Weibull Regression for a Right-Censored Endpoint with Interval-Censored Covariates

Description

The function SurvRegCens of this package allows estimation of a Weibull Regression for a right-censored endpoint, one interval-censored covariate, and an arbitrary number of non-censored covariates. Additional functions allow to switch between different parametrizations of Weibull regression used by different R functions (ConvertWeibull, WeibullReg, WeibullDiag), inference for the mean difference of two arbitrarily censored Normal samples (NormalMeanDiffCens), and estimation of canonical parameters from censored samples for several distributional assumptions (ParamSampleCens).

Details

Author(s)

Stanislas Hubeaux (maintainer), stan.hubeaux@bluewin.ch

Kaspar Rufibach, kaspar.rufibach@gmail.com
http://www.kasparrufibach.ch

We thank Sarah Haile for contributing the functions ConvertWeibull, WeibullReg, WeibullDiag to the package.

References

Hubeaux, S. (2013). Estimation from left- and/or interval-censored samples. Technical report, Biostatistics Oncology, F. Hoffmann-La Roche Ltd.

Hubeaux, S. (2013). Parametric Surival Regression Model with left- and/or interval-censored covariate. Technical report, Biostatistics Oncology, F. Hoffmann-La Roche Ltd.

Hubeaux, S. and Rufibach, K. (2014). SurvRegCensCov: Weibull Regression for a Right-Censored Endpoint with a Censored Covariate. Preprint, https://arxiv.org/abs/1402.0432.

Lynn, H. S. (2001). Maximum likelihood inference for left-censored HIV RNA data. Stat. Med., 20, 33–45.

Sattar, A., Sinha, S. K. and Morris, N. J. (2012). A Parametric Survival Model When a Covariate is Subject to Left-Censoring. Biometrics & Biostatistics, S3(2).

Examples

# The main functions in this package are illustrated in their respective help files.

Cumulative distribution function

Description

Evaluates the cumulative distribution function using the integral of its density function.

Usage

CDF(c, density)

Arguments

Note

Function not intended to be invoked by the user.

Author(s)

Stanislas Hubeaux, stan.hubeaux@bluewin.ch

Kaspar Rufibach, kaspar.rufibach@gmail.com
http://www.kasparrufibach.ch

Transformation of survreg output for the Weibull distribution

Description

Transforms output from survreg using the Weibull distribution to a more natural parameterization. See details and the vignette for more information.

Usage

ConvertWeibull(model, conf.level = 0.95)

Arguments

Details

The survreg function fits a Weibull accelerated failure time model of the form

\log t = \mu + \alpha^T Z + \sigma W,

where Z is a matrix of covariates, and W has the extreme value distribution, \mu is the intercept, \alpha is a vector of parameters for each of the covariates, and \sigma is the scale. The usual parameterization of the model, however, is defined by hazard function

h(t|Z) = \gamma \lambda t^{\gamma - 1} \exp(\beta^T Z).

The transformation is as follows: \gamma = 1/\sigma, \lambda = \exp(-\mu/\sigma), and \beta=-\alpha/\sigma, and estimates of the standard errors can be found using the delta method.

The Weibull distribution has the advantage of having two separate interpretations. The first, via proportional hazards, leads to a hazard ratio, defined by \exp \beta. The second, of accelerated failure times, leads to an event time ratio (also known as an acceleration factor), defined by \exp (-\beta/\gamma).

Further details regarding the transformations of the parameters and their standard errors can be found in Klein and Moeschberger (2003, Chapter 12). An explanation of event time ratios for the accelerated failure time interpretation of the model can be found in Carroll (2003). A general overview can be found in the vignette("weibull") of this package.

Value

Author(s)

Sarah R. Haile, Epidemiology, Biostatistics and Prevention Institute (EBPI), University of Zurich, sarah.haile@uzh.ch

References

Carroll, K. (2003). On the use and utility of the Weibull model in the analysis of survival data. Controlled Clinical Trials, 24, 682–701.

