Cox martingale residuals

\(M_i = \delta_i - \exp(x_i'\beta)\hat H_0(t_i)\): observed events minus expected. Bounded above by 1 and unbounded below, hence strongly left-skewed – do not read them as if they were normal. Their use is functional form: plot them against a covariate not in the model, and curvature tells you the scale it belongs on.

Usage

morie_cox_martingale_residuals(fit)

Arguments

fit

a fit from morie_efron_tie_correction or morie_breslow_tie_correction.

Value

list with residuals, expected, event, cumhazard, times.

References

Therneau, T. M., Grambsch, P. M. and Fleming, T. R. (1990). Martingale-based residuals for survival models. Biometrika, 77(1), 147-160.

Examples

if (requireNamespace("ranger", quietly = TRUE)) {
  set.seed(1)
  X <- matrix(rnorm(60), ncol = 1)
  tt <- rexp(60, exp(X * 0.5))
  f <- morie_efron_tie_correction(tt, rep(1, 60), X)
  round(mean(morie_cox_martingale_residuals(f)$residuals), 8)
}
#> [1] 0