pseudoCure: A pseudo-observations approach for analyzing survival data with a cure fraction

Description

A collection of easy-to-use tools for regression analysis of survival data with a cure fraction. The modeling framework is based on the Cox proportional hazards mixture cure model and the bounded cumulative hazard model. The pseudo-observations approach is utilized to assess covariate effects and embedded in the variable selection procedure.

Author(s)

Maintainer: Sy Han (Steven) Chiou schiou@smu.edu

Authors:

• Chien-Lin Su marksu740824@gmail.com

• Feng-Chang Lin flin@bios.unc.edu

Dental data for illustration

Description

Data on the survival of teeth with many predictors

Usage

data(Teeth500)

Format

A data frame containing the following variables:

time

tooth survival time subject to right censoring.

event

Tooth loss status: 1 = lost, 0 = not lost.

molar

Molar indicator; 1 = molar tooth, 0 = non-molar tooth.

mobil

Mobility score, on a scale from 0 to 5.

bleed

Bleeding on probing, expressed as a percentage.

plaque

Plaque score, expressed as a percentage.

pocket

Periodontal probing depth.

cal

Clinical Attachment Level.

fgm

Free Gingival Margin.

filled

Number of filled surfaces.

decay_new

New decayed surfaces.

decay_recur

Recurrent decayed surfaces.

crown

Crown indicator; 1 = tooth has a crown, 0 = no crown.

endo

Endodontic therapy indicator; 1 = endo therapy performed, 0 = no endo therapy.

filled_tooth

Filled tooth indicator; 1 = filled, 0 = not filled.

decayed_tooth

Decayed tooth indicator; 1 = decayed, 0 = not decayed.

total_tooth

Total number of teeth.

gender

Gender; 1 = male, 0 = female

diabetes

Diabetes indicator; 1 = diabetes, 0 = no diabetes.

tobacco_ever

Tobacco use indicator; 1 = had tobacco use, 0 = never had tobacco use.

A data frame with 500 observations and 20 variables.

Details

The data is a subset of the original dataset included in the MST package under the name Teeth. This subset contains the time to the first tooth loss due to periodontal reasons.

References

Calhoun, Peter and Su, Xiaogang and Nunn, Martha and Fan, Juanjuan (2018) Constructing Multivariate Survival Trees: The MST Package for R. Journal of Statistical Software, 83(12).

Generalized Estimating Equation with Gaussian family

Description

Fits a generalized estimating equation (GEE) model with Gaussian family with different link functions. The geelm function also supports LASSO or SCAD regularization.

Usage

geelm(
  formula,
  data,
  subset,
  id,
  link = c("identity", "log", "cloglog", "logit"),
  corstr = c("independence", "exchangeable", "ar1"),
  lambda,
  exclude,
  penalty = c("lasso", "scad"),
  nfolds = 5,
  nlambda = 200,
  binit,
  tol = 1e-07,
  maxit = 100
)

Arguments

Value

An object of class "geelm" representing a linear model fit with GEE.

Examples

gendat <- function() {
  id <- gl(50, 4, 200)
  visit <- rep(1:4, 50)
  x1 <- rbinom(200, 1, 0.6)
  x2 <- runif(200, 0, 1)
  phi <- 1 + 2 * x1
  rhomat <- 0.667^outer(1:4, 1:4, function(x, y) abs(x - y))
  chol.u <- chol(rhomat)
  noise <- as.vector(sapply(1:50, function(x) chol.u %*% rnorm(4)))
  e <- sqrt(phi) * noise
  y <- 1 + 3 * x1 - 2 * x2 + e
  dat <- data.frame(y, id, visit, x1, x2)
  dat
}

set.seed(1); str(dat <- gendat())
geelm(y ~ x1 + x2, id = id, data = dat, corstr = "ar1")

Kaplan-Meier estimate

Description

This function exclusively returns the Kaplan-Meier survival estimate and the corresponding time points. It does not provide standard errors or any additional outputs that are typically included with the survfit() function.

Usage

km(time, status)

Arguments

Value

A data frame with the Kaplan-Meier survival estimates, containing:

Examples

data(Teeth500)
km(Teeth500$time, Teeth500$event)

Maller-Zhou test

Description

Performs the Maller-Zhou test.

Usage

mzTest(time, status)

Arguments

Value

A list containing the Maller-Zhou test results, including the test statistic, p-value, and the number of observed events.

Examples

data(Teeth500)
mzTest(Teeth500$time, Teeth500$event)

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()
)

Arguments

Value

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

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))

Package options for pseudoCure

Description

This function provides the fitting options for the pCure() function.

Usage

pCure.control(
  binit1 = NULL,
  binit2 = NULL,
  corstr = c("independence", "exchangeable", "ar1"),
  nlambda1 = 100,
  nlambda2 = 100,
  tol = 1e-07,
  maxit = 100
)

Arguments

Value

A list with control parameters.

See Also

pCure

Plot method for 'geelm' objects

Description

Plot method for 'geelm' objects

Usage

## S3 method for class 'geelm'
plot(x, type = c("residuals", "cv", "trace"), ...)

Arguments

Value

A ggplot object representing the residual plot, cross-validation plot, or the trace plot for an object of class "geelm". This can be further modified using "ggplot2" functions.

Plot method for 'pCure' objects

Description

Plot method for 'pCure' objects

Usage

## S3 method for class 'pCure'
plot(x, part = "both", type = c("residuals", "cv", "trace"), ...)

Arguments

Value

A ggplot object representing the residual plot, cross-validation plot, or the trace plot for an object of class "pCure". This can be further modified using "ggplot2" functions.