Klein, J. and Moeschberger, M. (2003). Survival analysis: techniques for censored and truncated data. 2nd edition, Springer.

See Also

This function is used by WeibullReg.

Examples

data(larynx)
ConvertWeibull(survreg(Surv(time, death) ~ stage + age, larynx), conf.level = 0.95)

Log-likelihood functions for estimation of canonical parameters from a censored sample

Description

Computes the log-likelihood function for a censored sample, according to a specified distributional assumptions. Available distributions are Normal, Weibull, Logistic, and Gamma.

Usage

LoglikNormalCens(x, data, lowerbound, vdelta)
LoglikWeibullCens(x, data, lowerbound, vdelta)
LoglikLogisticCens(x, data, lowerbound, vdelta)
LoglikGammaCens(x, data, lowerbound, vdelta)

Arguments

Note

Function not intended to be invoked by the user.

Author(s)

Stanislas Hubeaux, stan.hubeaux@bluewin.ch

Kaspar Rufibach, kaspar.rufibach@gmail.com
http://www.kasparrufibach.ch

References

Hubeaux, S. (2013). Estimation from left- and/or interval-censored samples. Technical report, Biostatistics Oncology, F. Hoffmann-La Roche Ltd.

Lynn, H. S. (2001). Maximum likelihood inference for left-censored HIV RNA data. Stat. Med., 20, 33–45.

Log likelihood function to compute mean difference between two normally distributed censored samples.

Description

Reparametrization of the log likelihood function for a normally distributed censored sample such that the mean difference is a parameter of the function, thus allowing to be made inference on. The mean difference is computed as sample 1 - sample 2.

Usage

LoglikNormalDeltaCens(x, data1, lowerbound1, vdelta1, data2,
                      lowerbound2, vdelta2)

Arguments

Note

Function not intended to be invoked by the user.

Author(s)

Stanislas Hubeaux, stan.hubeaux@bluewin.ch

Kaspar Rufibach, kaspar.rufibach@gmail.com
http://www.kasparrufibach.ch

References

Hubeaux, S. (2013). Estimation from left- and/or interval-censored samples. Technical report, Biostatistics Oncology, F. Hoffmann-La Roche Ltd.

Lynn, H. S. (2001). Maximum likelihood inference for left-censored HIV RNA data. Stat. Med., 20, 33–45.

Log-likelihood function of a Weibull Survival Regression Model allowing for an interval-censored covariate.

Description

Computes the log-likelihood function of a Weibull Survival Regression Model allowing for an interval-censored covariate.

Usage

LoglikWeibullSurvRegCens(x, data_y, data_delta_loglik, data_cov_noncens = NULL, 
                         data_cov_cens, density, data_r_loglik, data_lowerbound,
                         intlimit = 10^-10)

Arguments

Note

Function not intended to be invoked by the user.

Author(s)

Stanislas Hubeaux, stan.hubeaux@bluewin.ch

Kaspar Rufibach, kaspar.rufibach@gmail.com
http://www.kasparrufibach.ch

References

Hubeaux, S. (2013). Parametric Surival Regression Model with left- and/or interval-censored covariate. Technical report, Biostatistics Oncology, F. Hoffmann-La Roche Ltd.

Sattar, A., Sinha, S. K. and Morris, N. J. (2012). A Parametric Survival Model When a Covariate is Subject to Left-Censoring. Biometrics & Biostatistics, S3(2).

Maximum Likelihood Estimator for the mean difference between two censored normally distributed samples

Description

Computes estimates of the parameters of two censored Normal samples, as well as the mean difference between the two samples.

Usage

NormalMeanDiffCens(censdata1, censdata2, conf.level = 0.95, 
     null.values = c(0, 0, 1, 1))

Arguments

Value

A table with estimators and inference for the means and standard deviations of both samples, as well as the difference \Delta between the mean of the first and second sample. Hypothesis tests are for the values in null.values and for the null hypothesis of no mean difference.

