Package 'Temporal' reference manual

Title:	Parametric Time to Event Analysis
Description:	Performs maximum likelihood based estimation and inference on time to event data, possibly subject to non-informative right censoring. FitParaSurv() provides maximum likelihood estimates of model parameters and distributional characteristics, including the mean, median, variance, and restricted mean. CompParaSurv() compares the mean, median, and restricted mean survival experiences of two treatment groups. Candidate distributions include the exponential, gamma, generalized gamma, log-normal, and Weibull.
Authors:	Zachary McCaw [aut, cre]
Maintainer:	Zachary McCaw <[email protected]>
License:	GPL-3
Version:	0.3.0.1
Built:	2024-11-16 03:19:00 UTC
Source:	https://github.com/zrmacc/temporal

Compare Parametric Survival Distribution

Description

Compares the means and medians of parametric survival distributions fit to two treatment arms. Available distributions include: exponential, gamma, generalized gamma, log-normal, and Weibull.

Usage

CompParaSurv(
  data,
  arm_name = "arm",
  dist1 = "weibull",
  dist0 = NULL,
  eps = 1e-06,
  init1 = NULL,
  init0 = NULL,
  maxit = 10,
  report = FALSE,
  reps = NULL,
  sig = 0.05,
  status_name = "status",
  tau = NULL,
  time_name = "time"
)
CompParaSurv(
  data,
  arm_name = "arm",
  dist1 = "weibull",
  dist0 = NULL,
  eps = 1e-06,
  init1 = NULL,
  init0 = NULL,
  maxit = 10,
  report = FALSE,
  reps = NULL,
  sig = 0.05,
  status_name = "status",
  tau = NULL,
  time_name = "time"
)

Arguments

`data`	Data.frame.
`arm_name`	Name of the column containing the treatment group, coded as 1 for treatment, 0 for reference.
`dist1`	Distribution to fit for the target group. Selected from among: exp, gamma, gengamma, log-normal, and weibull.
`dist0`	Distribution to fit for the reference group. Same choices as for the target group. If omitted, defaults to the distribution specified for the target group.
`eps`	Tolerance for Newton-Raphson iterations.
`init1`	Initial parameter values for the target group.
`init0`	Initial parameter values for the reference group.
`maxit`	Maximum number of Newton-Raphson iterations.
`report`	Report fitting progress?
`reps`	Number of permutation replicates, if requesting permutation p-values.
`sig`	Significance level, for constructing confidence intervals.
`status_name`	Name of the status indicator, 1 if observed, 0 if censored.
`tau`	Optional truncation times for calculating RMST.
`time_name`	Name of column containing the time to event.

Details

Status should be coded as 0 for censored and 1 for observed. Arm is coded as 0 for reference, 1 for target. Tau is an optional numeric vector of truncation times for calculating restricted mean survival time, which is the area under the survival curve up to the specified truncation point.

Value

An object of class contrast containing the following:

Model1: The fitted model for the target group.
Model0: The fitted model for the reference group.
Contrast: Contrasts of means and medians.
RMST: Contrasts of the RMSTs, if 'tau' was specified.

Examples


set.seed(100)
# Weibull and Weibull, different means and medians.
n <- 1e3

# Generate data.
df1 <- GenData(n = n, dist = "weibull", theta = c(1, 1), p = 0.2)
df1$arm <- 1
df0 <- GenData(n = n, dist = "weibull", theta = c(1, 2), p = 0.2)
df0$arm <- 0
data <- rbind(df1, df0)

# Comparison.
comp <- CompParaSurv(data, dist1 = "weibull")

# Add RMST at time 1.
comp <- CompParaSurv(data, dist1 = "weibull", tau = 1)

# Calculate permutation p-values (slow).
comp <-  CompParaSurv(data, dist1 = "weibull", tau = 1, reps = 100)

set.seed(100)
# Weibull and Weibull, different means and medians.
n <- 1e3

# Generate data.
df1 <- GenData(n = n, dist = "weibull", theta = c(1, 1), p = 0.2)
df1$arm <- 1
df0 <- GenData(n = n, dist = "weibull", theta = c(1, 2), p = 0.2)
df0$arm <- 0
data <- rbind(df1, df0)

# Comparison.
comp <- CompParaSurv(data, dist1 = "weibull")

# Add RMST at time 1.
comp <- CompParaSurv(data, dist1 = "weibull", tau = 1)

# Calculate permutation p-values (slow).
comp <-  CompParaSurv(data, dist1 = "weibull", tau = 1, reps = 100)

Contrast of Survival Distributions.

