Package 'EMGCR'

Liver Cancer Data

Description

A sample of 2,766 patients diagnosed with liver cancer between 2012 and 2016, whose cancer grades were well identified. Available individual-level covariates include age at diagnosis, sex, pathological grade of the liver cancer, number of relapses, and median household income.

Usage

data(liver)

Format

A data frame with 2,766 observations and 10 variables:

ID

Unique patient identifier

age

Age as a factor (e.g., age group)

ageNumeric

Age as a numeric variable

grade

Pathological grade of liver cancer (I, II, III, IV)

medh

Median household income as factor (possibly grouped)

medhNumeric

Median household income as numeric

relapse

Number of relapses after first diagnosis

sex

Sex of patient: 1 = male, 0 = female

status

Event indicator: 1 = death, 0 = censored

time

Survival time in months

Details

The grade of the disease is categorized into four levels:

1. Grade I – Well differentiated

2. Grade II – Moderately differentiated

3. Grade III – Poorly differentiated

4. Grade IV – Undifferentiated/anaplastic

Examples

data(liver)
head(liver)

---

Liver Cancer Data 2

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, time to treatment, tumor size, radiation indicator, and chemotherapy indicator. The grade of diseas is categorized into four levels: well-differentiated (Grade I), moderately differentiated (Grade II), poorly differentiated (Grade III), and undifferentiated/anaplastic (Grade IV).

Usage

data(liver2)

Format

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

ID

Unique patient identifier

time

Survival time in months

status

censored = 0, dead due to liver cancer = 1

sex

Sex of patient: Male=1, Female=0

age

Scaled age of diagnosis

medh

Scaled median household income of the subject

race

While = 1, Other = 0

grade

Pathological grade of liver cancer

chemo

chemotherapy = 1, non = 0

radio

radiation = 1, non = 0

Examples

data(liver2)
head(liver2)

---

Fit a Mixture Cure Rate (MCR) Survival Model

Description

Fits a cure rate model using a flexible link function and a variety of survival distributions. The model accounts for a cured fraction through a logistic-type link and estimates the model via an EM-like algorithm.

Usage

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

Arguments

formula	A two-part formula of the form Surv(time, status) ~ x | w, where x are covariates for the survival part, and w are covariates for the cure fraction.
data	A data frame containing the variables in the model.
dist	A character string indicating the baseline distribution. Supported values are "weibull", "exponential", "rayleigh", "lognormal", "loglogistic", and "invgauss".
link	A character string specifying the link function for the cure fraction. Options are "logit", "probit", "plogit", "rplogit", and "cauchit".
tau	A numeric value used when link = "plogit" or "rplogit". Defaults to 1.
maxit	Maximum number of iterations for the EM-like algorithm. Defaults to 1000.
tol	Convergence tolerance. Defaults to 1e-5.

Value

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

coefficients	Estimated regression coefficients for the survival part.
coefficients_cure	Estimated coefficients for the cure part.
scale	Estimated scale parameter of the baseline distribution.
loglik	Final log-likelihood value.
n	Number of observations used in the model.
deleted	Number of incomplete cases removed before fitting.
ep	Estimated standard errors.
iter	Number of iterations used for convergence.
dist	Distribution used.
link	Link function used.
tau	Tau parameter used (if applicable).

Examples

require(EMGCR)

data(liver2)
names(liver2)
liver2$sex <- factor(liver2$sex)
liver2$grade <- factor(liver2$grade)
liver2$radio <- factor(liver2$radio)
liver2$chemo <- factor(liver2$chemo)
str(liver2)
model <- MCRfit(
  survival::Surv(time, status) ~ age + sex + grade + radio + chemo |
    age + medh + grade + radio + chemo,
  dist = "loglogistic",
  link = "plogit",
  tau = 0.15,
  data = liver2
)
model

---

Plot multiple MCR model fits against Kaplan-Meier curve

Description

Plot multiple MCR model fits against Kaplan-Meier curve

Usage

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

Arguments

...	One or more fitted MCR objects from MCRfit().

Value

A ggplot object with Kaplan-Meier and survival curves for each model.

---

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

object	An object of class MCR, typically returned by MCRfit.
type	Character. Type of residual to use in the QQ-plot. Options are "cox-snell" or "quantile". Defaults to "cox-snell".
envelope	Logical. Whether to add a simulation envelope to the QQ-plot. Default is FALSE.
nsim	Integer. Number of simulations used to construct the envelope. Default is 100.
censor	Logical vector or NULL. Censoring indicator used when simulating data for the envelope. Required only when envelope = TRUE and type = "cox-snell".
...	Additional arguments (currently ignored).

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)
fit <- MCRfit(survival::Surv(time, status) ~ age + medh + relapse + grade | sex + grade,
              data = liver, dist = "weibull", link = "logit")
qqMCR(fit, type = "quantile", envelope = TRUE, nsim = 50, censor = liver$status)

---

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

object	An object of class MCR, typically returned from MCRfit.
type	Type of residual.
...	Additional arguments (not used).

Value

A numeric vector of residuals.

Examples

data(liver)
names(liver)

model <- MCRfit(
 survival::Surv(time, status) ~ age + medh + relapse + grade | sex + age + medh + grade,
 data = liver
)
summary(residuals(model,type="quantile"))

---

Generate Random Samples for Mixture Cure Rate (MCR) Model

Description

Simulates survival data from a mixture cure rate model with covariates and user-defined link and latency distributions. Censoring is applied randomly.

Usage

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

Arguments

n	Integer. Number of observations to simulate.
x	Matrix or numeric. Covariate matrix for the latency component (must include intercept if needed).
w	Matrix or numeric. Covariate matrix for the cure component (no intercept assumed).
censor	Numeric. Maximum censoring time (uniformly distributed).
alpha	Numeric. Shape parameter for the survival distribution.
beta	Numeric vector. Coefficients for the latency part.
eta	Numeric vector. Coefficients for the cure part.
dist	Character. Distribution for the latency part. Options: "weibull", "lognormal", "loglogistic", "invgauss", "exponential", "rayleigh".
link	Character. Link function for cure component. Options: "logit", "probit","plogit" ,"rplogit", "cauchit".
tau	A numeric value used when link = "plogit" or "rplogit". Defaults to 1.

Value

A list with elements:

time

Observed (possibly censored) survival time.

status

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

x

Covariate matrix for the latency component.

w

Covariate matrix for the cure component.

pCcensur

Percentage of cured individuals.

pUCcensur

Percentage of censored cases 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")

---