Author(s)

Stanislas Hubeaux, stan.hubeaux@bluewin.ch

Kaspar Rufibach, kaspar.rufibach@gmail.com
http://www.kasparrufibach.ch

References

Hubeaux, S. (2013). Estimation from left- and/or interval-censored samples. Technical report, Biostatistics Oncology, F. Hoffmann-La Roche Ltd.

Lynn, H. S. (2001). Maximum likelihood inference for left-censored HIV RNA data. Stat. Med., 20, 33–45.

Examples

## example with interval-censored Normal samples
n <- 500
prop.cens <- 0.35
mu <- c(0, 2)
sigma <- c(1, 1)

set.seed(2013)

## Sample 1:
LOD1 <- qnorm(prop.cens, mean = mu[1], sd = sigma[1])
x1 <- rnorm(n, mean = mu[1], sd = sigma[1])
s1 <- censorContVar(x1, LLOD = LOD1)

## Sample 2:
LOD2 <- qnorm(0.35, mean = mu[2], sd = sigma[2])
x2 <- rnorm(n, mean = mu[2], sd = sigma[2])
s2 <- censorContVar(x2, LLOD = LOD2)

## inference on distribution parameters and mean difference:
NormalMeanDiffCens(censdata1 = s1, censdata2 = s2)

Maximum Likelihood Estimator of parameters from a censored sample

Description

Computes maximum likelihood estimators of the canonical parameters for several distributions, based on a censored sample.

Usage

ParamSampleCens(censdata, dist = c("normal", "logistic", "gamma", "weibull")[1], 
     null.values = c(0, 1), conf.level = 0.95, initial = NULL)

Arguments

Value

Note

Functions with similar functionality are provided in the package fitdistrplus.

Author(s)

Stanislas Hubeaux, stan.hubeaux@bluewin.ch

Kaspar Rufibach, kaspar.rufibach@gmail.com
http://www.kasparrufibach.ch

References

Hubeaux, S. (2013). Estimation from left- and/or interval-censored samples. Technical report, Biostatistics Oncology, F. Hoffmann-La Roche Ltd.

Lynn, H. S. (2001). Maximum likelihood inference for left-censored HIV RNA data. Stat. Med., 20, 33–45.

Examples

n <- 500
prop.cens <- 0.35

## example with a left-censored Normally distributed sample
set.seed(2013)
mu <- 3.5
sigma <- 1
LOD <- qnorm(prop.cens, mean = mu, sd = sigma)
x1 <- rnorm(n, mean = mu, sd = sigma)
s1 <- censorContVar(x1, LLOD = LOD)
ParamSampleCens(censdata = s1)


## example with an interval-censored Normal sample
set.seed(2013)
x2 <- rnorm(n, mean = mu, sd = sigma)
LOD <- qnorm(prop.cens / 2, mean = mu, sd = sigma)
UOD <- qnorm(1 - prop.cens / 2, mean = mu, sd = sigma)
s2 <- censorContVar(x2, LLOD = LOD, ULOD = UOD)
ParamSampleCens(censdata = s2)


## Not run: 
## compare to fitdistrplus
library(fitdistrplus)
s2 <- as.data.frame(s2)
colnames(s2) <- c("left", "right")
summary(fitdistcens(censdata = s2, distr = "norm"))

## End(Not run)

Weibull Survival Regression Model with a censored covariate

Description

Computes estimators for the shape and scale parameter of the Weibull distribution, as well as for the vector of regression parameters in a parametric survival model with potentially right-censored time-to-event endpoint distributed according to a Weibull distribution. The regression allows for one potentially interval-censored and an arbitrary number of non-censored covariates.

