residuals.cph {Design} | R Documentation

## Residuals for a cph Fit

### Description

Calculates martingale, deviance, score or Schoenfeld residuals (scaled or unscaled) or influence statistics for a Cox proportional hazards model. This is a slightly modified version of Therneau's `residuals.coxph` function. It assumes that `x=TRUE` and `y=TRUE` were specified to `cph`, except for martingale residuals, which are stored with the fit by default.

### Usage

    ## S3 method for class 'cph':
    residuals(object,
          type=c("martingale", "deviance", "score", "schoenfeld",
                 "dfbeta", "dfbetas", "scaledsch"), collapse, weighted, ...)

### Arguments

`object` | a `cph` object
`type` | character string indicating the type of residual desired; the default is martingale. Only enough of the string to determine a unique match is required. Instead of the usual residuals, `type="dfbeta"` may be specified to obtain approximate leave-out-one Delta βs. Use `type="dfbetas"` to normalize the Delta βs for the standard errors of the regression coefficient estimates. Scaled Schoenfeld residuals (`type="scaledsch"`, Grambsch and Therneau, 1993) better reflect the log hazard ratio function than ordinary Schoenfeld residuals, and they are on the regression coefficient scale. The weights use Grambsch and Therneau's "average variance" method.
`collapse` | Vector indicating which rows to collapse(sum) over. In time-dependent models more than one row data can pertain to a single individual. If there were 4 individuals represented by 3, 1, 2 and 4 rows of data respectively, then `collapse=c(1,1,1, 2, 3,3, 4,4,4,4)` could be used to obtain per subject rather than per observation residuals.
`weighted` | ignored; only accepts `FALSE`
`...` | unused

### Value

The object returned will be a vector for martingale and deviance residuals and matrices for score and schoenfeld residuals, dfbeta, or dfbetas. There will be one row of residuals for each row in the input data (without `collapse`). One column of score and Schoenfeld residuals will be returned for each column in the model.matrix. The scaled Schoenfeld residuals are used in the `cox.zph` function.
The score residuals are each individual's contribution to the score vector. Two transformations of this are often more useful: `dfbeta` is the approximate change in the coefficient vector if that observation were dropped, and `dfbetas` is the approximate change in the coefficients, scaled by the standard error for the coefficients.

### References

T. Therneau, P. Grambsch, and T.Fleming. "Martingale based residuals for survival models", Biometrika, March 1990.

P. Grambsch, T. Therneau. "Proportional hazards tests and diagnostics based on weighted residuals", unpublished manuscript, Feb 1993.

### See Also

`cph`, `coxph`, `residuals.coxph`, `cox.zph`, `naresid`

### Examples

    # fit <- cph(Surv(start, stop, event) ~ (age + surgery)* transplant,
    #            data=jasa1)
    # mresid <- resid(fit, collapse=jasa1$id)

    # Get unadjusted relationships for several variables
    # Pick one variable that's not missing too much, for fit

    n <- 1000    # define sample size
    set.seed(17) # so can reproduce the results
    age            <- rnorm(n, 50, 10)
    blood.pressure <- rnorm(n, 120, 15)
    cholesterol    <- rnorm(n, 200, 25)
    sex            <- factor(sample(c('female','male'), n,TRUE))
    cens   <- 15*runif(n)
    h      <- .02*exp(.04*(age-50)+.8*(sex=='Female'))
    d.time <- -log(runif(n))/h
    death  <- ifelse(d.time <= cens,1,0)
    d.time <- pmin(d.time, cens)

    f <- cph(Surv(d.time, death) ~ age + blood.pressure + cholesterol, iter.max=0)
    res <- resid(f) # This re-inserts rows for NAs, unlike f$resid
    yl <- quantile(res, c(10/length(res),1-10/length(res)), na.rm=TRUE)
    # Scale all plots from 10th smallest to 10th largest residual
    par(mfrow=c(2,2), oma=c(3,0,3,0))
    p <- function(x) {
      s <- !is.na(x+res)
      plot(lowess(x[s], res[s], iter=0), xlab=label(x), ylab="Residual",
           ylim=yl, type="l")
    }
    p(age); p(blood.pressure); p(cholesterol)
    mtext("Smoothed Martingale Residuals", outer=TRUE)

    # Assess PH by estimating log relative hazard over time
    f <- cph(Surv(d.time,death) ~ age + sex + blood.pressure, x=TRUE, y=TRUE)
    r <- resid(f, "scaledsch")
    tt <- as.numeric(dimnames(r)[[1]])
    par(mfrow=c(3,2))
    for(i in 1:3) {
      g <- areg.boot(I(r[,i]) ~ tt, B=20)
      plot(g, boot=FALSE)  # shows bootstrap CIs
    }                  # Focus on 3 graphs on right
    # Easier approach:
    plot(cox.zph(f))    # invokes plot.cox.zph
    par(mfrow=c(1,1))

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