add_pi.survreg: Prediction Intervals for Accelerated Failure Time Models

In ciTools: Confidence or Prediction Intervals, Quantiles, and Probabilities for Statistical Models

Description

This function is one of the methods for add_pi, and is called automatically when add_pi is used on a fit of class survreg.

Usage

## S3 method for class 'survreg'
add_pi(
  df,
  fit,
  alpha = 0.05,
  names = NULL,
  yhatName = "median_pred",
  nSims = 10000,
  method = "naive",
  ...
)

Arguments

df	A data frame of new data.
fit	An object of class survreg.
alpha	A real number between 0 and 1. Controls the confidence level of the interval estimates.
names	NULL or character vector of length two. If NULL, prediction bounds automatically will be named by add_pi, otherwise, the lower prediction bound will be named names[1] and the upper prediction bound will be named names[2].
yhatName	A string. Name of the predictions vector.
nSims	A positive integer. Determines the number of bootstrap replicates if method = "boot".
method	A string. Determines the method used to calculate prediction intervals. Must be one of either "naive" or "boot".
...	Additional arguments.

Details

add_pi.survreg creates prediction intervals for the survival time $T$ conditioned on the covariates of the survreg model. In simple terms, this function calculates error bounds within which one can expect to observe a new survival time. Like other parametric survival methods in ciTools, prediction intervals are limited to unweighted lognormal, exponential, weibull, and loglogistic AFT models.

Two methods are available for creating prediction intervals, the "naive" method (Meeker and Escobar, chapter 8) and a simulation method that implements a parametric bootstrap routine. The "naive" method calculates quantiles of the fitted survival time distribution to determine prediction intervals. The parametric bootstrap method simulates new survival times from the conditional survival time distribution, taking into account the uncertainty in the regression coefficients. The bootstrap method is similar to the one implemented in add_pi.glm.

Note: Due to a limitation, the Surv object must be specified in survreg function call. See the examples section for one way to do this.

Note: add_pi.survreg cannot inspect the convergence of fit. Poor maximum likelihood estimates will result in poor prediction intervals. Inspect any warning messages given from survreg.

Value

A dataframe, df, with predicted medians, upper and lower prediction bounds attached.

References

For a discussion prediction intervals of accelerated failure time models: Meeker, William Q., and Luis A. Escobar. Statistical methods for reliability data. John Wiley & Sons, 2014. (Chapter 8)

See Also

add_ci.survreg for confidence intervals for survreg objects, add_probs.survreg for conditional survival probabilities of survreg objects, and add_quantile.survreg for survival time quantiles of survreg objects.

Examples

## Define a data set.
df <- survival::stanford2
## remove a covariate with missing values.
df <- df[, 1:4]
## next, create the Surv object inside the survreg call:
fit <- survival::survreg(survival::Surv(time, status) ~ age + I(age^2),
                         data = df, dist = "lognormal")
add_pi(df, fit, alpha = 0.1, names = c("lwr", "upr"))

## Try a different model:
fit2 <- survival::survreg(survival::Surv(time, status) ~ age + I(age^2),
                          data = df, dist = "weibull")
add_pi(df, fit2, alpha = 0.1, names = c("lwr", "upr"))

ciTools documentation built on Jan. 13, 2021, 7 a.m.