summary.emfrail function

Summary for emfrail objects

## S3 method for class 'emfrail'
summary(object, lik_ci = TRUE, print_opts = list(coef
  = TRUE, dist = TRUE, fit = TRUE, frailty = TRUE, adj_se = TRUE,
  verbose_frailty = TRUE), ...)

Arguments

• object: An object of class emfrail
• lik_ci: Logical. Should the confidence intervals for the frailty parameter be calculated based on the likelihood? If not, they are calculated with the delta method.
• print_opts: A list with options for printing the summary object. These include coef, dist, fit, frailty, adj_se, verbose_frailty.
• ...: Ignored

Returns

An object of class emfrail_summary, with some more human-readable results from an emfrail object.

Details

Regardless of the fitted model, the following fields will be present in this object: est_dist (an object of class emfrail_distribution) with the estimated distribution, loglik (a named vector with the log-likelihoods of the no-frailty model, the frailty model, the likelihood ratio test statistic and the p-value of the one-sided likelihood ratio test), theta (a named vector with the estimated value of the parameter $\theta$, the standard error, and the limits of a 95

is a data frame with the following columns: id (cluster identifier), z (empirical Bayes frailty estimates), and optional lower_q and upper_q as the 2.5

For the the PVF or gamma distributions, the field fr_var contains a transformation of theta to correspond to the frailty variance. The fields pvf_pars and stable_pars are for quantities that are calculated only when the distribution is PVF or stable. If the model contains covariates, the field coefmat contains the corresponding estimates. The p-values are based on the adjusted standard errors, if they have been calculated successfully (i.e. if they appear when prining the summary object). Otherwise, they are based on the regular standard errors.

Examples

data("bladder")
mod_gamma <- emfrail(Surv(start, stop, status) ~ treatment + cluster(id), bladder1)
summary(mod_gamma)
summary(mod_gamma, print_opts = list(frailty_verbose = FALSE))

# plot the Empirical Bayes estimates of the frailty
# easy way:
plot(mod_gamma, type = "hist")

# a fancy graph:
sum_mod <- summary(mod_gamma)
library(dplyr)
library(ggplot2)

# Create a plot just with the points
pl1 <- sum_mod$frail %>%
  arrange(z) %>%
  mutate(x = 1:n()) %>%
  ggplot(aes(x = x, y = z)) +
  geom_point()

# If the quantiles of the posterior distribution are
# known, then error bars can be added:
if(!is.null(sum_mod$frail$lower_q))
  pl1 <- pl1 + geom_errorbar(aes(ymin = lower_q, ymax = upper_q), alpha = 0.5)

pl1

# The plot can be made interactive!
# ggplot2 gives a warning about the "id" aesthetic, just ignore it
pl2 <- sum_mod$frail %>%
  arrange(z) %>%
  mutate(x = 1:n()) %>%
  ggplot(aes(x = x, y = z)) +
  geom_point(aes(id = id))

if(!is.null(sum_mod$z$lower_q))
  pl2 <- pl2 + geom_errorbar(aes(ymin = lower_q, ymax = upper_q, id = id), alpha = 0.5)

library(plotly)
ggplotly(pl2)

# Proportional hazards test
off_z <- log(sum_mod$frail$z)[match(bladder1$id, sum_mod$frail$id)]

zph1 <- cox.zph(coxph(Surv(start, stop, status) ~ treatment + cluster(id), data = bladder1))

# no sign of non-proportionality
zph2 <- cox.zph(coxph(Surv(start, stop, status) ~ treatment + offset(off_z), data = bladder1))

zph2
# the p-values are even larger; the frailty "corrects" for proportionality.

See Also

predict.emfrail, plot.emfrail