curegmifs: Fit penalized parametric mixture cure model using the GMIFS algorithm

Description

Fits a penalized Weibull or exponential mixture cure model using the generalized monotone incremental forward stagewise (GMIFS) algorithm (Hastie et al 2007) and yields solution paths for parameters in the incidence and latency portions of the model.

Usage

curegmifs(
  formula,
  data,
  subset,
  x_latency = NULL,
  model = c("weibull", "exponential"),
  penalty_factor_inc = NULL,
  penalty_factor_lat = NULL,
  epsilon = 0.001,
  thresh = 1e-05,
  scale = TRUE,
  maxit = 10000,
  inits = NULL,
  verbose = TRUE,
  suppress_warning = FALSE,
  na.action = na.omit,
  ...
)

Value

b_path: Matrix representing the solution path of the coefficients in the incidence portion of the model. Row is step and column is variable.
beta_path: Matrix representing the solution path of the coefficients in the latency portion of the model. Row is step and column is variable.
b0_path: Vector representing the solution path of the intercept in the incidence portion of the model.
rate_path: Vector representing the solution path of the rate parameter for the Weibull or exponential density in the latency portion of the model.
logLik: Vector representing the log-likelihood for each step in the solution path.
x_incidence: Matrix representing the design matrix of the incidence predictors.
x_latency: Matrix representing the design matrix of the latency predictors.
y: Vector representing the survival object response as returned by the Surv function
model: Character string indicating the type of regression model used for the latency portion of mixture cure model ("weibull" or "exponential").
scale: Logical value indicating whether the predictors were centered and scaled.
alpha_path: Vector representing the solution path of the shape parameter for the Weibull density in the latency portion of the model.
call: the matched call.
warning: message indicating whether the maximum number of iterations was achieved which may indicate the model did not converge.

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.

epsilon

small numeric value reflecting the 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 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 not supplied or improperly supplied, initialization is automatically provided by the function.

verbose

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

suppress_warning

logical, if TRUE, suppresses echoing the warning that the maximum number of iterations was reached so that the algorithm may not have converged. Instead, warning is returned as part of the output with this message.

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.

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.

Examples

Run this code

library(survival)
withr::local_seed(1234)
temp <- generate_cure_data(n = 100, j = 10, n_true = 10, a = 1.8)
training <- temp$training

fit <- curegmifs(Surv(Time, Censor) ~ .,
  data = training, x_latency = training,
  model = "weibull", thresh = 1e-4, maxit = 2000, epsilon = 0.01,
  verbose = FALSE
)