cv_cureem {hdcuremodels}

Fit penalized mixture cure model using the E-M algorithm with cross-validation for parameter tuning

Description

Fits a penalized parametric and semi-parametric mixture cure model (MCM) using the E-M algorithm with with k-fold cross-validation for parameter tuning. The lasso (L1), MCP and SCAD penalty are supported for the Cox MCM while only lasso is currently supported for parametric MCMs. When FDR controlled variable selection is used, the model-X knockoffs method is applied and indices of selected variables are returned.

Usage

cv_cureem(
  formula,
  data,
  subset,
  x.latency = NULL,
  model = "cox",
  penalty = "lasso",
  penalty.factor.inc = NULL,
  penalty.factor.lat = NULL,
  fdr.control = FALSE,
  fdr = 0.2,
  grid.tuning = FALSE,
  thresh = 0.001,
  scale = TRUE,
  maxit = NULL,
  inits = NULL,
  lambda.inc.list = NULL,
  lambda.lat.list = NULL,
  nlambda.inc = NULL,
  nlambda.lat = NULL,
  gamma.inc = 3,
  gamma.lat = 3,
  lambda.min.ratio.inc = 0.1,
  lambda.min.ratio.lat = 0.1,
  n_folds = 5,
  measure.inc = "c",
  one.se = FALSE,
  cure_cutoff = 5,
  parallel = FALSE,
  seed = NULL,
  verbose = TRUE,
  ...
)

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.

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 "cox", "weibull", or "exponential" (default is "cox").

penalty

type of penalty function. Can be "lasso", "MCP", or "SCAD" (default is "lasso").

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).

grid.tuning

logical, if TRUE a 2-D grid tuning approach is used to select the optimal pair of \lambda_b and \lambda_{\beta} penalty parameters for the incidence and latency portions of the model, respectively. Otherwise the \lambda_b and \lambda_{\beta} are selected from a 1-D sequence and are equal to one another (default is FALSE).

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^-3).

scale

logical, if TRUE the predictors are centered and scaled.

maxit

maximum number of passes over the data for each lambda. If not specified, 100 is applied when penalty = "lasso" and 1000 is applied when penalty = "MCP" or penalty = "SCAD".

inits

an optional list specifiying the initial value for the incidence intercept (itct), a numeric vector for the unpenalized incidence coefficients (b_u), and a numeric vector for unpenalized latency coefficients (beta_u). For parametric models, it should also include a numeric value for the rate parameter (lambda) when model = "weibull" or model = "exponential", and a numeric value for the shape parameter (alpha) when model = "weibull". When model = "cox", it should also include a numeric vector for the latency survival probabilities S_u(t_i|w_i) for i=1,...,N (survprob). Penalized coefficients are initialized to zero. If inits is not specified or improperly specified, initialization is automatically provided by the function.

lambda.inc.list

a numeric vector used to search for the optimal \lambda_b tuning parameter. If not supplied, the function computes a \lambda_b sequence based on nlambda.inc and lambda.min.ratio.inc. If grid.tuning=FALSE, the same sequence should be used for both \lambda_b and \lambda_{\beta}.

lambda.lat.list

a numeric vector used to search for the optimal \lambda_{\beta} tuning parameter. If not supplied, the function computes a \lambda_{\beta} sequence based on nlambda.lat and lambda.min.ratio.lat. If grid.tuning=FALSE, the same sequence should be used for both \lambda_b and \lambda_{\beta}.

nlambda.inc

an integer specifying the number of values to search for the optimal \lambda_b tuning parameter; default is 10 if grid.tuning=TRUE and 50 otherwise.

nlambda.lat

an integer specifying the number of values to search for the optimal \lambda_{\beta} tuning parameter; default is 10 if grid.tuning=TRUE and 50 otherwise.

gamma.inc

numeric value for the penalization parameter \gamma for variables in the incidence portion of the model when penalty = "MCP" or penalty = "SCAD" (default is 3).

gamma.lat

numeric value for the penalization parameter \gamma for variables in the latency portion of the model when penalty = "MCP" or penalty = "SCAD" (default is 3).

lambda.min.ratio.inc

numeric value in (0,1) representing the smallest value for \lambda_b as a fraction of lambda.max.inc, the data-derived entry value at which essentially all penalized variables in the incidence portion of the model have a coefficient estimate of 0 (default is 0.1).

lambda.min.ratio.lat

numeric value in (0.1) representing the smallest value for \lambda_{\beta} as a fraction of lambda.max.lat, the data-derived entry value at essentially all penalized variables in the latency portion of the model have a coefficient estimate of 0 (default is 0.1).

n_folds

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

measure.inc

character string specifying the evaluation criterion used in selecting the optimal \lambda_b. Can be "c" or "auc"; default is "c". If measure.inc="c", the C-statistic using the cure status weighting (CSW) method proposed by Asano and Hirakawa (2017) is used to select both \lambda_b and \lambda_{\beta}. If measure.inc="auc", the AUC for cure prediction using the mean score imputation (MSI) method proposed by Asano et al. (2014) is used 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 doMC 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).

...

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.inc

Expected penalized complete-data log-likelihood for the incidence portion of the model.

logLik.lat

Expected penalized complete-data log-likelihood for the latency portion of the model.

selected.lambda.inc

Value of \lambda_b selected using cross-validation. NULL when fdr.control is TRUE.

selected.lambda.lat

Value of \lambda_{\beta} selected 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 no variables are 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 no variables are selected, int(0) will be returned.

call

the matched call.

References

Archer, K. J., Fu, H., Mrozek, K., Nicolet, D., Mims, A. S., Uy, G. L., Stock, W., Byrd, J. C., Hiddemann, W., Braess, J., Spiekermann, K., Metzeler, K. H., Herold, T., Eisfeld, A.-K. (2024) Identifying long-term survivors and those at higher or lower risk of relapse among patients with cytogenetically normal acute myeloid leukemia using a high-dimensional mixture cure model. Journal of Hematology & Oncology, 17:28.

See Also

cureem

Examples

library(survival)
set.seed(1234)
temp <- generate_cure_data(N = 200, J = 25, nTrue = 5, A = 1.8)
training <- temp$Training
fit.cv <- cv_cureem(Surv(Time, Censor) ~ ., data = training,
                 x.latency = training, fdr.control = FALSE,
                 grid.tuning = FALSE, nlambda.inc = 10, nlambda.lat = 10,
                 n_folds = 2, seed = 23, verbose = TRUE)
fit.cv.fdr <- cv_cureem(Surv(Time, Censor) ~ ., data = training,
                 x.latency = training, model = "weibull", penalty = "lasso",
                 fdr.control = TRUE, grid.tuning = FALSE, nlambda.inc = 10,
                 nlambda.lat = 10, n_folds = 2, seed = 23, verbose = TRUE)