Usage

SurvRegCens(formula, data = parent.frame(), Density, initial, conf.level = 0.95, 
          intlimit = 10^-10, namCens = "VarCens", trace = 0, reltol = 10^-8)

Arguments

Details

The time-to-event distributed according to a Weibull distribution, i.e. time-to-event \sim Weibull(\lambda,\gamma), has conditional density given by,

f_{Y_i}(t|\mathbf{x}_i,\boldsymbol{\beta}) =\gamma \lambda t^{\gamma-1} \exp\left(\mathbf{x}_i\boldsymbol{\beta}\right)\exp\left( - \lambda t^{\gamma} \exp\left(\mathbf{x}_i\boldsymbol{\beta}\right) \right),

conditional hazard function given by,

h_i(t|\mathbf{x}_i,\boldsymbol{\beta})= \lambda \gamma t^{\gamma-1} \exp\left( \mathbf{x}_i\boldsymbol{\beta} \right),

and conditional survival function given by,

S_i(t|\mathbf{x}_i,\boldsymbol{\beta}) = \exp\left(-\lambda t^{\gamma} \exp\left(\mathbf{x}_i\boldsymbol{\beta}\right)\right),

where \mathbf{x}_i collects the values of each covariate for observation i and \boldsymbol{\beta} represents the regression parameters.

Value

SurvRegCens returns an object of class "src", a list containing the following components:

The methods print.src, summary.src, coef.src, and logLik.src are used to print or obtain a summary, coefficients, or the value of the log-likelihood at the maximum.

Author(s)

Stanislas Hubeaux, stan.hubeaux@bluewin.ch

Kaspar Rufibach, kaspar.rufibach@gmail.com
http://www.kasparrufibach.ch

References

Hubeaux, S. (2013). Parametric Surival Regression Model with left- and/or interval-censored covariate. Technical report, Biostatistics Oncology, F. Hoffmann-La Roche Ltd.

Hubeaux, S. and Rufibach, K. (2014). SurvRegCensCov: Weibull Regression for a Right-Censored Endpoint with a Censored Covariate. Preprint, https://arxiv.org/abs/1402.0432.

Sattar, A., Sinha, S. K. and Morris, N. J. (2012). A Parametric Survival Model When a Covariate is Subject to Left-Censoring. Biometrics & Biostatistics, S3(2).

Examples

## Not run: 
## --------------------------------------------------------------
## 1 censored-covariate and 2 non-censored covariates 
## no censoring, to compare result with survival::survreg
## modify prop.cens to introduce left-censoring of covariate
## --------------------------------------------------------------

set.seed(158)
n <- 100
lambda <- exp(-2)
gamma <- 1.5

## vector of regression parameters: the last entry is the one for the censored covariate
beta <- c(0.3, -0.2, 0.25) 
true <- c(lambda, gamma, beta)

## non-censored covariates
var1 <- rnorm(n, mean = 4, sd = 0.5)
var2 <- rnorm(n, mean = 4, sd = 0.5)

## Generate censored covariate. 
## For generation of Weibull survival times, do not left-censor it yet.
var3 <- rnorm(n, mean = 5, sd = 0.5)

## simulate from a Weibull regression model
time <- TimeSampleWeibull(covariate_noncens = data.frame(var1, var2), 
          covariate_cens = var3, lambda = lambda, gamma = gamma, beta = beta) 

## left-censor covariate
## prop.cens specifies the proportion of observations that should be left-censored
prop.cens <- 0
LOD <- qnorm(prop.cens, mean = 5, sd = 0.5)
var3.cens <- censorContVar(var3, LLOD = LOD)

## censor survival time
event <- matrix(1, nrow = n, ncol = 1)
time.cens <- rexp(n, rate = 0.5)
ind.time <- (event >= time.cens)
event[ind.time] <- 0
time[ind.time] <- time.cens[ind.time]

## specify the density for the censored covariate:
## For simplicity, we take here the "true" density we simulate from. In an application,
## you might want to use a density with parameters estimated from the censored covariate,
## e.g. using the function ParamSampleCens. See example in Hubeaux & Rufibach (2014).
DensityCens <- function(value){return(dnorm(value, mean = 5, sd = 0.5))}

## use Weibull regression where each censored covariate value is set 
## to LOD ("naive" method)
naive <- survreg(Surv(time, event) ~ var1 + var2 + var3.cens[, 2], dist = "weibull")
initial <- as.vector(ConvertWeibull(naive)$vars[, 1])

