student_confint {marp}

A function to calculate Studentized bootstrap confidence interval

Description

A function to calculate Studentized bootstrap confidence interval

Usage

student_confint(
  n,
  B,
  t,
  m,
  BB,
  par_hat,
  mu_hat,
  pr_hat,
  haz_hat,
  weights,
  alpha,
  y,
  best.model,
  which.model = 1
)

Arguments

n

number of inter-event times

B

number of bootstrap samples

t

user-specified time intervals (used to compute hazard rate)

m

the number of iterations in nlm

BB

number of double-bootstrap samples

par_hat

estimated parameters

mu_hat

estimated mean inter-event times

pr_hat

estimated time to event probability

haz_hat

estimated hazard rates

weights

model weights

alpha

significance level

y

user-specified time point (used to compute time-to-event probability)

best.model

best model based on information criterion (i.e. AIC)

which.model

user-specified generating (or true underlying if known) model

Value

returns list of Studentized bootstrap intervals (including the model-averaged approach).

mu_lower_gen

Lower limit of the studentized bootstrap confidence interval of the estimated mean based on the generating model

mu_upper_gen

Upper limit of the studentized bootstrap confidence interval of the estimated mean based on the generating model

mu_lower_best

Lower limit of the studentized bootstrap confidence interval of the estimated mean based on the best model

mu_upper_best

Upper limit of the studentized bootstrap confidence interval of the estimated mean based on the best model

pr_lower_gen

Lower limit of the studentized bootstrap confidence interval of the estimated probabilities based on the generating model

pr_upper_gen

Upper limit of the studentized bootstrap confidence interval of the estimated probabilities based on the generating model

pr_lower_best

Lower limit of the studentized bootstrap confidence interval of the estimated probabilities based on the best model

pr_upper_best

Upper limit of the studentized bootstrap confidence interval of the estimated probabilities based on the best model

haz_lower_gen

Lower limit of the studentized bootstrap confidence interval of the estimated hazard rates based on the generating model

haz_upper_gen

Upper limit of the studentized bootstrap confidence interval of the estimated hazard rates based on the generating model

haz_lower_best

Lower limit of the studentized bootstrap confidence interval of the estimated hazard rates based on the best model

haz_upper_best

Upper limit of the studentized bootstrap confidence interval of the estimated hazard rates based on the best model

mu_lower_ma

Lower limit of model-averaged studentized bootstrap confidence interval of the estimated mean

mu_upper_ma

Upper limit of model-averaged studentized bootstrap confidence interval of the estimated mean

pr_lower_ma

Lower limit of model-averaged studentized bootstrap confidence interval of the estimated probabilities

pr_upper_ma

Upper limit of model-averaged studentized bootstrap confidence interval of the estimated probabilities

haz_lower_ma

Lower limit of model-averaged studentized bootstrap confidence interval of the estimated hazard rates

haz_upper_ma

Upper limit of model-averaged studentized bootstrap confidence interval of the estimated hazard rates

Examples

# generate random data
set.seed(42)
data <- rgamma(30, 3, 0.01)

# set some parameters
n <- 30 # sample size
m <- 10 # number of iterations for MLE optimization
t <- seq(100,200,by=10) # time intervals
y <- 304 # cut-off year for estimating probablity
B <- 100 # number of bootstraps
BB <- 100 # number of double bootstraps
par_hat <- c(
  3.41361e-03, 2.76268e+00, 2.60370e+00, 3.30802e+02, 5.48822e+00, 2.92945e+02, NA,
  9.43071e-03, 2.47598e+02, 1.80102e+00, 6.50845e-01, 7.18247e-01)
mu_hat <- c(292.94512, 292.94513, 319.72017, 294.16945, 298.87286, 292.94512)
pr_hat <- c(0.60039, 0.42155, 0.53434, 0.30780, 0.56416, 0.61795)
haz_hat <-   matrix(c(
  -5.67999, -5.67999, -5.67999, -5.67999, -5.67999, -5.67999,
  -5.67999, -5.67999, -5.67999, -5.67999, -5.67999, -6.09420,
  -5.99679, -5.91174, -5.83682, -5.77031, -5.71085, -5.65738,
  -5.60904, -5.56512, -5.52504, -5.48833, -6.09902, -5.97017,
  -5.85769, -5.75939, -5.67350, -5.59856, -5.53336, -5.47683,
  -5.42805, -5.38621, -5.35060, -6.17146, -6.09512, -6.02542,
  -5.96131, -5.90194, -5.84668, -5.79498, -5.74642, -5.70064,
  -5.65733, -5.61624, -5.92355, -5.80239, -5.70475, -5.62524,
  -5.55994, -5.50595, -5.46106, -5.42359, -5.39222, -5.36591,
  -5.34383, -5.79111, -5.67660, -5.58924, -5.52166, -5.46879,
  -5.42707, -5.39394, -5.36751, -5.34637, -5.32946, -5.31596
),length(t),6)
weights <- c(0.00000, 0.21000, 0.02000, 0.55000, 0.00000, 0.22000) # model weights
alpha <- 0.05 # confidence level
y <- 304 # cut-off year for estimating probablity
best.model <- 2
which.model <- 2 # specify the generating model#'

# construct Studentized bootstrap confidence interval
marp::student_confint(
  n,B,t,m,BB,par_hat,mu_hat,pr_hat,haz_hat,weights,alpha,y,best.model,which.model
)