Description

Defines the object class returned by the comparison function.

Slots

Dist1: Distribution fit to the target group, string.
Dist0: Distribution fit to the reference group, string.
Model1: Fitted model for the target group, fit.
Model0: Fitted model for the reference group, fit.
Location: Contrasts of means and medians, data.frame.
RMST: Contrasts of RMSTs, data.frame.

Contrast Locations

Description

Compare the means and medians of the fitted distributions for two treatment arms.

Usage

ContrastLocs(fit1, fit0, sig = 0.05)
ContrastLocs(fit1, fit0, sig = 0.05)

Arguments

`fit1`	Fitted parametric survival distribution for arm 1.
`fit0`	Fitted parametric survival distribution for arm 0.
`sig`	Significance level.

Value

Data.frame contrasting the difference and ratio of the mean and median at each time point.

Contrast RMSTs

Description

Compare the restricted mean survival times of the fitted distributions for two treatment arms.

Usage

ContrastRMSTs(fit1, fit0, sig = 0.05)
ContrastRMSTs(fit1, fit0, sig = 0.05)

Arguments

`fit1`	Fitted parametric survival distribution for arm 1.
`fit0`	Fitted parametric survival distribution for arm 0.
`sig`	Significance level, for

Value

Data.frame contrasting the difference and ratio of RMSTs at each time point.

Set Default Parameters

Description

Function to select default parameter values for each distribution.

Usage

DefaultParam(dist)
DefaultParam(dist)

Arguments

dist

String, distribution name.

Value

Numeric parameter ist.

Distributions

Description

Distributions

Usage

DistProperName(dist)
DistProperName(dist)

Arguments

dist

Argument passed to FitParaSurv

Value

String.

Difference of Estimates

Description

Calculate CIs and p-value for the difference of estimates.

Usage

EstDiff(est1, se1, est0, se0, sig = 0.05)
EstDiff(est1, se1, est0, se0, sig = 0.05)

Arguments

`est1`	Arm 1 estimate.
`se1`	Arm 1 standard error.
`est0`	Arm 0 estimate.
`se0`	Arm 0 standard error.
`sig`	Significance level.

Value

Data.frame containing estimated difference, its standard error, lower and upper confidence bounds, and a p-value assessing the null hypothesis of no difference.

Ratio of Estimates

Description

Calculate CIs and p-value for the ratio of estimates.

Usage

EstRatio(est1, se1, est0, se0, sig = 0.05)
EstRatio(est1, se1, est0, se0, sig = 0.05)

Arguments

`est1`	Arm 1 estimate.
`se1`	Arm 1 standard error.
`est0`	Arm 0 estimate.
`se0`	Arm 0 standard error.
`sig`	Significance level.

Value

Data.frame containing estimated ratio, its standard error, lower and upper confidence bounds, and a p-value assessing the null hypothesis that the ratio is unity.

Extract Observed Estimates

Description

Helper function for permutation inference.

Usage

ExtractObsEst(fit1, fit0)
ExtractObsEst(fit1, fit0)

Arguments

`fit1`	Fitted parametric survival distribution for arm 1.
`fit0`	Fitted parametric survival distribution for arm 0.

Value

Numeric vector.

Fitted Survival Distribution

Description

Defines the object class returned by fitting functions.

Slots

Distribution: Fitted distribution, string.
Parameters: Parameters, data.frame.
Information: Information components, matrix.
Outcome: Properties of the fitted distribution, data.frame.
RMST: Estimated restricted mean survival times, data.frame
S: Fitted survival function, function.

