pope: Fit Proportional Odds Regression Model with Piecewise Exponential baseline distribution.

Usage

pope(
  formula,
  data,
  n_int = NULL,
  rho = NULL,
  tau = NULL,
  hessian = TRUE,
  approach = c("mle", "bayes"),
  hyper_parms = list(h1_gamma = 0, h2_gamma = 4, mu_beta = 0, sigma_beta = 4),
  ...
)

Arguments

formula: an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted.
data: an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which pope is called.
n_int: number of intervals of the PE distribution. If NULL, default value (square root of n) is used.
rho: the time grid of the PE distribution. If NULL, the function timeGrid is used to compute rho.
tau: the maximum time of follow-up. If NULL, tau = max(time), where time is the vector of observed survival times.
hessian: logical; If TRUE (default), the hessian matrix is returned when approach="mle".
approach: approach to be used to fit the model (mle: maximum likelihood; bayes: Bayesian approach).
hyper_parms: a list containing the hyper-parameters of the prior distributions (when approach = "bayes"). If not specified, default values are used.
...: Arguments passed to either `rstan::optimizing` or `rstan::sampling` .

Value

pope returns an object of class "pope" containing the fitted model.

Examples

# \donttest{
# ML approach:
library(YPPE)
mle <- pope(Surv(time, status)~arm, data=ipass, n_int=10, approach="mle")
summary(mle)
#> Call:
#> pope(formula = Surv(time, status) ~ arm, data = ipass, n_int = 10, 
#>     approach = "mle")
#> 
#> Proportional odds coefficients:
#>      Estimate    StdErr z.value p.value
#> arm -0.051702  0.103114 -0.5014  0.6161
#> 
#> --- 
#> loglik = -2821.851   AIC = 5665.702 

