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,
  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.
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: 0.03893173 
#> 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: 3.330828 
#> 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     0.5514232 0.5750925 0.5908706 0.6486018 0.6315953 0.6615158 0.6475695
#> Min      0.1919192 0.3720636 0.4318947 0.5247777 0.4999633 0.5416780 0.5432238
#> 0.25 Qt. 0.4054983 0.4326005 0.5056009 0.5330110 0.5330110 0.5819999 0.5859288
#> Median   0.6362098 0.5369578 0.5155505 0.5450753 0.5461533 0.5949445 0.6091759
#> 0.75 Qt. 0.6742424 0.7018313 0.6757791 0.8073438 0.7434037 0.7520246 0.6958370
#> Max      0.8492462 0.8320093 0.8255278 0.8328010 0.8354450 0.8369321 0.8036820
#>                730
#> Mean     0.6292095
#> Min      0.5569337
#> 0.25 Qt. 0.5915718
#> Median   0.6105764
#> 0.75 Qt. 0.6746757
#> Max      0.7122901
#>              91.25     182.5    273.75       365    456.25     547.5    638.75
#> Mean     0.5514232 0.5750925 0.5908706 0.6486018 0.6315953 0.6615158 0.6475695
#> Min      0.1919192 0.3720636 0.4318947 0.5247777 0.4999633 0.5416780 0.5432238
#> 0.25 Qt. 0.4054983 0.4326005 0.5056009 0.5330110 0.5330110 0.5819999 0.5859288
#> Median   0.6362098 0.5369578 0.5155505 0.5450753 0.5461533 0.5949445 0.6091759
#> 0.75 Qt. 0.6742424 0.7018313 0.6757791 0.8073438 0.7434037 0.7520246 0.6958370
#> Max      0.8492462 0.8320093 0.8255278 0.8328010 0.8354450 0.8369321 0.8036820
#>                730
#> Mean     0.6292095
#> Min      0.5569337
#> 0.25 Qt. 0.5915718
#> Median   0.6105764
#> 0.75 Qt. 0.6746757
#> Max      0.7122901
#> 
#> Model type: alasso 
#>              91.25     182.5    273.75       365    456.25     547.5    638.75
#> Mean     0.5438734 0.6253119 0.6246102 0.6566693 0.6505558 0.6767926 0.6664697
#> Min      0.1161616 0.4108091 0.5219790 0.5361901 0.5334362 0.5378952 0.5394197
#> 0.25 Qt. 0.3891753 0.5148460 0.5289428 0.5577034 0.5361901 0.6129380 0.6162614
#> Median   0.7121212 0.5690552 0.5697782 0.5913443 0.6003684 0.6309677 0.6296160
#> 0.75 Qt. 0.7286432 0.8005930 0.6859652 0.7864692 0.7680248 0.7872057 0.7359087
#> Max      0.7732657 0.8312563 0.8163858 0.8116394 0.8147596 0.8149562 0.8111427
#>                730
#> Mean     0.6646070
#> Min      0.5620190
#> 0.25 Qt. 0.6241618
#> Median   0.6301660
#> 0.75 Qt. 0.7335408
#> Max      0.7731476
#>              91.25     182.5    273.75       365    456.25     547.5    638.75
#> Mean     0.5438734 0.6253119 0.6246102 0.6566693 0.6505558 0.6767926 0.6664697
#> Min      0.1161616 0.4108091 0.5219790 0.5361901 0.5334362 0.5378952 0.5394197
#> 0.25 Qt. 0.3891753 0.5148460 0.5289428 0.5577034 0.5361901 0.6129380 0.6162614
#> Median   0.7121212 0.5690552 0.5697782 0.5913443 0.6003684 0.6309677 0.6296160
#> 0.75 Qt. 0.7286432 0.8005930 0.6859652 0.7864692 0.7680248 0.7872057 0.7359087
#> Max      0.7732657 0.8312563 0.8163858 0.8116394 0.8147596 0.8149562 0.8111427
#>                730
#> Mean     0.6646070
#> Min      0.5620190
