Compare high-dimensional Cox models by model validation

Usage

compare_by_validate(
  x,
  time,
  event,
  model.type = c("lasso", "alasso", "flasso", "enet", "aenet", "mcp", "mnet", "scad",
    "snet"),
  method = c("bootstrap", "cv", "repeated.cv"),
  boot.times = NULL,
  nfolds = NULL,
  rep.times = NULL,
  tauc.type = c("CD", "SZ", "UNO"),
  tauc.time,
  rule = c("lambda.min", "lambda.1se"),
  seed = 1001,
  trace = TRUE
)

Arguments

x: Matrix of training data used for fitting the model; on which to run the validation.
time: Survival time. Must be of the same length with the number of rows as x.
event: Status indicator, normally 0 = alive, 1 = dead. Must be of the same length with the number of rows as x.
model.type: Model types to compare. Could be at least two of "lasso", "alasso", "flasso", "enet", "aenet", "mcp", "mnet", "scad", or "snet".
method: Validation method. Could be "bootstrap", "cv", or "repeated.cv".
boot.times: Number of repetitions for bootstrap.
nfolds: Number of folds for cross-validation and repeated cross-validation.
rep.times: Number of repeated times for repeated cross-validation.
tauc.type: Type of time-dependent AUC. Including "CD" proposed by Chambless and Diao (2006)., "SZ" proposed by Song and Zhou (2008)., "UNO" proposed by Uno et al. (2007).
tauc.time: Numeric vector. Time points at which to evaluate the time-dependent AUC.
rule: Model selection criterion for glmnet models, `"lambda.min"` or `"lambda.1se"`. Defaults to `"lambda.min"`.
seed: A random seed for cross-validation fold division.
trace: Logical. Output the validation progress or not. Default is TRUE.

References

Chambless, L. E. and G. Diao (2006). Estimation of time-dependent area under the ROC curve for long-term risk prediction. Statistics in Medicine 25, 3474–3486.

Song, X. and X.-H. Zhou (2008). A semiparametric approach for the covariate specific ROC curve with survival outcome. Statistica Sinica 18, 947–965.

Uno, H., T. Cai, L. Tian, and L. J. Wei (2007). Evaluating prediction rules for t-year survivors with censored regression models. Journal of the American Statistical Association 102, 527–537.

Examples

data(smart)
x <- as.matrix(smart[, -c(1, 2)])[1:1000, ]
time <- smart$TEVENT[1:1000]
event <- smart$EVENT[1:1000]

# Compare lasso and adaptive lasso by 5-fold cross-validation
cmp.val.cv <- compare_by_validate(
  x, time, event,
  model.type = c("lasso", "alasso"),
  method = "cv", nfolds = 5, tauc.type = "UNO",
  tauc.time = seq(0.25, 2, 0.25) * 365, seed = 1001
)
#> Starting model 1 : lasso 
#> Start fold 1 
#> Start fold 2 
#> Start fold 3 
#> Start fold 4 
#> Start fold 5 
#> Starting model 2 : alasso 
#> Start fold 1 
#> Start fold 2 
#> Start fold 3 
#> Start fold 4 
#> Start fold 5 

