pseudoCure (version 1.0.0)

pCure: Cure Rate Model with pseudo-observation approach

Description

Fits either a mixture cure model or a bounded cumulative hazard (promotion time) model with pseudo-observation approach.

Usage

pCure(
  formula1,
  formula2,
  time,
  status,
  data,
  subset,
  t0,
  model = c("mixture", "promotion"),
  nfolds = 5,
  lambda1 = NULL,
  exclude1 = NULL,
  penalty1 = c("lasso", "scad"),
  lambda2 = NULL,
  exclude2 = NULL,
  penalty2 = c("lasso", "scad"),
  control = list()
)

Value

An object of class "pCure" representing a cure model fit.

Arguments

formula1

A formula object starting with ~ for the model formula. This specifies the covariates in the incidence component and the long-term component under the mixture cure model and the bounded cumulative model, respectively.

formula2

A formula object starting with ~ for the model formula. This specifies the covariates in the latency component and the short-term component under the mixture cure model and the bounded cumulative model, respectively.

time

A numeric vector for the observed survival times.

status

A numeric vector for the event indicator; 0 indicates right-censoring and 1 indicates events.

data

An optional data frame that contains the covariates and response variables (time and event).

subset

An optional logical vector specifying a subset of observations to be used in the fitting process.

t0

A vector of times, where the pseudo-observations are constructed. When not specified, the default values are the 10, 20, ..., 90th percentiles of uncensored event times.

model

A character string specifying the underlying model. The available functional form are "mixture" and "promotion" correspond to the mixture cure model and the bounded cumulative model, respectively.

nfolds

An optional integer value specifying the number of folds. The default value is 5.

lambda1, lambda2

An option for specifying the tuning parameter used in penalization. When this is unspecified or has a NULL value, penalization will not be applied and pCure() will uses all covariates specified in the formulas. Alternatively, this can be specified as a vector numeric vector of non-negative values or "auto" for auto selection.

exclude1, exclude2

A character string specifying which variables to exclude from variable selection. Variables matching elements in this string will not be penalized during the variable selection process. in variable selection.

penalty1, penalty2

A character string specifying the penalty function. The available options are "lasso" and "scad".

control

A list of control parameters. See detail.

References

Su, C.-L., Chiou, S., Lin, F.-C., and Platt, R. W. (2022) Analysis of survival data with cure fraction and variable selection: A pseudo-observations approach Statistical Methods in Medical Research, 31(11): 2037--2053.

Examples

## Function to generate simulated data under the PHMC model
simMC <- function(n) {
  p <- 10
  a <- c(1, 0, -1, 0, 0, 0, 0, 0, 0, 0) # incidence coefs.
  b <- c(-1, 0, 1, 0, 0, 0, 0, 0, 0, 0) # latency coefs.
  X <- data.frame(x = matrix(runif(n * p), n))
  X$x.3 <- 1 * (X$x.3 > .5)
  X$x.4 <- 1 * (X$x.4 > .5)
  X[,5:10] <- apply(X[,5:10], 2, qnorm)  
  time <- -3 * exp(-colSums(b * t(X))) * log(runif(n))
  cure.prob <- 1 / (1 + exp(-2 - colSums(a * t(X))))
  Y <- rbinom(n, 1, cure.prob) 
  cen <- rexp(n, .02)
  dat <- NULL  
  dat$Time <- pmin(time / Y, cen)
  dat$Status <- 1 * (dat$Time == time)
  data.frame(dat, X)
}

## Fix seed and generate data
set.seed(1); datMC <- simMC(200)

## Oracle model with an unpenalized PHMC model
summary(fit1 <- pCure(~ x.1 + x.3, ~ x.1 + x.3, Time, Status, datMC))


## Penalized PHMC model with tuning parameters selected by 10-fold cross validation
## User specifies the range of tuning parameters
summary(fit2 <- pCure(~ ., ~ ., Time, Status, datMC, lambda1 = 1:10 / 10, lambda2 = 1:10 / 10))

## Penalized PHMC model given tuning parameters
summary(update(fit2, lambda1 = 0.7, lambda2 = 0.4))