cureem: Fit penalized mixture cure model using the E-M algorithm

Description

Fits penalized parametric and semi-parametric mixture cure models (MCM) using the E-M algorithm with user-specified penalty parameters. The lasso (L1), MCP, and SCAD penalty are supported for the Cox MCM while only lasso is currently supported for parametric MCMs.

Usage

cureem(
  formula,
  data,
  subset,
  x_latency = NULL,
  model = c("cox", "weibull", "exponential"),
  penalty = c("lasso", "MCP", "SCAD"),
  penalty_factor_inc = NULL,
  penalty_factor_lat = NULL,
  thresh = 0.001,
  scale = TRUE,
  maxit = NULL,
  inits = NULL,
  lambda_inc = 0.1,
  lambda_lat = 0.1,
  gamma_inc = 3,
  gamma_lat = 3,
  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.
logLik_inc: Vector representing the expected penalized complete-data log-likelihood for the incidence portion of the model for each step in the solution path.
logLik_lat: Vector representing the expected penalized complete-data log-likelihood for the latency portion of the model 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.
method: Character string indicating the EM algorithm was used in fitting the mixture cure 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.
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.

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 "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.

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

integer specifying the 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 values. This includes:

itct the incidence intercept.
b_u a numeric vector for the unpenalized incidence coefficients for the incidence portion of the model.
beta_u a numeric vector for unpenalized latency coefficients in the incidence portion of the model.
lambda a numeric value for the rate parameter when fitting either a Weibull or exponential MCM using model = "weibull" or model = "exponential".
alpha a numeric value for the shape parameter when fitting a Weibull MCM using model = "weibull".
survprob a numeric vector for the latency survival probabilities \(S_u(t_i|w_i)\) for i=1,...,N when fitting a Cox MCM model = "cox".

Penalized coefficients are initialized to zero. If inits is not specified or improperly specified, initialization is automatically provided by the function.

lambda_inc

numeric value for the penalization parameter \(\lambda\) for variables in the incidence portion of the model.

lambda_lat

numeric value for the penalization parameter \(\lambda\) for variables in the latency portion of the model.

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).

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

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.

Examples

Run this code

library(survival)
withr::local_seed(1234)
temp <- generate_cure_data(n = 80, j = 100, n_true = 10, a = 1.8)
training <- temp$training
fit <- cureem(Surv(Time, Censor) ~ .,
  data = training, x_latency = training,
  model = "cox", penalty = "lasso", lambda_inc = 0.1,
  lambda_lat = 0.1, gamma_inc = 6, gamma_lat = 10
)