALSE by default), the draws of auxiliary variable W is returned by the function
• parallel: see jagsUI::jags() function

Returns

A Bqrjm object is a list with the following elements:

• mean: list of posterior mean for each parameter
• median: list of posterior median for each parameter
• modes: list of posterior mode for each parameter
• StErr: list of standard error for each parameter
• StDev: list of standard deviation for each parameter
• ICs: list of the credibility interval at 0.95 for each parameters excepted for covariance parameters in covariance matrix of random effects. Otherwise, use save_jagsUI=TRUE to have the associated quantiles.
• data: data included in argument
• sims.list: list of the MCMC chains of the parameters and random effects
• control: list of arguments giving details about the estimation
• random_effect: list for each quantile including both posterior mean and posterior standard deviation of subject-specific random effects
• out_jagsUI: only if save_jagsUI=TRUE in argument: list including posterior mean, median, quantiles (2.5%, 25%, 50%, 75%, 97.5%), standart deviation for each parameter and each random effect. Moreover, this list also returns the MCMC draws, the Gelman and Rubin diagnostics (see output of jagsUI objects)

Examples

#---- load data
data(dataLong)

#---- Fit quantile regression joint model for the first quartile
qrjm_75 <- qrjm(formFixed = y ~ visit,
               formRandom = ~ visit,
               formGroup = ~ ID,
               formSurv = Surv(time, event) ~ X1 + X2,
               survMod = "weibull",
               param = "value",
               timeVar= "visit",
               data = dataLong,
               tau = 0.75)

#---- Visualize the trace for beta parameters
jagsUI::traceplot(qrjm_75$out_jagsUI, parameters = "beta")

#---- Get the estimated coefficients: posterior means
qrjm_75$mean

#---- Summary of output
summary(qrjm_75)

References

Ming Yang, Sheng Luo, and Stacia DeSantis (2019). Bayesian quantile regression joint models: Inference and dynamic predictions. Statistical Methods in Medical Research, 28(8):2524-2537. doi: 10.1177/0962280218784757.

Author(s)

Antoine Barbieri