BeQut: Bayesian Estimation for Quantile Regression Mixed Models

Description

Using a Bayesian estimation procedure, this package fits linear quantile regression models such as linear quantile models, linear quantile mixed models, quantile regression joint models for time-to-event and longitudinal data. The estimation procedure is based on the asymmetric Laplace distribution and the 'JAGS' software is used to get posterior sample (Yang, Luo, DeSantis (2019) doi:10.1177/0962280218784757).

Author(s)

Maintainer: Antoine Barbieri antoine.barbieri@u-bordeaux.fr

Authors:

• Hélène Jacqmin-Gadda helene.jacqmin-gadda@u-bordeaux.fr

dataLong

Description

'dataLong' is a dataset simulated from a joint model for longitudinal and time-to-event data. This dataset is used to illustrate both 'lqmm' and 'qrjm' functions.

Usage

data(dataLong)

Format

A data.frame with 1562 observations from 300 subjects. The columns are:

ID

integer: number for patient identification.

visit

numeric: measurement times for the repeated blood pressure measurements.

y

numeric: longitudinal measurements.

time

numeric: time to event (or censoring).

event

integer: event indicator. Coded as 0 = right-censoring, and 1 = event.

X1

integer: time-independent binary explanatory variable.

X2

numeric: time-independent continuous explanatory variable.

Examples

data(dataLong)

deviance returns the deviance based on the conditional likelihood associated with the survival part.

Description

deviance returns the deviance based on the conditional likelihood associated with the survival part.

Usage

deviance(object, M = 1000, conditional = "survival", verbose = TRUE)

Arguments

Value

An object which is a list with the following elements:

deviance

Numerical object returning the deviance

likelihood

(Conditional) likelihood

sims.list

list of individual quantities as likelihood, draws of random effects, hazard and survival functions

control

list of arguments giving details about the deviance

Author(s)

Antoine Barbieri and Baptiste Courrèges

Examples

#---- load data
data(dataLong)

#---- Fit quantile regression joint model for the median
qrjm_50 <- qrjm(formFixed = y ~ visit,
               formRandom = ~ visit,
               formGroup = ~ ID,
               formSurv = survival::Surv(time, event) ~ X1 + X2,
               survMod = "weibull",
               param = "value",
               timeVar= "visit",
               data = dataLong,
               save_va = TRUE,
               parallel = FALSE,
               tau = 0.5)

deviance(qrjm_50, M=200)

lqm fits linear quantile regression model

Description

Function using 'JAGS' software to estimate the linear quantile regression model assuming asymmetric Laplace distribution for residual error.

Usage

lqm(
  formula,
  data,
  tau = 0.5,
  n.chains = 3,
  n.iter = 10000,
  n.burnin = 5000,
  n.thin = 1,
  n.adapt = NULL,
  save_jagsUI = TRUE,
  parallel = FALSE
)

Arguments

Value

A Blqm object which 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

Rhat

Gelman and Rubin diagnostic for all parameters

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

W

list including both posterior mean and posterior standard deviation of subject-specific random variable W

out_jagsUI

only if save_jagsUI=TRUE in argument: list including posterior mean, median, quantiles (2.5%, 25%, 50%, 75%, 97.5%), standard 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)

Author(s)

Antoine Barbieri

Examples

#---- Use data
data(wave)

#---- Fit regression model for the first quartile
lqm_025 <- lqm(formula = h110d~vent_vit_moy,
               data = wave,
               n.iter = 1000,
               n.burnin = 500,
               tau = 0.25)

#---- Get the posterior mean of parameters
lqm_025$mean

#---- Visualize the trace for beta parameters
jagsUI::traceplot(lqm_025$out_jagsUI, parameters = "beta" )

#---- Summary of output
summary(lqm_025)

lqmm fits linear quantile mixed model

Description

Function using 'JAGS' software to estimate the linear quantile mixed model assuming asymmetric Laplace distribution for residual error.

Usage

lqmm(
  formFixed,
  formRandom,
  formGroup,
  data,
  tau,
  RE_ind = FALSE,
  n.chains = 3,
  n.iter = 10000,
  n.burnin = 5000,
  n.thin = 1,
  n.adapt = NULL,
  precision = 10,
  save_jagsUI = TRUE,
  parallel = FALSE
)

Arguments

Value

A Blqmm 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)

Author(s)

Antoine Barbieri

References

Marco Geraci and Matteo Bottai (2014). Linear quantile mixed models. Statistics and Computing, 24(3):461-479. doi: 10.1007/s11222-013-9381-9.

Examples

#---- Use dataLong dataset
data(dataLong)

#---- Fit regression model for the first quartile
lqmm_075 <- lqmm(formFixed = y ~ visit,
                 formRandom = ~ visit,
                 formGroup = ~ ID,
                 data = dataLong,
                 tau = 0.75,
                 n.iter = 10000,
                 n.burnin = 1000)

#---- Get the posterior means
lqmm_075$mean

#---- Visualize the trace for beta parameters
jagsUI::traceplot(lqmm_075$out_jagsUI, parameters = "beta")

#---- Summary of output
summary(lqmm_075)

qrjm fits quantile regression joint model

Description

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

Usage

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

Value

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)

Author(s)

Antoine Barbieri

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.

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)

Data of wave

Description

Data including environmental measurements around Bordeaux from CANDHIS database and data from InfoClimat website. CANDHIS national in situ wave measurement database. The measurements were carried out within the framework of a collaboration between the Grand Port Maritime de Nantes St-Nazaire, the École Centrale de Nantes and CEREMA. In addition, data from the InfoClimat site over the same period are used.

Usage

data(wave)

Format

A data.frame with 453 observations (rows) and 25 variables with explicit names. The first variables are:

date

date of measure

temperature

temperature

pression

pressure

humidite_relative

Humidity

point2rose

Dew point temperature

visibilite_horiz

visibility

vent_cite_moy

wind speed average

vent_vit_rafale

maximum of wind speed

precipitation_cum

cumulative rainfall by day

References

InfoClimat (https://www.infoclimat.fr/climatologie/stations_principales.php?)

Examples

data(wave)