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Residuals for Parametric Regression Models for Failure Time Data

Source: R/survival_analysis.R
residuals_liferegr.Rd

Obtains the response, martingale, deviance, dfbeta, and likelihood displacement residuals for a parametric regression model for failure time data.

Usage

residuals_liferegr(
  object,
  type = c("response", "martingale", "deviance", "dfbeta", "dfbetas", "working",
    "ldcase", "ldresp", "ldshape", "matrix"),
  collapse = FALSE,
  weighted = (type %in% c("dfbeta", "dfbetas"))
)

Arguments

object

The output from the phregr call.

type

The type of residuals desired, with options including "response", "martingale", "deviance", "dfbeta", "dfbetas", "working", "ldcase", "ldresp", "ldshape", and "matrix".

collapse

Whether to collapse the residuals by id.

weighted

Whether to compute weighted residuals.

Value

Either a vector or a matrix of residuals, depending on the specified type:

  • response residuals are on the scale of the original data.

  • martingale residuals are event indicators minus the cumulative hazards for event or right-censored data.

  • working residuals are on the scale of the linear predictor.

  • deviance residuals are on the log-likelihood scale.

  • dfbeta residuals are returned as a matrix, where the \(i\)-th row represents the approximate change in the model coefficients resulting from the inclusion of subject \(i\).

  • dfbetas residuals are similar to dfbeta residuals, but each column is scaled by the standard deviation of the corresponding coefficient.

  • matrix residuals are a matrix of derivatives of the log-likelihood function. Let \(L\) be the log-likelihood, \(p\) be the linear predictor (\(X\beta\)), and \(s\) be \(log(\sigma)\). Then the resulting matrix contains six columns: \(L\), \(\partial L/\partial p\), \(\partial^2 L/\partial p^2\), \(\partial L/\partial s\), \(\partial^2 L/\partial s^2\), and \(\partial L^2/\partial p\partial s\).

  • ldcase residulas are likelihood displacement for case weight perturbation.

  • ldresp residuals are likelihood displacement for response value perturbation.

  • ldshape residuals are likelihood displacement related to the shape parameter.

Details

The algorithms follow the residuals.survreg function in the survival package, except for martingale residuals, which are defined only for event or right-censored data for exponential, weibull, lognormal, and loglogistic distributions.

References

Escobar, L. A. and Meeker, W. Q. Assessing influence in regression analysis with censored data. Biometrics 1992; 48:507-528.

Author

Kaifeng Lu, kaifenglu@gmail.com

Examples


library(dplyr)

fit1 <- liferegr(
  data = tobin %>% mutate(time = ifelse(durable>0, durable, NA)),
  time = "time", time2 = "durable",
  covariates = c("age", "quant"), dist = "normal")

resid <- residuals_liferegr(fit1, type = "response")
head(resid)
#> [1] 3.0496868 5.0125418 0.5416331 0.2560716 1.8501772 2.4098780