Externally validate high-dimensional Cox models with time-dependent AUC

Usage

validate_external(
  object,
  x,
  time,
  event,
  x_new,
  time_new,
  event_new,
  tauc.type = c("CD", "SZ", "UNO"),
  tauc.time
)

Arguments

object: Model object fitted by hdnom::fit_*().
x: Matrix of training data used for fitting the model.
time: Survival time of the training data. Must be of the same length with the number of rows as x.
event: Status indicator of the training data, normally 0 = alive, 1 = dead. Must be of the same length with the number of rows as x.
x_new: Matrix of predictors for the external validation data.
time_new: Survival time of the external validation data. Must be of the same length with the number of rows as x_new.
event_new: Status indicator of the external validation data, normally 0 = alive, 1 = dead. Must be of the same length with the number of rows as x_new.
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.

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)
# Use the first 1000 samples as training data
# (the data used for internal validation)
x <- as.matrix(smart[, -c(1, 2)])[1:1000, ]
time <- smart$TEVENT[1:1000]
event <- smart$EVENT[1:1000]

# Take the next 1000 samples as external validation data
# In practice, usually use data collected in other studies
x_new <- as.matrix(smart[, -c(1, 2)])[1001:2000, ]
time_new <- smart$TEVENT[1001:2000]
event_new <- smart$EVENT[1001:2000]

# Fit Cox model with lasso penalty
fit <- fit_lasso(
  x, survival::Surv(time, event),
  nfolds = 5, rule = "lambda.1se", seed = 11
)

# External validation with time-dependent AUC
val.ext <- validate_external(
  fit, x, time, event,
  x_new, time_new, event_new,
  tauc.type = "UNO",
  tauc.time = seq(0.25, 2, 0.25) * 365
)

print(val.ext)
#> High-Dimensional Cox Model External Validation Object
#> Model type: lasso 
#> 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(val.ext)
#> Time-Dependent AUC Summary at Evaluation Time Points
#>         91.25     182.5    273.75       365    456.25     547.5    638.75
#> AUC 0.4971912 0.5710299 0.6293697 0.6144638 0.6352992 0.6495091 0.6544655
#>           730
#> AUC 0.6602009
plot(val.ext)
#>         91.25     182.5    273.75       365    456.25     547.5    638.75
#> AUC 0.4971912 0.5710299 0.6293697 0.6144638 0.6352992 0.6495091 0.6544655
#>           730
#> AUC 0.6602009


# # Test fused lasso, MCP, and Snet models
# data(smart)
# # Use first 600 samples as training data
# # (the data used for internal validation)
# x <- as.matrix(smart[, -c(1, 2)])[1:600, ]
# time <- smart$TEVENT[1:600]
# event <- smart$EVENT[1:600]
#
# # Take 500 samples as external validation data.
# # In practice, usually use data collected in other studies.
# x_new <- as.matrix(smart[, -c(1, 2)])[1001:1500, ]
# time_new <- smart$TEVENT[1001:1500]
# event_new <- smart$EVENT[1001:1500]
#
# flassofit <- fit_flasso(x, survival::Surv(time, event), nfolds = 5, seed = 11)
# scadfit <- fit_mcp(x, survival::Surv(time, event), nfolds = 5, seed = 11)
# mnetfit <- fit_snet(x, survival::Surv(time, event), nfolds = 5, seed = 11)
#
# val.ext1 <- validate_external(
#   flassofit, x, time, event,
#   x_new, time_new, event_new,
#   tauc.type = "UNO",
#   tauc.time = seq(0.25, 2, 0.25) * 365)
#
# val.ext2 <- validate_external(
#   scadfit, x, time, event,
#   x_new, time_new, event_new,
#   tauc.type = "CD",
#   tauc.time = seq(0.25, 2, 0.25) * 365)
#
# val.ext3 <- validate_external(
#   mnetfit, x, time, event,
#   x_new, time_new, event_new,
#   tauc.type = "SZ",
#   tauc.time = seq(0.25, 2, 0.25) * 365)
#
# print(val.ext1)
# summary(val.ext1)
# plot(val.ext1)
#
# print(val.ext2)
# summary(val.ext2)
# plot(val.ext2)
#
# print(val.ext3)
# summary(val.ext3)
# plot(val.ext3)