residuals_phregr function

Residuals for Proportional Hazards Regression Models

Obtains the martingale, deviance, score, or Schoenfeld residuals for a proportional hazards regression model.

residuals_phregr(
  fit_phregr,
  type = c("martingale", "deviance", "score", "schoenfeld", "dfbeta", "dfbetas",
    "scaledsch"),
  collapse = FALSE,
  weighted = (type %in% c("dfbeta", "dfbetas"))
)

Arguments

• fit_phregr: The output from the phregr call.
• type: The type of residuals desired, with options including "martingale", "deviance", "score", "schoenfeld", "dfbeta", "dfbetas", and "scaledsch".
• collapse: Whether to collapse the residuals by id. This is not applicable for Schoenfeld type residuals.
• weighted: Whether to compute weighted residuals.

Returns

For martingale and deviance residuals, the result is a vector with one element corresponding to each subject (without collapse). For score residuals, the result is a matrix where each row represents a subject and each column corresponds to a variable. The row order aligns with the input data used in the original fit. For Schoenfeld residuals, the result is a matrix with one row for each event and one column per variable. These rows are sorted by time within strata, with the attributes stratum and time included.

Score residuals represent each individual's contribution to the score vector. Two commonly used transformations of this are dfbeta, which represents the approximate change in the coefficient vector if the observation is excluded, and dfbetas, which gives the approximate change in the coefficients scaled by the standard error of the coefficients.

Details

For score and Schoenfeld type residuals, the proportional hazards model must include at least one covariate. The algorithms for deviance, dfbeta, dfbetas, and scaledsch residuals follow the residuals.coxph function in the survival package.

Examples

library(dplyr)

# Example 1 with right-censored data
fit1 <- phregr(data = rawdata %>% filter(iterationNumber == 1) %>%
                 mutate(treat = 1*(treatmentGroup == 1)),
               stratum = "stratum",
               time = "timeUnderObservation", event = "event",
               covariates = "treat")

ressco <- residuals_phregr(fit1, type = "score")

# Example 2 with counting process data
fit2 <- phregr(data = heart %>% mutate(rx = as.numeric(transplant) - 1),
               time = "start", time2 = "stop", event = "event",
               covariates = c("rx", "age"), id = "id", robust = TRUE)

resssch <- residuals_phregr(fit2, type = "scaledsch")

References

Terry M. Therneau, Patricia M. Grambsch, and Thomas M. Fleming. Martingale based residuals for survival models. Biometrika 1990; 77:147-160.

Patricia M. Grambsch and Terry M. Therneau. Proportional hazards tests and diagnostics based on weighted residuals. Biometrika 1994; 81:515-26.

Author(s)

Kaifeng Lu, kaifenglu@gmail.com