print(cmp.val.cv)
#> High-Dimensional Cox Model Validation Object
#> Random seed: 1001 
#> Validation method: k-fold cross-validation
#> Cross-validation folds: 5 
#> Model type: lasso 
#> glmnet model alpha: 1 
#> glmnet model lambda: 0.01685262 
#> glmnet model penalty factor: not specified
#> Time-dependent AUC type: UNO 
#> Evaluation time points for tAUC: 91.25 182.5 273.75 365 456.25 547.5 638.75 730
#> 
#> High-Dimensional Cox Model Validation Object
#> Random seed: 1001 
#> Validation method: k-fold cross-validation
#> Cross-validation folds: 5 
#> Model type: alasso 
#> glmnet model alpha: 1 
#> glmnet model lambda: 0.1086075 
#> glmnet model penalty factor: specified
#> Time-dependent AUC type: UNO 
#> Evaluation time points for tAUC: 91.25 182.5 273.75 365 456.25 547.5 638.75 730
#> 
summary(cmp.val.cv)
#> Model type: lasso 
#>              91.25     182.5    273.75       365    456.25     547.5    638.75
#> Mean     0.5512447 0.5892787 0.6118296 0.6703934 0.6522846 0.6827941 0.6663543
#> Min      0.1969697 0.3638949 0.4933239 0.5227411 0.5015440 0.5406118 0.5414032
#> 0.25 Qt. 0.3883162 0.5121101 0.5066906 0.5287065 0.5287065 0.5808059 0.6044632
#> Median   0.6446701 0.5253751 0.5113647 0.6234958 0.6227553 0.6684507 0.6421704
#> 0.75 Qt. 0.7272727 0.6715544 0.6681714 0.8021683 0.7318710 0.7476227 0.6869896
#> Max      0.7989950 0.8734591 0.8795973 0.8748553 0.8765461 0.8764793 0.8567451
#>                730
#> Mean     0.6497359
#> Min      0.5685657
#> 0.25 Qt. 0.6045935
#> Median   0.6472902
#> 0.75 Qt. 0.6660511
#> Max      0.7621791
#>              91.25     182.5    273.75       365    456.25     547.5    638.75
#> Mean     0.5512447 0.5892787 0.6118296 0.6703934 0.6522846 0.6827941 0.6663543
#> Min      0.1969697 0.3638949 0.4933239 0.5227411 0.5015440 0.5406118 0.5414032
#> 0.25 Qt. 0.3883162 0.5121101 0.5066906 0.5287065 0.5287065 0.5808059 0.6044632
#> Median   0.6446701 0.5253751 0.5113647 0.6234958 0.6227553 0.6684507 0.6421704
#> 0.75 Qt. 0.7272727 0.6715544 0.6681714 0.8021683 0.7318710 0.7476227 0.6869896
#> Max      0.7989950 0.8734591 0.8795973 0.8748553 0.8765461 0.8764793 0.8567451
#>                730
#> Mean     0.6497359
#> Min      0.5685657
#> 0.25 Qt. 0.6045935
#> Median   0.6472902
#> 0.75 Qt. 0.6660511
#> Max      0.7621791
#> 
#> Model type: alasso 
#>              91.25     182.5    273.75       365    456.25     547.5    638.75
#> Mean     0.5507595 0.5930334 0.6119896 0.6708129 0.6531152 0.6855229 0.6689000
#> Min      0.1969697 0.3483014 0.4834263 0.5191235 0.4992296 0.5515548 0.5520277
#> 0.25 Qt. 0.3840206 0.5043381 0.5043835 0.5302921 0.5302921 0.5741340 0.5934681
#> Median   0.6362098 0.5201011 0.5120325 0.6202395 0.6167865 0.6642097 0.6377153
#> 0.75 Qt. 0.7537688 0.7019551 0.6681626 0.8014144 0.7345390 0.7536005 0.6947551
#> Max      0.7828283 0.8904711 0.8919432 0.8829948 0.8847287 0.8841155 0.8665338
#>                730
#> Mean     0.6501607
#> Min      0.5536751
#> 0.25 Qt. 0.5934151
#> Median   0.6453506
#> 0.75 Qt. 0.6715423
#> Max      0.7868205
#>              91.25     182.5    273.75       365    456.25     547.5    638.75
#> Mean     0.5507595 0.5930334 0.6119896 0.6708129 0.6531152 0.6855229 0.6689000
#> Min      0.1969697 0.3483014 0.4834263 0.5191235 0.4992296 0.5515548 0.5520277
#> 0.25 Qt. 0.3840206 0.5043381 0.5043835 0.5302921 0.5302921 0.5741340 0.5934681
#> Median   0.6362098 0.5201011 0.5120325 0.6202395 0.6167865 0.6642097 0.6377153
#> 0.75 Qt. 0.7537688 0.7019551 0.6681626 0.8014144 0.7345390 0.7536005 0.6947551
#> Max      0.7828283 0.8904711 0.8919432 0.8829948 0.8847287 0.8841155 0.8665338
#>                730
#> Mean     0.6501607
#> Min      0.5536751
#> 0.25 Qt. 0.5934151
#> Median   0.6453506
#> 0.75 Qt. 0.6715423
#> Max      0.7868205
#> 
plot(cmp.val.cv)
#>              91.25     182.5    273.75       365    456.25     547.5    638.75
#> Mean     0.5512447 0.5892787 0.6118296 0.6703934 0.6522846 0.6827941 0.6663543
#> Min      0.1969697 0.3638949 0.4933239 0.5227411 0.5015440 0.5406118 0.5414032
#> 0.25 Qt. 0.3883162 0.5121101 0.5066906 0.5287065 0.5287065 0.5808059 0.6044632
#> Median   0.6446701 0.5253751 0.5113647 0.6234958 0.6227553 0.6684507 0.6421704
#> 0.75 Qt. 0.7272727 0.6715544 0.6681714 0.8021683 0.7318710 0.7476227 0.6869896
#> Max      0.7989950 0.8734591 0.8795973 0.8748553 0.8765461 0.8764793 0.8567451
#>                730
#> Mean     0.6497359
#> Min      0.5685657
#> 0.25 Qt. 0.6045935
#> Median   0.6472902
#> 0.75 Qt. 0.6660511
#> Max      0.7621791
#>              91.25     182.5    273.75       365    456.25     547.5    638.75
#> Mean     0.5507595 0.5930334 0.6119896 0.6708129 0.6531152 0.6855229 0.6689000
#> Min      0.1969697 0.3483014 0.4834263 0.5191235 0.4992296 0.5515548 0.5520277
#> 0.25 Qt. 0.3840206 0.5043381 0.5043835 0.5302921 0.5302921 0.5741340 0.5934681
#> Median   0.6362098 0.5201011 0.5120325 0.6202395 0.6167865 0.6642097 0.6377153
#> 0.75 Qt. 0.7537688 0.7019551 0.6681626 0.8014144 0.7345390 0.7536005 0.6947551
#> Max      0.7828283 0.8904711 0.8919432 0.8829948 0.8847287 0.8841155 0.8665338
#>                730
#> Mean     0.6501607
#> Min      0.5536751
#> 0.25 Qt. 0.5934151
#> Median   0.6453506
#> 0.75 Qt. 0.6715423
#> Max      0.7868205