#> 0.25 Qt. 0.6241618
#> Median   0.6301660
#> 0.75 Qt. 0.7335408
#> Max      0.7731476
#> 
plot(cmp.val.cv)
#>              91.25     182.5    273.75       365    456.25     547.5    638.75
#> Mean     0.5514232 0.5750925 0.5908706 0.6486018 0.6315953 0.6615158 0.6475695
#> Min      0.1919192 0.3720636 0.4318947 0.5247777 0.4999633 0.5416780 0.5432238
#> 0.25 Qt. 0.4054983 0.4326005 0.5056009 0.5330110 0.5330110 0.5819999 0.5859288
#> Median   0.6362098 0.5369578 0.5155505 0.5450753 0.5461533 0.5949445 0.6091759
#> 0.75 Qt. 0.6742424 0.7018313 0.6757791 0.8073438 0.7434037 0.7520246 0.6958370
#> Max      0.8492462 0.8320093 0.8255278 0.8328010 0.8354450 0.8369321 0.8036820
#>                730
#> Mean     0.6292095
#> Min      0.5569337
#> 0.25 Qt. 0.5915718
#> Median   0.6105764
#> 0.75 Qt. 0.6746757
#> Max      0.7122901
#>              91.25     182.5    273.75       365    456.25     547.5    638.75
#> Mean     0.5438734 0.6253119 0.6246102 0.6566693 0.6505558 0.6767926 0.6664697
#> Min      0.1161616 0.4108091 0.5219790 0.5361901 0.5334362 0.5378952 0.5394197
#> 0.25 Qt. 0.3891753 0.5148460 0.5289428 0.5577034 0.5361901 0.6129380 0.6162614
#> Median   0.7121212 0.5690552 0.5697782 0.5913443 0.6003684 0.6309677 0.6296160
#> 0.75 Qt. 0.7286432 0.8005930 0.6859652 0.7864692 0.7680248 0.7872057 0.7359087
#> Max      0.7732657 0.8312563 0.8163858 0.8116394 0.8147596 0.8149562 0.8111427
#>                730
#> Mean     0.6646070
#> Min      0.5620190
#> 0.25 Qt. 0.6241618
#> Median   0.6301660
#> 0.75 Qt. 0.7335408
#> Max      0.7731476

plot(cmp.val.cv, interval = TRUE)
#>              91.25     182.5    273.75       365    456.25     547.5    638.75
#> Mean     0.5514232 0.5750925 0.5908706 0.6486018 0.6315953 0.6615158 0.6475695
#> Min      0.1919192 0.3720636 0.4318947 0.5247777 0.4999633 0.5416780 0.5432238
#> 0.25 Qt. 0.4054983 0.4326005 0.5056009 0.5330110 0.5330110 0.5819999 0.5859288
#> Median   0.6362098 0.5369578 0.5155505 0.5450753 0.5461533 0.5949445 0.6091759
#> 0.75 Qt. 0.6742424 0.7018313 0.6757791 0.8073438 0.7434037 0.7520246 0.6958370
#> Max      0.8492462 0.8320093 0.8255278 0.8328010 0.8354450 0.8369321 0.8036820
#>                730
#> Mean     0.6292095
#> Min      0.5569337
#> 0.25 Qt. 0.5915718
#> Median   0.6105764
#> 0.75 Qt. 0.6746757
#> Max      0.7122901
#>              91.25     182.5    273.75       365    456.25     547.5    638.75
#> Mean     0.5438734 0.6253119 0.6246102 0.6566693 0.6505558 0.6767926 0.6664697
#> Min      0.1161616 0.4108091 0.5219790 0.5361901 0.5334362 0.5378952 0.5394197
#> 0.25 Qt. 0.3891753 0.5148460 0.5289428 0.5577034 0.5361901 0.6129380 0.6162614
#> Median   0.7121212 0.5690552 0.5697782 0.5913443 0.6003684 0.6309677 0.6296160
#> 0.75 Qt. 0.7286432 0.8005930 0.6859652 0.7864692 0.7680248 0.7872057 0.7359087
#> Max      0.7732657 0.8312563 0.8163858 0.8116394 0.8147596 0.8149562 0.8111427
#>                730
#> Mean     0.6646070
#> Min      0.5620190
#> 0.25 Qt. 0.6241618
#> Median   0.6301660
#> 0.75 Qt. 0.7335408
#> Max      0.7731476