Restricted Spatial Frailty Model

Fit a Restricted Spatial Frailty model

rsfm(data, formula, family, area = NULL,
            model = NULL, neigh = NULL,
            proj = "none", nsamp = 1000,
            fast = TRUE, approach = "inla", priors,
            ...)

Arguments

data

a data frame or list containing the variables in the model.
formula

an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted.
family

"exponential", "weibull", "weibullcure", "loglogistic", "gamma", "lognormal" or "pwe".
area

areal variable name in data.
model

spatial model adopted. Examples: "besag", "besag2" or "r_besag". See INLA::inla.list.models() for other models.
neigh

neighborhood structure. A SpatialPolygonsDataFrame or sf object
proj

"none" or "rhz".
nsamp

number of samples. Default = 1000.
fast

TRUE to use the reduction operator.
approach

"inla" or "mcmc". "mcmc" has less model options.
priors

a list containing:

  • prior_prec: a vector of size two, representing shape and scale for the gamma distribution applied for model precision
...

other parameters used in ?INLA::inla or ?R2OpenBUGS::bugs

Value

$unrestricted

A list containing

  • $sample: a sample of size nsamp for all parameters in the model

  • $summary_fixed: summary measures for the coefficients

  • $summary_hyperpar: summary measures for hyperparameters

  • $summary_random: summary measures for random quantities

$restricted

A list containing

  • $sample: a sample of size nsamp for all parameters in the model

  • $summary_fixed: summary measures for the coefficients

  • $summary_hyperpar: summary measures for hyperparameters

  • $summary_random: summary measures for random quantities

$out

INLA or BUGS output

$time

time elapsed for fitting the model

Examples

set.seed(123456)

##-- Spatial structure
data("neigh_RJ")

##-- Individuals and regions
n_reg <- length(neigh_RJ)
n_id <- sample(x = 3:5, size = n_reg, replace = TRUE)
coefs <- c(0.1, -0.3)
tau <- 1 # Scale of spatial effect

##-- Data
data <- rsurv(n_id = n_id,
              coefs = coefs, cens = 0.5, scale = FALSE,
              cens_type = "right", hazard = "weibull",
              hazard_params = list(weibull = list(alpha = 0.8, variant = 0)),
              spatial = "ICAR",
              neigh = neigh_RJ, tau = tau, confounding = "linear", proj = "none")

##-- Models
weibull_inla <- rsfm(data = data,
                     formula = surv(time = L, event = status) ~ X1 + X2,
                     family = "weibull", model = "none",
                     proj = "rhz", nsamp = 1000, approach = "inla")

rsfm_inla <- rsfm(data = data,
                  formula = surv(time = L, event = status) ~ X1 + X2,
                  family = "weibull", area = "reg",
                  model = "r_besag", neigh = neigh_RJ,
                  proj = "rhz", nsamp = 1000, approach = "inla")

weibull_inla$unrestricted$summary_fixed
#>                  mean    median      mode       sd     lower     upper
#> (Intercept) -0.522919 -0.522370 -0.519158 0.078081 -0.685750 -0.382050
#> X1           0.096648  0.097850  0.095730 0.074469 -0.040455  0.247275
#> X2          -0.067236 -0.065394 -0.067907 0.075124 -0.197489  0.087755
rsfm_inla$unrestricted$summary_fixed
#>                  mean    median      mode       sd     lower     upper
#> (Intercept) -0.414717 -0.412980 -0.412209 0.081163 -0.573901 -0.260027
#> X1           0.099152  0.097447  0.102316 0.081560 -0.057273  0.246594
#> X2          -0.028440 -0.023735 -0.048134 0.311641 -0.610567  0.617034
rsfm_inla$restricted$summary_fixed
#>                  mean    median      mode       sd     lower     upper
#> (Intercept) -0.405960 -0.405639 -0.401211 0.079557 -0.568732 -0.259484
#> X1           0.139742  0.140272  0.141981 0.078376 -0.024353  0.270532
#> X2          -0.108584 -0.107503 -0.107639 0.077109 -0.247772  0.058602