Exponential Distribution Parameter Estimation

Description

Estimates parameters for exponential event times subject to non-informative right censoring. The exponential distribution is parameterized in terms of the rate $\lambda$ :

$f(t) = \lambda e^{-\lambda t}, t>0$

Usage

FitExp(
  data,
  sig = 0.05,
  status_name = "status",
  tau = NULL,
  time_name = "time"
)
FitExp(
  data,
  sig = 0.05,
  status_name = "status",
  tau = NULL,
  time_name = "time"
)

Arguments

`data`	Data.frame.
`sig`	Significance level, for CIs.
`status_name`	Name of the status indicator, 1 if observed, 0 if censored.
`tau`	Optional truncation times for calculating RMSTs.
`time_name`	Name of column containing the time to event.

Value

An object of class fit containing the following:

Parameters: The estimated model parameters.
Information: The observed information matrix.
Outcome: The fitted mean, median, and variance of the time to event distribution.
RMST: The estimated RMSTs, if tau was specified.

Examples

# Generate exponential event time data with 20% censoring.
data <- GenData(n = 1e3, dist = "exp", theta = c(2), p = 0.2)

# Estimate parameters.
fit <- FitParaSurv(data, dist = "exp")
# Generate exponential event time data with 20% censoring.
data <- GenData(n = 1e3, dist = "exp", theta = c(2), p = 0.2)

# Estimate parameters.
fit <- FitParaSurv(data, dist = "exp")

Gamma Distribution Parameter Estimation

Description

Estimates parameters for gamma event times subject to non-informative right censoring. The gamma distribution is parameterized in terms of the shape $\alpha$ and rate $\lambda$ :

$f(t) = \frac{\lambda}{\Gamma(\alpha)}(\lambda t)^{\alpha-1}e^{-\lambda t}, t>0$

Usage

FitGamma(
  data,
  eps = 1e-06,
  init = list(),
  maxit = 10,
  report = FALSE,
  sig = 0.05,
  status_name = "status",
  tau = NULL,
  time_name = "time"
)
FitGamma(
  data,
  eps = 1e-06,
  init = list(),
  maxit = 10,
  report = FALSE,
  sig = 0.05,
  status_name = "status",
  tau = NULL,
  time_name = "time"
)

Arguments

`data`	Data.frame.
`eps`	Tolerance for Newton-Raphson iterations.
`init`	List with initial values for the 'shape' $\alpha$ and 'rate' $\lambda$ .
`maxit`	Maximum number of NR iterations.
`report`	Report fitting progress?
`sig`	Significance level, for CIs.
`status_name`	Name of the status indicator, 1 if observed, 0 if censored.
`tau`	Optional truncation times for calculating RMSTs.
`time_name`	Name of column containing the time to event.

Value

An object of class fit containing the following:

Parameters: The estimated shape $\alpha$ and rate $\lambda$ .
Information: The observed information matrix.
Outcome: The fitted mean, median, and variance.
RMST: The estimated RMSTs, if tau was specified.

Examples

# Generate Gamma data with 20% censoring.
data <- GenData(n = 1e3, dist = "gamma", theta = c(2, 2), p = 0.2)

# Estimate parameters.
fit <- FitParaSurv(data, dist = "gamma")
# Generate Gamma data with 20% censoring.
data <- GenData(n = 1e3, dist = "gamma", theta = c(2, 2), p = 0.2)

# Estimate parameters.
fit <- FitParaSurv(data, dist = "gamma")

Gamma Parameter Estimation without Censoring

Description

Paramter estimation for gamma event times without censoring.

Usage

FitGammaComplete(data, eps = 1e-06)
FitGammaComplete(data, eps = 1e-06)

Arguments

`data`	Data.frame.
`eps`	Tolerance for Newton-Raphson iterations.

Value

Numeric vector containing the estimated shape and rate parameters.

