Package {EMGCR}

Fit a Mixture Cure Rate (MCR) Survival Model

Description

Fits a mixture cure rate model by the Expectation-Maximization (EM) algorithm, with a flexible link function for the incidence (cure) component and a choice of survival distributions for the latency component.

Usage

MCRfit(
  formula,
  data,
  dist = "weibull",
  link = "logit",
  tau = 1,
  maxit = 1000,
  tol = 1e-05
)

Arguments

Details

In the latency component, the covariates enter through the scale parameter \lambda_i = \exp(x_i^\top \beta), as in an accelerated failure time model (the same convention as survreg). A positive coefficient therefore means longer survival times for uncured individuals. With shape parameter \alpha, the survival functions of the uncured are:

• exponential: S(t) = \exp(-t/\lambda);

• Rayleigh: S(t) = \exp\{-(t/\lambda)^2\};

• Weibull: S(t) = \exp\{-(t/\lambda)^\alpha\};

• log-normal: \log T \sim N(\log \lambda, \alpha^2);

• log-logistic: S(t) = 1/\{1 + (t/\lambda)^\alpha\};

• inverse Gaussian: mean \lambda and shape \alpha.

Value

An object of class "MCR", which is a list containing:

Examples

require(EMGCR)

data(liver)
names(liver)
liver$sex <- factor(liver$sex)
liver$grade <- factor(liver$grade)
liver$radio <- factor(liver$radio)
liver$chemo <- factor(liver$chemo)
str(liver)
model <- MCRfit(
  survival::Surv(time, status) ~ age + sex + grade + radio + chemo |
    age + medh + grade + radio + chemo,
  dist = "loglogistic",
  link = "plogit",
  tau = 0.15,
  data = liver
)
summary(model)

Liver Cancer Data

Description

A sample of 1,736 patients who have been diagnosed with liver cancer between 2012 and 2016, whose cancer grades are well identified. Available individual-level covariates include age at diagnosis, sex, race, grade of liver cancer, median household income, radiation indicator, and chemotherapy indicator. The grade of disease is categorized into four levels: well-differentiated (Grade I), moderately differentiated (Grade II), poorly differentiated (Grade III), and undifferentiated/anaplastic (Grade IV).

Usage

data(liver)

Format

A data frame with 1,736 observations and 10 variables:

ID

Unique patient identifier

time

Survival time in months

status

Event indicator: death due to liver cancer = 1, censored = 0

sex

Sex of patient: male = 1, female = 0

age

Scaled age of diagnosis

medh

Scaled median household income of the subject

race

Race: white = 1, other = 0

grade

Pathological grade of liver cancer (1 = I, 2 = II, 3 = III, 4 = IV)

chemo

Chemotherapy: yes = 1, no = 0

radio

Radiation: yes = 1, no = 0

Examples

data(liver)
head(liver)

Compare fitted MCR models with the Kaplan-Meier curve

Description

Plots the Kaplan-Meier estimate of the survival function together with the population survival function implied by one or more fitted mixture cure rate models.

Usage

## S3 method for class 'MCR'
plot(...)

Arguments

Details

For each model, the fitted population survival function is averaged over the observations,

\hat S_{pop}(t) = \frac{1}{n} \sum_{i=1}^n \{1 - \hat\theta_i + \hat\theta_i \hat S(t \mid x_i)\},

where \hat\theta_i is the estimated probability of being uncured and \hat S(t \mid x_i) is the estimated survival function of the uncured. The Kaplan-Meier curve (dashed) is computed from the data of the first model, so all models should be fitted to the same data. Curves are coloured by latency distribution.

Value

A ggplot object.

QQ-Plot of Residuals for MCR Model

Description

Produces a Q-Q plot of residuals from a Mixture Cure Rate (MCR) model fitted via MCRfit. Optionally, a simulation envelope can be included for Cox-Snell residuals.

Usage

qqMCR(
  object,
  type = c("cox-snell", "quantile"),
  envelope = FALSE,
  nsim = 100,
  censor = NULL,
  ...
)

Arguments

Details

The function generates QQ-plots of either Cox-Snell or quantile residuals. When envelope = TRUE and type = "cox-snell", a simulation envelope is added using Monte Carlo replications.

Value

A QQ-plot is produced as a side effect. Nothing is returned.

See Also

MCRfit, residuals.MCR

Examples

data(liver)
liver$sex <- factor(liver$sex)
liver$grade <- factor(liver$grade)
liver$radio <- factor(liver$radio)
liver$chemo <- factor(liver$chemo)

fit <- MCRfit(
  survival::Surv(time, status) ~ age + sex + grade + radio + chemo |
    age + medh + grade + radio + chemo,
  dist = "loglogistic", link = "plogit", tau = 0.15,
  data = liver
)
qqMCR(fit, type = "quantile", envelope = TRUE, nsim = 50, censor = liver$status)

Generate Random Samples for Mixture Cure Rate (MCR) Model

Description

Simulates survival data from a mixture cure rate model with covariates, a chosen link function for the incidence part and a chosen latency distribution. Censoring times are drawn from a uniform distribution on (0, \code{censor}).

Usage

rMCM(
  n,
  x,
  w,
  censor,
  alpha,
  beta,
  eta,
  dist = "weibull",
  link = "logit",
  tau = 1
)

Arguments

Value

A tibble with columns:

time

Observed (possibly censored) survival time.

status

Event indicator (1 = event, 0 = censored).

x1, x2, ...

Columns of x without the intercept.

w1, w2, ...

Columns of w.

It also has two attributes: "pCcensur", the percentage of cured individuals, and "pUCcensur", the percentage of censored observations among the uncured.

Examples

# Example: Simulating survival data using the inverse Gaussian distribution
library(EMGCR)

n <- 500
beta <- c(1, -1, -2)
eta <- c(0.5, -0.5)
alpha <- 1.5

p <- length(beta)
q <- length(eta)

set.seed(10)
X <- matrix(rnorm(n*(p-1),0,1),n,p-1)
X <- cbind(1,X)

set.seed(20)
W <- matrix(runif(n*q,-1,1),n,q)
W <- scale(W)

max_censoring <- 10

set.seed(1234)
sim_data <- rMCM(n=n, x = X, w = W,
                 censor = max_censoring,
                 beta = beta, eta = eta,
                 alpha = alpha,
                 link = "logit", dist = "invgauss", tau = 1)

names(sim_data)
head(sim_data)
attributes(sim_data)
attr(sim_data, "pCcensur")
attr(sim_data, "pUCcensur")

Compute residuals for MCR model

Description

This function computes Global Cox-Snell and randomized quantile residuals for objects of class MCR.

Usage

## S3 method for class 'MCR'
residuals(object, type = c("cox-snell", "quantile"), ...)

Arguments

Value

A numeric vector of residuals of class "MCRresiduals". Printing it shows the first six residuals and a summary; use as.vector() to drop the class.

Examples

data(liver)
liver$sex <- factor(liver$sex)
liver$grade <- factor(liver$grade)
liver$radio <- factor(liver$radio)
liver$chemo <- factor(liver$chemo)

model <- MCRfit(
  survival::Surv(time, status) ~ age + sex + grade + radio + chemo |
    age + medh + grade + radio + chemo,
  dist = "loglogistic", link = "plogit", tau = 0.15,
  data = liver
)
residuals(model, type = "quantile")