Schoenfeld residuals and the proportional-hazards test

s_i = x_i minus the weighted risk-set mean at each event time. Grambsch and Therneau's scaled version tests proportional hazards by regressing the residuals on time.

Usage

Schoenfeld(time, event, X, beta, vcov = NULL, scaled = TRUE)

morie_survival_schoenfeld(time, event, X, beta, vcov = NULL, scaled = TRUE)

Arguments

time: observed follow-up times.
event: event indicator, 1 = event, 0 = censored.
X: covariate matrix, one row per subject.
beta: fitted coefficient vector.
vcov: covariance matrix of beta, used to scale the residuals.
scaled: whether to return the scaled residuals.

Value

list with the residuals, the event times, and the proportional-hazards test statistic and p-value.

References

Grambsch, P. M. and Therneau, T. M. (1994). Proportional hazards tests and diagnostics based on weighted residuals. Biometrika 81(3), 515-526.

Examples

ST <- c(5, 6, 6, 2.5, 4, 4, 3, 3, 1, 2, 2, 3, 7, 8, 9, 10)
SE <- c(1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1)
SX <- matrix((seq_along(ST) - 1)%%2, ncol = 1)
Schoenfeld(ST, SE, SX, 0.3, vcov = matrix(0.25, 1, 1))
#> $time
#>  [1]  1.0  2.0  2.5  3.0  4.0  5.0  6.0  7.0  9.0 10.0
#> 
#> $residuals
#>             [,1]
#>  [1,] -0.5744425
#>  [2,]  0.3932834
#>  [3,]  0.3883744
#>  [4,] -0.5744425
#>  [5,] -0.5192047
#>  [6,] -0.5030794
#>  [7,] -0.5744425
#>  [8,] -0.5744425
#>  [9,] -0.5744425
#> [10,]  0.0000000
#> 
#> $n_events
#> [1] 10
#> 
#> $ties_dropped
#> [1] 2
#> 
#> $p
#> [1] 1
#> 
#> $method
#> [1] "Grambsch and Therneau (1994) scaled Schoenfeld residuals and the correlation-with-time PH test"
#> 
#> $scaled
#>             [,1]
#>  [1,] -1.1361063
#>  [2,]  1.2832085
#>  [3,]  1.2709359
#>  [4,] -1.1361063
#>  [5,] -0.9980116
#>  [6,] -0.9576986
#>  [7,] -1.1361063
#>  [8,] -1.1361063
#>  [9,] -1.1361063
#> [10,]  0.3000000
#> 
#> $ph_test
#> $ph_test[[1]]
#> $ph_test[[1]]$rho
#> [1] -0.2120096
#> 
#> $ph_test[[1]]$z
#> [1] -0.6360289
#> 
#> $ph_test[[1]]$p_value
#> [1] 0.5247576
#> 
#> 
#> 
#> $ph_violated
#> [1] FALSE
#>