Generalized Gamma Distribution Parameter Estimation

Description

Estimates parameters for generalized gamma event times subject to non-informative right censoring. The gamma distribution is parameterized in terms of the shape parameters $(\alpha,\beta)$ , and the rate $\lambda$ :

$f(t) = \frac{\beta\lambda}{\Gamma(\alpha)} (\lambda t)^{\alpha\beta-1}e^{-(\lambda t)^{\beta}}, t>0$

Usage

FitGenGamma(
  data,
  beta_lower = 0.1,
  beta_upper = 10,
  eps = 1e-06,
  init = list(),
  maxit = 10,
  report = FALSE,
  sig = 0.05,
  status_name = "status",
  tau = NULL,
  time_name = "time"
)
FitGenGamma(
  data,
  beta_lower = 0.1,
  beta_upper = 10,
  eps = 1e-06,
  init = list(),
  maxit = 10,
  report = FALSE,
  sig = 0.05,
  status_name = "status",
  tau = NULL,
  time_name = "time"
)

Arguments

`data`	Data.frame.
`beta_lower`	If dist="gen-gamma", lower limit on possible values for beta.
`beta_upper`	If dist="gen-gamma", upper limit on possible values for beta.
`eps`	Tolerance for Newton-Raphson iterations.
`init`	List with initial values for the shape 'alpha', 'beta' and rate 'lambda' parameters.
`maxit`	Maximum number of NR iterations.
`report`	Report fitting progress?
`sig`	Significance level, for CIs.
`status_name`	Name of the status indicator, 1 if observed, 0 if censored.
`tau`	Optional truncation times for calculating RMSTs.
`time_name`	Name of column containing the time to event.

Value

An object of class fit containing the following:

Parameters: The estimated shape $(\alpha,\beta)$ and rate $\lambda$ parameters.
Information: The observed information matrix.
Outcome: The fitted mean, median, and variance.
RMST: The estimated RMSTs, if tau was specified.

Examples

set.seed(103)
# Generate generalized gamma data with 20% censoring.
data <- GenData(n = 1e4, dist = "gen-gamma", theta = c(2, 2, 2), p = 0.2)

# Estimate parameters.
fit <- FitParaSurv(data, dist = "gen-gamma", report = TRUE)
set.seed(103)
# Generate generalized gamma data with 20% censoring.
data <- GenData(n = 1e4, dist = "gen-gamma", theta = c(2, 2, 2), p = 0.2)

# Estimate parameters.
fit <- FitParaSurv(data, dist = "gen-gamma", report = TRUE)

Generalized Gamma Parameter Estimation without Censoring

Description

Paramter estimation for generalized gamma event times without censoring.

Usage

FitGenGammaComplete(data, beta_lower = 0.1, beta_upper = 10)
FitGenGammaComplete(data, beta_lower = 0.1, beta_upper = 10)

Arguments

`data`	Data.frame.
`beta_lower`	Lower limit on possible values for beta.
`beta_upper`	Upper limit on possible values for beta.

Value

Numeric vector containing the estimated shape and rate parameters.

Log-Normal Distribution Parameter Estimation

Description

Estimates parameters for log-normal event times subject to non-informative right censoring. The log-normal distribution is parameterized in terms of the location $\mu$ and scale $\sigma$ :

$f(t) = \phi\left(\frac{\ln t-\mu}{\sigma}\right)\frac{1}{t\sigma}, t>0$

Usage

FitLogNormal(
  data,
  eps = 1e-06,
  init = list(),
  maxit = 10,
  report = FALSE,
  sig = 0.05,
  status_name = "status",
  tau = NULL,
  time_name = "time"
)
FitLogNormal(
  data,
  eps = 1e-06,
  init = list(),
  maxit = 10,
  report = FALSE,
  sig = 0.05,
  status_name = "status",
  tau = NULL,
  time_name = "time"
)

Arguments

`data`	Data.frame.
`eps`	Tolerance for Newton-Raphson iterations.
`init`	List with initial values for the location ('loc') $\mu$ and 'scale' $\sigma$ .
`maxit`	Maximum number of NR iterations.
`report`	Report fitting progress?
`sig`	Significance level, for CIs.
`status_name`	Name of the status indicator, 1 if observed, 0 if censored.
`tau`	Optional truncation times for calculating RMSTs.
`time_name`	Name of column containing the time to event.