## use new method that takes into account the left-censoring of one covariate
data <- data.frame(time, event, var3.cens, var1, var2)
formula <- formula(Surv(time, event) ~  Surv(time = var3.cens[, 1], time2 = var3.cens[, 2], 
                      type = "interval2") + var1 + var2)
cens1 <- SurvRegCens(formula = formula, data = data, Density = DensityCens, initial = initial, 
                      namCens = "biomarker")
summary(cens1)
coef(cens1)
logLik(cens1)

## compare estimates
tab <- data.frame(cbind(true, initial, cens1$coeff[, 1]))
colnames(tab) <- c("true", "naive", "Weibull MLE")
rownames(tab) <- rownames(cens1$coeff)
tab

## compare confidence intervals
ConvertWeibull(naive)$HR[, 2:3]
cens1$coeff[, 7:8]


## --------------------------------------------------------------
## model without the non-censored covariates
## --------------------------------------------------------------
naive2 <- survreg(Surv(time, event) ~ var3.cens[, 2], dist = "weibull")
initial2 <- as.vector(ConvertWeibull(naive2)$vars[, 1])

## use new method that takes into account the left-censoring of one covariate
formula <- formula(Surv(time, event) ~ Surv(time = var3.cens[, 1], time2 = var3.cens[, 2], 
                      type = "interval2"))
cens2 <- SurvRegCens(formula = formula, data = data, Density = DensityCens, initial = initial2, 
                      namCens = "biomarker")
summary(cens2)

## compare estimates
tab <- data.frame(cbind(true[c(1, 2, 5)], initial2, cens2$coeff[, 1]))
colnames(tab) <- c("true", "naive", "Weibull MLE")
rownames(tab) <- rownames(cens2$coeff)
tab

## compare confidence intervals
ConvertWeibull(naive2)$HR[, 2:3]
cens2$coeff[, 7:8]

## End(Not run)

Generate time-to-event data according to a Weibull regression model

Description

Generates time-to-event data using the transform inverse sampling method, and such that the time-to-event is distributed according to a Weibull distribution induced by censored and/or non-censored covariates. Can be used to set up simulations.

Usage

TimeSampleWeibull(covariate_noncens = NULL, covariate_cens, lambda, gamma, beta)

Arguments

Note

The use of this function is illustrated in SurvRegCens.

Author(s)

Stanislas Hubeaux, stan.hubeaux@bluewin.ch

Diagnostic Plot of Adequacy of Weibull Distribution

Description

This function constructs a diagnostic plot of the adequacy of the Weibull distribution for survival data with respect to one categorical covariate. If the Weibull distribution fits the data well, then the lines produced should be linear and parallel.

Usage

WeibullDiag(formula, data = parent.frame(), labels = names(m$strata))

Arguments

Details

As discussed in Klein and Moeschberger (2003), one method for checking the adequacy of the Weibull model with a categorical covariate is to produce stratified Kaplan-Meier estimates (KM), which can be transformed to estimate the log cumulative hazard for each stratum. Then in a plot of \log(t) versus \log(-\log(KM)), the lines should be linear and parallel. This can be seen as the log cumulative hazard for the Weibull distribution is

\log H(t) = \log \lambda + \alpha \log t.

Value

Produces a plot of log Time vs. log Estimated Cumulative Hazard for each level of the predictor (similarly to what can be obtained using plot.survfit and the fun = "cloglog" option), as well as a data set containing that information.

Author(s)

Sarah R. Haile, Epidemiology, Biostatistics and Prevention Institute (EBPI), University of Zurich, sarah.haile@uzh.ch

References

Klein, J. and Moeschberger, M. (2003). Survival analysis: techniques for censored and truncated data. 2nd edition, Springer.

See Also

Requires survival. A similar plot can be produced using plot.survfit and the option fun = "cloglog".

Examples

data(larynx)
WeibullDiag(Surv(time, death) ~ stage, data = larynx)

Function to be integrated in function SurvRegCens

Description

Function to be integrated to compute log-likelihood function for the Weibull survival regression model with a censored covariate.