# Bayesian approach:
bayes <- pope(Surv(time, status)~arm, data=ipass, n_int=10, approach="bayes")
#> 
#> SAMPLING FOR MODEL 'yppe' NOW (CHAIN 1).
#> Chain 1: 
#> Chain 1: Gradient evaluation took 0.000534 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 5.34 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1: 
#> Chain 1: 
#> Chain 1: Iteration:    1 / 2000 [  0%]  (Warmup)
#> Chain 1: Iteration:  200 / 2000 [ 10%]  (Warmup)
#> Chain 1: Iteration:  400 / 2000 [ 20%]  (Warmup)
#> Chain 1: Iteration:  600 / 2000 [ 30%]  (Warmup)
#> Chain 1: Iteration:  800 / 2000 [ 40%]  (Warmup)
#> Chain 1: Iteration: 1000 / 2000 [ 50%]  (Warmup)
#> Chain 1: Iteration: 1001 / 2000 [ 50%]  (Sampling)
#> Chain 1: Iteration: 1200 / 2000 [ 60%]  (Sampling)
#> Chain 1: Iteration: 1400 / 2000 [ 70%]  (Sampling)
#> Chain 1: Iteration: 1600 / 2000 [ 80%]  (Sampling)
#> Chain 1: Iteration: 1800 / 2000 [ 90%]  (Sampling)
#> Chain 1: Iteration: 2000 / 2000 [100%]  (Sampling)
#> Chain 1: 
#> Chain 1:  Elapsed Time: 3.691 seconds (Warm-up)
#> Chain 1:                3.589 seconds (Sampling)
#> Chain 1:                7.28 seconds (Total)
#> Chain 1: 
#> 
#> SAMPLING FOR MODEL 'yppe' NOW (CHAIN 2).
#> Chain 2: 
#> Chain 2: Gradient evaluation took 0.000483 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 4.83 seconds.
#> Chain 2: Adjust your expectations accordingly!
#> Chain 2: 
#> Chain 2: 
#> Chain 2: Iteration:    1 / 2000 [  0%]  (Warmup)
#> Chain 2: Iteration:  200 / 2000 [ 10%]  (Warmup)
#> Chain 2: Iteration:  400 / 2000 [ 20%]  (Warmup)
#> Chain 2: Iteration:  600 / 2000 [ 30%]  (Warmup)
#> Chain 2: Iteration:  800 / 2000 [ 40%]  (Warmup)
#> Chain 2: Iteration: 1000 / 2000 [ 50%]  (Warmup)
#> Chain 2: Iteration: 1001 / 2000 [ 50%]  (Sampling)
#> Chain 2: Iteration: 1200 / 2000 [ 60%]  (Sampling)
#> Chain 2: Iteration: 1400 / 2000 [ 70%]  (Sampling)
#> Chain 2: Iteration: 1600 / 2000 [ 80%]  (Sampling)
#> Chain 2: Iteration: 1800 / 2000 [ 90%]  (Sampling)
#> Chain 2: Iteration: 2000 / 2000 [100%]  (Sampling)
#> Chain 2: 
#> Chain 2:  Elapsed Time: 3.723 seconds (Warm-up)
#> Chain 2:                3.62 seconds (Sampling)
#> Chain 2:                7.343 seconds (Total)
#> Chain 2: 
#> 
#> SAMPLING FOR MODEL 'yppe' NOW (CHAIN 3).
#> Chain 3: 
#> Chain 3: Gradient evaluation took 0.000444 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 4.44 seconds.
#> Chain 3: Adjust your expectations accordingly!
#> Chain 3: 
#> Chain 3: 
#> Chain 3: Iteration:    1 / 2000 [  0%]  (Warmup)
#> Chain 3: Iteration:  200 / 2000 [ 10%]  (Warmup)
#> Chain 3: Iteration:  400 / 2000 [ 20%]  (Warmup)
#> Chain 3: Iteration:  600 / 2000 [ 30%]  (Warmup)
#> Chain 3: Iteration:  800 / 2000 [ 40%]  (Warmup)
#> Chain 3: Iteration: 1000 / 2000 [ 50%]  (Warmup)
#> Chain 3: Iteration: 1001 / 2000 [ 50%]  (Sampling)
#> Chain 3: Iteration: 1200 / 2000 [ 60%]  (Sampling)
#> Chain 3: Iteration: 1400 / 2000 [ 70%]  (Sampling)
#> Chain 3: Iteration: 1600 / 2000 [ 80%]  (Sampling)
#> Chain 3: Iteration: 1800 / 2000 [ 90%]  (Sampling)
#> Chain 3: Iteration: 2000 / 2000 [100%]  (Sampling)
#> Chain 3: 
#> Chain 3:  Elapsed Time: 3.77 seconds (Warm-up)
#> Chain 3:                3.495 seconds (Sampling)
#> Chain 3:                7.265 seconds (Total)
#> Chain 3: 
#> 
#> SAMPLING FOR MODEL 'yppe' NOW (CHAIN 4).
#> Chain 4: 
#> Chain 4: Gradient evaluation took 0.000482 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 4.82 seconds.
#> Chain 4: Adjust your expectations accordingly!
#> Chain 4: 
#> Chain 4: 
#> Chain 4: Iteration:    1 / 2000 [  0%]  (Warmup)
#> Chain 4: Iteration:  200 / 2000 [ 10%]  (Warmup)
#> Chain 4: Iteration:  400 / 2000 [ 20%]  (Warmup)
#> Chain 4: Iteration:  600 / 2000 [ 30%]  (Warmup)
#> Chain 4: Iteration:  800 / 2000 [ 40%]  (Warmup)
#> Chain 4: Iteration: 1000 / 2000 [ 50%]  (Warmup)
#> Chain 4: Iteration: 1001 / 2000 [ 50%]  (Sampling)
#> Chain 4: Iteration: 1200 / 2000 [ 60%]  (Sampling)
#> Chain 4: Iteration: 1400 / 2000 [ 70%]  (Sampling)
#> Chain 4: Iteration: 1600 / 2000 [ 80%]  (Sampling)
#> Chain 4: Iteration: 1800 / 2000 [ 90%]  (Sampling)
#> Chain 4: Iteration: 2000 / 2000 [100%]  (Sampling)
#> Chain 4: 
#> Chain 4:  Elapsed Time: 3.792 seconds (Warm-up)
#> Chain 4:                3.607 seconds (Sampling)
#> Chain 4:                7.399 seconds (Total)
#> Chain 4: 
summary(bayes)
#> Call:
#> pope(formula = Surv(time, status) ~ arm, data = ipass, n_int = 10, 
#>     approach = "bayes")
#> 
#> Proportional hazards coefficients:
#>       mean se_mean    sd   2.5%   25%    50%   75% 97.5%    n_eff Rhat
#> arm -0.049   0.002 0.107 -0.257 -0.12 -0.049 0.023  0.16 4362.482    1
#> --- 
#> Inference for Stan model: yppe.
#> 4 chains, each with iter=2000; warmup=1000; thin=1; 
#> post-warmup draws per chain=1000, total post-warmup draws=4000.
#> 
# }