Value

An object of class fit containing the following:

Parameters: The estimated location $\mu$ and scale $\sigma$ .
Information: The observed information matrix.
Outcome: The fitted mean, median, and variance.
RMST: The estimated RMSTs, if tau was specified.

Examples

# Generate log-normal data with 20% censoring.
data <- GenData(n = 1e3, dist = "log-normal", theta = c(0, 2), p = 0.2)

# Estimate parameters.
fit <- FitParaSurv(data, dist = "log-normal")
# Generate log-normal data with 20% censoring.
data <- GenData(n = 1e3, dist = "log-normal", theta = c(0, 2), p = 0.2)

# Estimate parameters.
fit <- FitParaSurv(data, dist = "log-normal")

Log-Normal Parameter Estimation without Censoring

Description

Log-Normal Parameter Estimation without Censoring

Usage

FitLogNormComplete(data)
FitLogNormComplete(data)

Arguments

data

Data.frame.

Value

Numeric vector containing the estimate location and scale parameters.

Fit Parametric Survival Distribution

Description

Estimates parametric survival distributions using event times subject to non-informative right censoring. Available distributions include: exponential, gamma, generalized gamma, log-normal, and Weibull.

Usage

FitParaSurv(
  data,
  beta_lower = 0.1,
  beta_upper = 10,
  dist = "weibull",
  eps = 1e-06,
  init = NULL,
  maxit = 10,
  report = FALSE,
  sig = 0.05,
  status_name = "status",
  tau = NULL,
  time_name = "time"
)
FitParaSurv(
  data,
  beta_lower = 0.1,
  beta_upper = 10,
  dist = "weibull",
  eps = 1e-06,
  init = NULL,
  maxit = 10,
  report = FALSE,
  sig = 0.05,
  status_name = "status",
  tau = NULL,
  time_name = "time"
)

Arguments

`data`	Data.frame containing the time to event and status.
`beta_lower`	If dist="gen-gamma", lower limit on possible values for beta.
`beta_upper`	If dist="gen-gamma", upper limit on possible values for beta.
`dist`	String, distribution to fit, selected from among: exp, gamma, gen-gamma log-normal, and weibull.
`eps`	Tolerance for Newton-Raphson iterations.
`init`	List of initial parameters. See individual distributions for the expected parameters.
`maxit`	Maximum number of NR iterations.
`report`	Report fitting progress?
`sig`	Significance level, for CIs.
`status_name`	Name of the status indicator, 1 if observed, 0 if censored.
`tau`	Optional truncation time for calculating RMSTs.
`time_name`	Name of column containing the time to event.

Value

An object of class fit containing the following:

Parameters: The estimated shape and rate parameters.
Information: The observed information matrix.
Outcome: The fitted mean, median, and variance.
RMST: The estimated RMSTs, if tau was specified.

Examples

# Generate Gamma data with 20% censoring.
data <- GenData(n = 1e3, dist = "gamma", theta = c(2, 2), p = 0.2)
# Fit gamma distribution.
fit <- FitParaSurv(data, dist = "gamma")

# Generate Weibull data with 10% censoring.
data <- GenData(n = 1e3, dist = "weibull", theta = c(2, 2), p = 0.1)
# Fit weibull distribution, calculate RMST at tau=0.5.
fit <- FitParaSurv(data, dist = "weibull", tau = 0.5)
# Generate Gamma data with 20% censoring.
data <- GenData(n = 1e3, dist = "gamma", theta = c(2, 2), p = 0.2)
# Fit gamma distribution.
fit <- FitParaSurv(data, dist = "gamma")

# Generate Weibull data with 10% censoring.
data <- GenData(n = 1e3, dist = "weibull", theta = c(2, 2), p = 0.1)
# Fit weibull distribution, calculate RMST at tau=0.5.
fit <- FitParaSurv(data, dist = "weibull", tau = 0.5)

Weibull Distribution Parameter Estimation

Description

Estimates parameters for Weibull event times subject to non-informative right censoring. The Weibull distribution is parameterized in terms of the shape $\alpha$ and rate $\lambda$ :