Usage

WeibullIntegrate(x, x_i_noncens = NULL, density, param_y_i,
                 param_delta_i, param_lambda, param_gamma,
                 param_beta, intlimit = 10^-10, ForIntegrate = TRUE)

Arguments

Note

Function is not intended to be invoked by the user.

Author(s)

Stanislas Hubeaux, stan.hubeaux@bluewin.ch

Weibull Regression for Survival Data

Description

WeibullReg performs Weibull regression using the survreg function, and transforms the estimates to a more natural parameterization. Additionally, it produces hazard ratios (corresponding to the proportional hazards interpretation), and event time ratios (corresponding to the accelerated failure time interpretation) for all covariates.

Usage

WeibullReg(formula, data = parent.frame(), conf.level = 0.95)

Arguments

Details

Details regarding the transformations of the parameters and their standard errors can be found in Klein and Moeschberger (2003, Chapter 12). An explanation of event time ratios for the accelerated failure time interpretation of the model can be found in Carroll (2003). A general overview can be found in the vignette("weibull") of this package, or in the documentation for ConvertWeibull.

Value

Author(s)

Sarah R. Haile, Epidemiology, Biostatistics and Prevention Institute (EBPI), University of Zurich, sarah.haile@uzh.ch

References

Carroll, K. (2003). On the use and utility of the Weibull model in the analysis of survival data. Controlled Clinical Trials, 24, 682–701.

Klein, J. and Moeschberger, M. (2003). Survival analysis: techniques for censored and truncated data. 2nd edition, Springer.

See Also

Requires the package survival. This function depends on ConvertWeibull. See also survreg.

Examples

data(larynx)
WR <- WeibullReg(Surv(time, death) ~ factor(stage) + age, data = larynx)
WR

Censor a vector of continuous numbers

Description

Given a vector of realizations of a continuous random variable, interval-, left-, or right-censor these numbers at given boundaries. Useful when setting up simulations involving censored observations.

Usage

censorContVar(x, LLOD = NA, ULOD = NA)

Arguments

Value

A data.frame as specified by code = interval2 in Surv.

Author(s)

Stanislas Hubeaux, stan.hubeaux@bluewin.ch

Kaspar Rufibach, kaspar.rufibach@gmail.com
http://www.kasparrufibach.ch

Examples

## random vector
x <- rnorm(200)

## interval-censor this vector at -1 and 0.5
censorContVar(x, -1, 0.5)

Extract coefficients of Weibull regression with an interval-censored covariate

Description

coef method for class "src".

Usage

## S3 method for class 'src'
coef(object, ...)

Arguments

Value

The function coef.src returns the estimated parameters of the Weibull regression when calling SurvRegCens.

Author(s)

Stanislas Hubeaux, stan.hubeaux@bluewin.ch

Kaspar Rufibach, kaspar.rufibach@gmail.com
http://www.kasparrufibach.ch

References

Hubeaux, S. (2013). Parametric Surival Regression Model with left- and/or interval-censored covariate. Technical report, Biostatistics Oncology, F. Hoffmann-La Roche Ltd.

Hubeaux, S. and Rufibach, K. (2014). SurvRegCensCov: Weibull Regression for a Right-Censored Endpoint with a Censored Covariate. Preprint, https://arxiv.org/abs/1402.0432.

Sattar, A., Sinha, S. K. and Morris, N. J. (2012). A Parametric Survival Model When a Covariate is Subject to Left-Censoring. Biometrics & Biostatistics, S3(2).

Examples

## See help file of function "SurvRegCens".

Survival Times of Larynx Cancer Patients

Description

A study of 90 males with laryngeal cancer was performed, comparing survival times. Each patient's age, year of diagnosis, and disease stage was noted, see Kardaun (1983) and Klein and Moeschberger (2003).

Usage

data(larynx)

Format

A data frame with 90 observations on the following 5 variables.

stage

Disease stage (1-4) from TNM cancer staging classification.

time

Time from first treatment until death, or end of study.

age

Age at diagnosis.

year

Year of diagnosis.

death

Indicator of death [1, if patient died at time t; 0, otherwise].

