validate function

Validate high-dimensional Cox models with time-dependent AUC

validate(
  x,
  time,
  event,
  model.type = c("lasso", "alasso", "flasso", "enet", "aenet", "mcp", "mnet", "scad",
    "snet"),
  alpha,
  lambda,
  pen.factor = NULL,
  gamma,
  lambda1,
  lambda2,
  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 type to validate. Could be one of "lasso", "alasso", "flasso", "enet", "aenet", "mcp", "mnet", "scad", or "snet".
• alpha: Value of the elastic-net mixing parameter alpha for enet, aenet, mnet, and snet models. For lasso, alasso, mcp, and scad models, please set alpha = 1. alpha=1: lasso (l1) penalty; alpha=0: ridge (l2) penalty. Note that for mnet and snet models, alpha can be set to very close to 0 but not 0 exactly.
• lambda: Value of the penalty parameter lambda to use in the model fits on the resampled data. From the fitted Cox model.
• pen.factor: Penalty factors to apply to each coefficient. From the fitted adaptive lasso or adaptive elastic-net model.
• gamma: Value of the model parameter gamma for MCP/SCAD/Mnet/Snet models.
• lambda1: Value of the penalty parameter lambda1 for fused lasso model.
• lambda2: Value of the penalty parameter lambda2 for fused lasso model.
• 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 resampling.
• trace: Logical. Output the validation progress or not. Default is TRUE.

Examples

data(smart)
x <- as.matrix(smart[, -c(1, 2)])[1:500, ]
time <- smart$TEVENT[1:500]
event <- smart$EVENT[1:500]
y <- survival::Surv(time, event)

fit <- fit_lasso(x, y, nfolds = 5, rule = "lambda.1se", seed = 11)

# Model validation by bootstrap with time-dependent AUC
# Normally boot.times should be set to 200 or more,
# we set it to 3 here only to save example running time.
val.boot <- validate(
  x, time, event,
  model.type = "lasso",
  alpha = 1, lambda = fit$lambda,
  method = "bootstrap", boot.times = 3,
  tauc.type = "UNO", tauc.time = seq(0.25, 2, 0.25) * 365,
  seed = 1010
)

# Model validation by 5-fold cross-validation with time-dependent AUC
val.cv <- validate(
  x, time, event,
  model.type = "lasso",
  alpha = 1, lambda = fit$lambda,
  method = "cv", nfolds = 5,
  tauc.type = "UNO", tauc.time = seq(0.25, 2, 0.25) * 365,
  seed = 1010
)

# Model validation by repeated cross-validation with time-dependent AUC
val.repcv <- validate(
  x, time, event,
  model.type = "lasso",
  alpha = 1, lambda = fit$lambda,
  method = "repeated.cv", nfolds = 5, rep.times = 3,
  tauc.type = "UNO", tauc.time = seq(0.25, 2, 0.25) * 365,
  seed = 1010
)

# bootstrap-based discrimination curves has a very narrow band
print(val.boot)
summary(val.boot)
plot(val.boot)

# k-fold cv provides a more strict evaluation than bootstrap
print(val.cv)
summary(val.cv)
plot(val.cv)

# repeated cv provides similar results as k-fold cv
# but more robust than k-fold cv
print(val.repcv)
summary(val.repcv)
plot(val.repcv)
# # Test fused lasso, SCAD, and Mnet models
#
# data(smart)
# x = as.matrix(smart[, -c(1, 2)])[1:500,]
# time = smart$TEVENT[1:500]
# event = smart$EVENT[1:500]
# y = survival::Surv(time, event)
#
# set.seed(1010)
# val.boot = validate(
#   x, time, event, model.type = "flasso",
#   lambda1 = 5, lambda2 = 2,
#   method = "bootstrap", boot.times = 10,
#   tauc.type = "UNO", tauc.time = seq(0.25, 2, 0.25) * 365,
#   seed = 1010)
#
# val.cv = validate(
#   x, time, event, model.type = "scad",
#   gamma = 3.7, alpha = 1, lambda = 0.05,
#   method = "cv", nfolds = 5,
#   tauc.type = "UNO", tauc.time = seq(0.25, 2, 0.25) * 365,
#   seed = 1010)
#
# val.repcv = validate(
#   x, time, event, model.type = "mnet",
#   gamma = 3, alpha = 0.3, lambda = 0.05,
#   method = "repeated.cv", nfolds = 5, rep.times = 3,
#   tauc.type = "UNO", tauc.time = seq(0.25, 2, 0.25) * 365,
#   seed = 1010)
#
# print(val.boot)
# summary(val.boot)
# plot(val.boot)
#
# print(val.cv)
# summary(val.cv)
# plot(val.cv)
#
# print(val.repcv)
# summary(val.repcv)
# plot(val.repcv)

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.