$f(t) = \alpha\lambda^{\alpha}t^{\alpha-1}e^{-(\lambda t)^{\alpha}}, t>0$

Usage

FitWeibull(
  data,
  init = list(),
  sig = 0.05,
  status_name = "status",
  tau = NULL,
  time_name = "time"
)
FitWeibull(
  data,
  init = list(),
  sig = 0.05,
  status_name = "status",
  tau = NULL,
  time_name = "time"
)

Arguments

`data`	Data.frame.
`init`	List containing the initial value for the shape, $\alpha$ .
`sig`	Significance level, for CIs.
`status_name`	Name of the status indicator, 1 if observed, 0 if censored.
`tau`	Optional truncation times for calculating RMSTs.
`time_name`	Name of column containing the time to event.

Value

An object of class fit containing the following:

Parameters: The estimated shape $\alpha$ and rate $\lambda$ .
Information: The observed information matrix.
Outcome: The fitted mean, median, and variance.
RMST: The estimated RMSTs, if tau was specified.

Examples

# Generate Weibull data with 20% censoring.
data <- GenData(n = 1e3, dist = "weibull", theta = c(2, 2), p = 0.2)

# Estimate parameters.
fit <- FitParaSurv(data, dist = "weibull")
# Generate Weibull data with 20% censoring.
data <- GenData(n = 1e3, dist = "weibull", theta = c(2, 2), p = 0.2)

# Estimate parameters.
fit <- FitParaSurv(data, dist = "weibull")

Gamma Observed Information

Description

Observed information for gamme event times without censoring.

Usage

GammaInfo(data, shape, rate)
GammaInfo(data, shape, rate)

Arguments

`data`	Data.frame.
`shape`	Shape parameter $\alpha$ .
`rate`	Rate parameter $\lambda$ .

Value

Numeric information matrix.

Gamma Profile Score for Shape

Description

Profile score equation for gamma event times without censoring.

Usage

GammaScore(data, shape)
GammaScore(data, shape)

Arguments

`data`	Data.frame.
`shape`	Shape parameter.

Value

Numeric score.

Data Generation with Censoring

Description

Generates data from survival distributions as parameterized in this package, with optional non-informative random right censoring.

Usage

GenData(n, dist = "exp", theta = NULL, p = 0)
GenData(n, dist = "exp", theta = NULL, p = 0)

Arguments

`n`	Integer sample size.
`dist`	String, distribution name selected from among: "exp","gamma","gen-gamma","log-normal","weibull".
`theta`	Numeric parameter vector. Elements will vary according to the distribution.
`p`	Expected censoring proportion.

Details

The parameter vector theta should contain the following elements, in order, depending on the distribution:

Exponential: Rate $\lambda$ .
Gamma: Shape $\alpha$ , rate $\lambda$ .
Generalized Gamma: Shape 1 $\alpha$ , shape 2 $\beta$ , rate $\lambda$ .
Log-Normal: Locaion $\mu$ , scale $\sigma$ .
Weibull: Shape $\alpha$ , rate $\lambda$ .

Value

Data.frame including the observation times and status.

Examples

# Gamma event times with shape 2 and rate 2.
# Expected censoring proportion of 20%.
data <- GenData(n = 1e3, dist = "gamma", theta = c(2, 2), p = 0.20)

# Generalized gamma event times with shapes (2,3) and rate 1.
# Expected censoring proportion of 15%.
data <- GenData(n = 1e3, dist = "gen-gamma", theta = c(2, 3, 1), p = 0.15)

# Log-normal event times with location 0 and rate 1.
# Expected censoring proportion of 10%.
data <- GenData(n = 1e3, dist = "log-normal", theta = c(0, 1), p = 0.10)

# Weibull event times with shape 2 and rate 2.
# Expected censoring proportion of 5%.
data <- GenData(n = 1e3, dist = "weibull", theta = c(2, 2), p = 0.05)
# Gamma event times with shape 2 and rate 2.
# Expected censoring proportion of 20%.
data <- GenData(n = 1e3, dist = "gamma", theta = c(2, 2), p = 0.20)