plot(cmp.val.cv, interval = TRUE)
#>              91.25     182.5    273.75       365    456.25     547.5    638.75
#> Mean     0.5512447 0.5892787 0.6118296 0.6703934 0.6522846 0.6827941 0.6663543
#> Min      0.1969697 0.3638949 0.4933239 0.5227411 0.5015440 0.5406118 0.5414032
#> 0.25 Qt. 0.3883162 0.5121101 0.5066906 0.5287065 0.5287065 0.5808059 0.6044632
#> Median   0.6446701 0.5253751 0.5113647 0.6234958 0.6227553 0.6684507 0.6421704
#> 0.75 Qt. 0.7272727 0.6715544 0.6681714 0.8021683 0.7318710 0.7476227 0.6869896
#> Max      0.7989950 0.8734591 0.8795973 0.8748553 0.8765461 0.8764793 0.8567451
#>                730
#> Mean     0.6497359
#> Min      0.5685657
#> 0.25 Qt. 0.6045935
#> Median   0.6472902
#> 0.75 Qt. 0.6660511
#> Max      0.7621791
#>              91.25     182.5    273.75       365    456.25     547.5    638.75
#> Mean     0.5507595 0.5930334 0.6119896 0.6708129 0.6531152 0.6855229 0.6689000
#> Min      0.1969697 0.3483014 0.4834263 0.5191235 0.4992296 0.5515548 0.5520277
#> 0.25 Qt. 0.3840206 0.5043381 0.5043835 0.5302921 0.5302921 0.5741340 0.5934681
#> Median   0.6362098 0.5201011 0.5120325 0.6202395 0.6167865 0.6642097 0.6377153
#> 0.75 Qt. 0.7537688 0.7019551 0.6681626 0.8014144 0.7345390 0.7536005 0.6947551
#> Max      0.7828283 0.8904711 0.8919432 0.8829948 0.8847287 0.8841155 0.8665338
#>                730
#> Mean     0.6501607
#> Min      0.5536751
#> 0.25 Qt. 0.5934151
#> Median   0.6453506
#> 0.75 Qt. 0.6715423
#> Max      0.7868205