Source

https://www.mcw.edu/-/media/MCW/Departments/Biostatistics/datafromsection18.txt?la=en

References

Kardaun, O. (1983). Statistical survival analysis of male larynx-cancer patients-a case study. Statistica Neerlandica, 37, 103–125.

Klein, J. and Moeschberger, M. (2003). Survival analysis: techniques for censored and truncated data. 2nd edition, Springer.

Examples

library(survival)
data(larynx)
Surv(larynx$time, larynx$death)

Extract value of log-likelihood at maximum for Weibull regression with an interval-censored covariate

Description

logLik method for class "src".

Usage

## S3 method for class 'src'
logLik(object, ...)

Arguments

Value

The function logLik.src returns the value of the log-likelihood at the maximum likelihood estimate, as well as the corresponding degrees of freedom.

Author(s)

Stanislas Hubeaux, stan.hubeaux@bluewin.ch

Kaspar Rufibach, kaspar.rufibach@gmail.com
http://www.kasparrufibach.ch

References

Hubeaux, S. (2013). Parametric Surival Regression Model with left- and/or interval-censored covariate. Technical report, Biostatistics Oncology, F. Hoffmann-La Roche Ltd.

Hubeaux, S. and Rufibach, K. (2014). SurvRegCensCov: Weibull Regression for a Right-Censored Endpoint with a Censored Covariate. Preprint, https://arxiv.org/abs/1402.0432.

Sattar, A., Sinha, S. K. and Morris, N. J. (2012). A Parametric Survival Model When a Covariate is Subject to Left-Censoring. Biometrics & Biostatistics, S3(2).

Examples

## See help file of function "SurvRegCens".

Print result of Weibull regression with an interval-censored covariate

Description

print method for class "src".

Usage

## S3 method for class 'src'
print(x, ...)

Arguments

Value

The function print.src returns the estimated parameters of the Weibull regression, incl. AIC, when calling SurvRegCens.

Author(s)

Stanislas Hubeaux, stan.hubeaux@bluewin.ch

Kaspar Rufibach, kaspar.rufibach@gmail.com
http://www.kasparrufibach.ch

References

Hubeaux, S. (2013). Parametric Surival Regression Model with left- and/or interval-censored covariate. Technical report, Biostatistics Oncology, F. Hoffmann-La Roche Ltd.

Hubeaux, S. and Rufibach, K. (2014). SurvRegCensCov: Weibull Regression for a Right-Censored Endpoint with a Censored Covariate. Preprint, https://arxiv.org/abs/1402.0432.

Sattar, A., Sinha, S. K. and Morris, N. J. (2012). A Parametric Survival Model When a Covariate is Subject to Left-Censoring. Biometrics & Biostatistics, S3(2).

Examples

## See help file of function "SurvRegCens".

Summarizing Weibull regression with an interval-censored covariate

Description

summary method for class "src".

Usage

## S3 method for class 'src'
summary(object, ...)

Arguments

Value

The function summary.src returns the estimated parameters, incl. statistical inference, of the Weibull regression, incl. AIC, when calling SurvRegCens.

Author(s)

Stanislas Hubeaux, stan.hubeaux@bluewin.ch

Kaspar Rufibach, kaspar.rufibach@gmail.com
http://www.kasparrufibach.ch

References

Hubeaux, S. (2013). Parametric Surival Regression Model with left- and/or interval-censored covariate. Technical report, Biostatistics Oncology, F. Hoffmann-La Roche Ltd.

Hubeaux, S. and Rufibach, K. (2014). SurvRegCensCov: Weibull Regression for a Right-Censored Endpoint with a Censored Covariate. Preprint, https://arxiv.org/abs/1402.0432.

Sattar, A., Sinha, S. K. and Morris, N. J. (2012). A Parametric Survival Model When a Covariate is Subject to Left-Censoring. Biometrics & Biostatistics, S3(2).

Examples

## See help file of function "SurvRegCens".