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Fit a penalized parametric mixture cure model using the generalized monotone incremental forward stagewise (GMIFS) algorithm (Hastie et al 2007) with cross-validation for model selection

Source: R/cv_curegmifs.R
cv_curegmifs.Rd

Fits a penalized Weibull or exponential mixture cure model using the generalized monotone incremental forward stagewise (GMIFS) algorithm with k-fold cross-validation to select the optimal iteration step along the solution path. When FDR controlled variable selection is used, the model-X knockoffs method is applied and indices of selected variables are returned.

Usage

cv_curegmifs(
  formula,
  data,
  subset,
  x_latency = NULL,
  model = c("weibull", "exponential"),
  penalty_factor_inc = NULL,
  penalty_factor_lat = NULL,
  fdr_control = FALSE,
  fdr = 0.2,
  epsilon = 0.001,
  thresh = 1e-05,
  scale = TRUE,
  maxit = 10000,
  inits = NULL,
  n_folds = 5,
  measure_inc = c("c", "auc"),
  one_se = FALSE,
  cure_cutoff = 5,
  parallel = FALSE,
  seed = NULL,
  verbose = TRUE,
  na.action = na.omit,
  ...
)

Arguments

formula

an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted. The response must be a survival object as returned by the Surv function while the variables on the right side of the formula are the covariates that are included in the incidence portion of the model.

data

a data.frame in which to interpret the variables named in the formula or in the subset argument. Rows with missing data are omitted (only na.action = na.omit is operational) therefore users may want to impute missing data prior to calling this function.

subset

an optional expression indicating which subset of observations to be used in the fitting process, either a numeric or factor variable should be used in subset, not a character variable. All observations are included by default.

x_latency

specifies the variables to be included in the latency portion of the model and can be either a matrix of predictors, a model formula with the right hand side specifying the latency variables, or the same data.frame passed to the data parameter. Note that when using the model formula syntax for x_latency it cannot handle x_latency = ~ ..

model

type of regression model to use for the latency portion of mixture cure model. Can be "weibull" or "exponential"; default is "weibull".

penalty_factor_inc

vector of binary indicators representing the penalty to apply to each incidence coefficient: 0 implies no shrinkage and 1 implies shrinkage. If not supplied, 1 is applied to all incidence variables.

penalty_factor_lat

vector of binary indicators representing the penalty to apply to each latency coefficient: 0 implies no shrinkage and 1 implies shrinkage. If not supplied, 1 is applied to all latency variables.

fdr_control

logical, if TRUE, model-X knockoffs are used for FDR-controlled variable selection and indices of selected variables are returned (default is FALSE).

fdr

numeric value in (0, 1) range specifying the target FDR level to use for variable selection when fdr_control = TRUE (default is 0.2).

epsilon

small numeric value reflecting incremental value used to update a coefficient at a given step (default is 0.001).

thresh

small numeric value. The iterative process stops when the differences between successive expected penalized complete-data log-likelihoods for both incidence and latency components are less than this specified level of tolerance (default is 10^-5).

scale

logical, if TRUE the predictors are centered and scaled.

maxit

integer specifying the maximum number of steps to run in the iterative algorithm (default is 10^4).

inits

an optional list specifying the initial values as follows:

  • itct a numeric value for the unpenalized incidence intercept.

  • b_u a numeric vector for the unpenalized incidence coefficients.

  • beta_u a numeric vector for unpenalized latency coefficients.

  • lambda a numeric value for the rate parameter.

  • alpha a numeric value for the shape parameter when model = "weibull".

If inits is not specified or improperly supplied, initialization is automatically provided by the function.

n_folds

an integer specifying the number of folds for the k-fold cross-validation procedure (default is 5).

measure_inc

character string specifying the evaluation criterion used in selecting the optimal \(\lambda_b\) which can be either

  • "c" specifying to use the C-statistic for cure status weighting (CSW) method proposed by Asano and Hirakawa (2017) to select both \(\lambda_b\) and \(\lambda_{\beta}\)

  • "auc" specifying to use the AUC for cure prediction using the mean score imputation (MSI) method proposed by Asano et al. (2014) to select \(\lambda_b\) while the C-statistic with CSW is used for \(\lambda_{\beta}\).

one_se

logical, if TRUE then the one standard error rule is applied for selecting the optimal parameters. The one standard error rule selects the most parsimonious model having evaluation criterion no more than one standard error worse than that of the best evaluation criterion (default is FALSE).

cure_cutoff

numeric value representing the cutoff time value that represents subjects not experiencing the event by this time are cured. This value is used to produce a proxy for the unobserved cure status when calculating C-statistic and AUC (default is 5 representing 5 years). Users should be careful to note the time scale of their data and adjust this according to the time scale and clinical application.

parallel

logical. If TRUE, parallel processing is performed for K-fold CV using foreach and the doParallel package is required.

seed

optional integer representing the random seed. Setting the random seed fosters reproducibility of the results.

verbose

logical, if TRUE running information is printed to the console (default is FALSE).

na.action

this function requires complete data so "na.omit" is invoked. Users can impute missing data as an alternative prior to model fitting.

...

additional arguments.

Value

b0

Estimated intercept for the incidence portion of the model.

b

Estimated coefficients for the incidence portion of the model.

beta

Estimated coefficients for the latency portion of the model.

alpha

Estimated shape parameter if the Weibull model is fit.

rate

Estimated rate parameter if the Weibull or exponential model is fit.

logLik

Log-likelihood value.

selected_step_inc

Iteration step selected for the incidence portion of the model using cross-validation. NULL when fdr_control is TRUE.

selected_step_lat

Iteration step selected for the latency portion of the model using cross-validation. NULL when fdr_control is TRUE.

max_c

Maximum C-statistic achieved

max_auc

Maximum AUC for cure prediction achieved; only output when measure_inc = "auc".

selected_index_inc

Indices of selected variables for the incidence portion of the model when fdr_control = TRUE. If none selected, int(0) will be returned.

selected_index_lat

Indices of selected variables for the latency portion of the model when fdr_control = TRUE. If none selected, int(0) will be returned.

call

the matched call.

References

Fu, H., Nicolet, D., Mrozek, K., Stone, R. M., Eisfeld, A. K., Byrd, J. C., Archer, K. J. (2022) Controlled variable selection in Weibull mixture cure models for high-dimensional data. Statistics in Medicine, 41(22), 4340–4366.

Hastie, T., Taylor J., Tibshirani R., Walther G. (2007) Forward stagewise regression and the monotone lasso. Electron J Stat, 1:1–29.

See also

curegmifs

Examples

library(survival)
withr::local_seed(123)
temp <- generate_cure_data(n = 100, j = 15, n_true = 3, a = 1.8, rho = 0.2)
training <- temp$training

fit.cv <- cv_curegmifs(Surv(Time, Censor) ~ .,
  data = training,
  x_latency = training, fdr_control = FALSE,
  maxit = 450, epsilon = 0.01, n_folds = 2,
  seed = 23, verbose = TRUE
)
#> Fold 1 out of 2 training...
#> Fold 2 out of 2 training...
#> Selected step: 27
#> Maximum C-statistic: 0.674984053587647
#> Fitting a final model...