Martingale residuals from a fitted Cox model

M_i = delta_i - H0(t_i) exp(x_i' beta): observed events minus expected. They sum to zero at the fitted beta, which is returned so the fit can be checked.

Usage

Martingale(time, event, X, beta)

morie_survival_martingale(time, event, X, beta)

Arguments

time: observed follow-up times.
event: event indicator, 1 = event, 0 = censored.
X: covariate matrix, one row per subject.
beta: fitted coefficient vector.

Value

list with the residuals, their sum, and the cumulative baseline hazard.

References

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

Examples

Martingale(time = c(1, 2, 3, 4, 5, 6, 7, 8), event = c(0, 1, 0, 1, 1, 0, 1, 0),
  X = c(1, 2, 3, 4, 5, 6, 7, 8), beta = 0.5)
#> $residuals
#> [1]  0.00000000  0.97980034 -0.03330361  0.88707941  0.71228910 -0.47435509
#> [7] -0.15961999 -1.91189015
#> 
#> $expected
#> [1] 0.00000000 0.02019966 0.03330361 0.11292059 0.28771090 0.47435509 1.15961999
#> [8] 1.91189015
#> 
#> $sum
#> [1] -3.608225e-16
#> 
#> $sums_to_zero
#> [1] TRUE
#> 
#> $max
#> [1] 0.9798003
#> 
#> $min
#> [1] -1.91189
#> 
#> $upper_bound
#> [1] 1
#> 
#> $n
#> [1] 8
#> 
#> $skewed
#> [1] TRUE
#> 
#> $method
#> [1] "M_i = delta_i - H0(t_i) exp(x_i' beta), Breslow baseline"
#>