View source: R/TTTE_Analytical.R
TTTE_Analytical | R Documentation |
This function allows to compute the TTT curve from a formula containing a factor type variable (classification variable).
TTTE_Analytical(
formula,
response = NULL,
scaled = TRUE,
data = NULL,
method = c("Barlow", "censored"),
partition_method = NULL,
silent = FALSE,
...
)
formula |
an object of class |
response |
an optional numeric vector with data of the response variable.
Using this argument is equivalent to define a formula with the
right side such as |
scaled |
logical. If |
data |
an optional data frame containing the variables (response and the
factor, if it is desired). If data is not specified, the variables
are taken from the environment from which |
method |
a character specifying the method of computation. There are two
options available: |
partition_method |
a list specifying cluster formation when the covariate in
|
silent |
logical. If TRUE, warnings of |
... |
further arguments passing to |
When method
argument is set as 'Barlow'
, this function
uses the original expression of empirical TTT presented by
\insertCiteBarlow1979;textualEstimationTools and used by
\insertCiteAarset1987;textualEstimationTools:
\phi_n\left( \frac{r}{n}\right) = \frac{\left( \sum_{i=1}^{r} T_{(i)} \right) +
(n-r)T_{(r)}}{\sum_{i=1}^{n} T_i}
where T_{(r)}
is the r^{th}
order statistic, with
r=1,2,\dots, n
, and n
is the sample size. On the other hand, the option
'censored' is an implementation based on integrals presented in
\insertCiteWestberg1994;textualEstimationTools, and using
survfit
to compute the Kaplan-Meier estimator:
\phi_n\left( \frac{r}{n}\right) = \sum_{j=1}^{r} \left[ \prod_{i=1}^{j}
\left( 1 - \frac{d_i}{n_i}\right) \right] \left(T_{(j)} - T_{(j-1)} \right)
A list with class object Empirical.TTT
containing a list with the
following information:
i/n' |
A matrix containing the empirical quantiles. This matrix has the number of columns equals to the number of levels of the factor considered (number of strata). |
phi_n |
A matrix containing the values of empirical TTT. his matrix has the number of columns equals to the number of levels of the factor considered (number of strata). |
strata |
A numeric named vector storing the number of observations per strata, and the name of each strata (names of the levels of the factor). |
Jaime Mosquera GutiƩrrez, jmosquerag@unal.edu.co
Barlow1979EstimationTools
\insertRefAarset1987EstimationTools
\insertRefKlefsjo1991EstimationTools
\insertRefWestberg1994EstimationTools
plot.EmpiricalTTT
library(EstimationTools)
#--------------------------------------------------------------------------------
# Example 1: Scaled empirical TTT from 'mgus1' data from 'survival' package.
TTT_1 <- TTTE_Analytical(Surv(stop, event == 'pcm') ~1, method = 'cens',
data = mgus1, subset=(start == 0))
head(TTT_1$`i/n`)
head(TTT_1$phi_n)
print(TTT_1$strata)
#--------------------------------------------------------------------------------
# Example 2: Scaled empirical TTT using a factor variable with 'aml' data
# from 'survival' package.
TTT_2 <- TTTE_Analytical(Surv(time, status) ~ x, method = "cens", data = aml)
head(TTT_2$`i/n`)
head(TTT_2$phi_n)
print(TTT_2$strata)
#--------------------------------------------------------------------------------
# Example 3: Non-scaled empirical TTT without a factor (arbitrarily simulated
# data).
set.seed(911211)
y <- rweibull(n=20, shape=1, scale=pi)
TTT_3 <- TTTE_Analytical(y ~ 1, scaled = FALSE)
head(TTT_3$`i/n`)
head(TTT_3$phi_n)
print(TTT_3$strata)
#--------------------------------------------------------------------------------
# Example 4: non-scaled empirical TTT without a factor (arbitrarily simulated
# data) using the 'response' argument (this is equivalent to Third example).
set.seed(911211)
y <- rweibull(n=20, shape=1, scale=pi)
TTT_4 <- TTTE_Analytical(response = y, scaled = FALSE)
head(TTT_4$`i/n`)
head(TTT_4$phi_n)
print(TTT_4$strata)
#--------------------------------------------------------------------------------
# Eample 5: empirical TTT with a continuously variant term for the shape
# parameter in Weibull distribution.
x <- runif(50, 0, 10)
shape <- 0.1 + 0.1*x
y <- rweibull(n = 50, shape = shape, scale = pi)
partitions <- list(method='quantile-based',
folds=5)
TTT_5 <- TTTE_Analytical(y ~ x, partition_method = partitions)
head(TTT_5$`i/n`)
head(TTT_5$phi_n)
print(TTT_5$strata)
plot(TTT_5) # Observe changes in Empirical TTT
#--------------------------------------------------------------------------------
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