nc_score_test: Score test of Northrop and Coleman

In longevity: Statistical Methods for the Analysis of Excess Lifetimes

Score test of Northrop and Coleman

Description

This function computes the score test with the piecewise generalized Pareto distribution under the null hypothesis that the generalized Pareto with a single shape parameter is an adequate simplification. The score test statistic is calculated using the observed information matrix; both hessian and score vector are obtained through numerical differentiation.

Usage

nc_score_test(
  time,
  time2 = NULL,
  event = NULL,
  thresh = 0,
  ltrunc = NULL,
  rtrunc = NULL,
  type = c("right", "left", "interval", "interval2"),
  weights = rep(1, length(time))
)

Arguments

time	excess time of the event of follow-up time, depending on the value of event
time2	ending excess time of the interval for interval censored data only.
event	status indicator, normally 0=alive, 1=dead. Other choices are TRUE/FALSE (TRUE for death). For interval censored data, the status indicator is 0=right censored, 1=event at time, 2=left censored, 3=interval censored. Although unusual, the event indicator can be omitted, in which case all subjects are assumed to have experienced an event.
thresh	a vector of thresholds
ltrunc	lower truncation limit, default to NULL
rtrunc	upper truncation limit, default to NULL
type	character string specifying the type of censoring. Possible values are "right", "left", "interval", "interval2".
weights	weights for observations

Details

The score test is much faster and perhaps less fragile than the likelihood ratio test: fitting the piece-wise generalized Pareto model is difficult due to the large number of parameters and multimodal likelihood surface.

The reference distribution is chi-square

Value

the value of a call to nc_test

Examples

set.seed(1234)
n <- 100L
x <- samp_elife(n = n,
                scale = 2,
                shape = -0.2,
                lower = low <- runif(n),
                upper = upp <- runif(n, min = 3, max = 20),
                type2 = "ltrt",
                family = "gp")
test <- nc_test(
  time = x,
  ltrunc = low,
  rtrunc = upp,
  thresh = quantile(x, seq(0, 0.5, by = 0.1)))
print(test)
plot(test)

longevity documentation built on Nov. 12, 2023, 5:07 p.m.