weibull_bstrp {marp}

A function to generate (double) bootstrap samples and fit Weibull renewal model

Description

A function to generate (double) bootstrap samples and fit Weibull renewal model

Usage

weibull_bstrp(n, t, B, BB, m, par_hat, mu_hat, pr_hat, haz_hat, y)

Arguments

n

number of inter-event times

t

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

B

number of bootstrap samples

BB

number of double-bootstrap samples

m

the number of iterations in nlm

par_hat

estimated parameters

mu_hat

estimated mean inter-event times

pr_hat

estimated time to event probability

haz_hat

estimated hazard rates

y

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

Value

returns list of estimates after fitting Weibull renewal model on (double) bootstrap samples

mu_star

Estimated mean from bootstrapped samples

pr_star

Estimated probability from bootstrapped samples

haz_star

Estimated hazard rates from bootstrapped samples

mu_var_hat

Variance of estimated mean

pr_var_hat

Variance of estimated probability

haz_var_hat

Variance of estimated hazard rates

mu_var_double

Variance of estimated mean of bootstrapped samples (via double-bootstrapping)

pr_var_double

Variance of estimated probability of bootstrapped samples (via double-bootstrapping)

haz_var_double

Variance of estimated hazard rates of bootstrapped samples (via double-bootstrapping)

mu_Tstar

Pivot quantity of the estimated mean

pr_Tstar

Pivot quantity of the estimated probability

haz_Tstar

Pivot quantity of the estimated hazard rates

Examples

# set some parameters
n <- 30 # sample size
t <- seq(100, 200, by = 10) # time intervals
B <- 100 # number of bootstraps
BB <- 100 # number of double-bootstraps
m <- 10 # number of iterations for MLE optimization
par_hat <- c(
  3.4136086430979953e-03, 2.7626793657057762e+00, 2.6037039674870583e+00, 3.3080162440951688e+02,
  5.4882183788378658e+00, 2.9294512422957860e+02, NA, 9.4307059277139432e-03,
  2.4759796859031687e+02, 1.8010183507666513e+00, 6.5084541680686814e-01, 7.1824719073918109e-01
)
mu_hat <- c(
  292.94512187913182, 292.94512912200048, 319.72017228620746, 294.16945213908519,
  298.87285747700128, 292.94512422957860
)
pr_hat <- c(
  0.60038574701819891, 0.42154974433034809, 0.53433568234281148, 0.30779792692414687,
  0.56416103510057725, 0.61794524610544410
)
haz_hat <-   matrix(c(
  -5.6799852941338829, -5.6799852941338829, -5.6799852941338829, -5.6799852941338829,
  -5.6799852941338829, -5.6799852941338829, -5.6799852941338829, -5.6799852941338829,
  -5.6799852941338829, -5.6799852941338829, -5.6799852941338829, -6.0942031084732298,
  -5.9967873794574516, -5.9117418563554684, -5.8368230853439300, -5.7703089176306639,
  -5.7108525626839901, -5.6573839062669986, -5.6090408956082456, -5.5651206740587922,
  -5.5250440506799734, -5.4883291920475745, -6.0990192429336094, -5.9701664705134210,
  -5.8576899644670348, -5.7593884711134971, -5.6734972529860741, -5.5985621349393231,
  -5.5333565788683616, -5.4768259914915305, -5.4280496904694857, -5.3862145095364315,
  -5.3505961502861927, -6.1714638710963881, -6.0951186680582552, -6.0254209583640863,
  -5.9613052806725335, -5.9019434350392981, -5.8466788789061646, -5.7949823391436279,
  -5.7464209045603756, -5.7006359661738628, -5.6573271297614109, -5.6162402596857071,
  -5.9235521978533958, -5.8023896004395645, -5.7047473880293342, -5.6252373537796752,
  -5.5599409055534252, -5.5059486025117375, -5.4610610586440487, -5.4235891601883868,
  -5.3922173604047572, -5.3659081375131672, -5.3438339586221275, -5.7911126719889303,
  -5.6765973314326752, -5.5892417143301261, -5.5216608261560411, -5.4687921205249133,
  -5.4270729562323066, -5.3939387902533049, -5.3675067327627373, -5.3463701567645607,
  -5.3294619641245422, -5.3159614865560094
),length(t),6)
y <- 304 # cut-off year for estimating probablity

# generate bootstrapped samples then fit renewal model
res <- marp::weibull_bstrp(n, t, B, BB, m, par_hat, mu_hat, pr_hat, haz_hat, y)