# Generalized gamma event times with shapes (2,3) and rate 1.
# Expected censoring proportion of 15%.
data <- GenData(n = 1e3, dist = "gen-gamma", theta = c(2, 3, 1), p = 0.15)

# Log-normal event times with location 0 and rate 1.
# Expected censoring proportion of 10%.
data <- GenData(n = 1e3, dist = "log-normal", theta = c(0, 1), p = 0.10)

# Weibull event times with shape 2 and rate 2.
# Expected censoring proportion of 5%.
data <- GenData(n = 1e3, dist = "weibull", theta = c(2, 2), p = 0.05)

Generalized Gamma Observed Information

Description

Observed information for the generalized gamma log likelihood in the absence of censoring.

Usage

GenGammaObsInfo(data, alpha, beta, lambda)
GenGammaObsInfo(data, alpha, beta, lambda)

Arguments

`data`	Data.frame.
`alpha`	First shape parameter.
`beta`	Second shape parameter.
`lambda`	Rate parameter.

Value

Numeric observed information matrix.

Generalized Gamma Profile Log Likelihood

Description

Profile log likelihood of the generalized gamma distribution as a function of the second shape parameter $\beta$ .

Usage

GenGammaProfileLogLik(data, beta)
GenGammaProfileLogLik(data, beta)

Arguments

`data`	Data.frame.
`beta`	Second shape parameter.

Value

Numeric profile log likelihood.

Generalized Gamma Rate MLE

Description

Profile MLE of the generalized gamma rate given the shape parameters.

Usage

GenGammaRate(data, alpha, beta)
GenGammaRate(data, alpha, beta)

Arguments

`data`	Data.frame.
`alpha`	First shape parameter.
`beta`	Second shape parameter.

Value

Numeric MLE of the rate $\lambda$ .

Generalized Gamma Score Equation

Description

Score equation for the generalized gamma log likelihood in the absence of censoring.

Usage

GenGammaScore(data, alpha, beta, lambda)
GenGammaScore(data, alpha, beta, lambda)

Arguments

`data`	Data.frame.
`alpha`	First shape parameter.
`beta`	Second shape parameter.
`lambda`	Rate parameter.

Value

Numeric score vector.

Generalized Gamma Shape MLE

Description

Profile MLE of the first shape parameter $\alpha$ of the generalized gamma given the second shape parameter $\beta$ .

Usage

GenGammaShape(data, beta)
GenGammaShape(data, beta)

Arguments

`data`	Data.frame.
`beta`	Second shape parameter.

Value

Numeric MLE of the rate $\alpha$ .

Log-Normal Observed Information

Description

Observed information for log-normal event times without censoring.

Usage

LogNormInfo(data, loc, scale, log_scale = FALSE)
LogNormInfo(data, loc, scale, log_scale = FALSE)

Arguments

`data`	Data.frame.
`loc`	Location parameter.
`scale`	Scale parameter.
`log_scale`	Is the scale parameter logged?

Value

Numeric score.

Log-Normal Score Equation

Description

Score equation for log-normal event times without censoring.

Usage

LogNormScore(data, loc, scale)
LogNormScore(data, loc, scale)

Arguments

`data`	Data.frame.
`loc`	Location parameter.
`scale`	Scale parameter.

Value

Numeric score.

Newton Raphson Estimation

Description

Newton Raphson Estimation

Usage

NewtonRaphson(init, obj, eps = 1e-06, maxit = 10, report = FALSE)
NewtonRaphson(init, obj, eps = 1e-06, maxit = 10, report = FALSE)

Arguments

`init`	Initial value.
`obj`	Objective function.
`eps`	Tolerance for Newton-Raphson iterations.
`maxit`	Maximum number of NR iterations.
`report`	Report fitting progress?

Value

Numeric parameter estimate.

Newton Raphson Update Iteration

Description

Newton Raphson Update Iteration

Usage

NRUpdate(obj, state)
NRUpdate(obj, state)

Arguments

`obj`	Objective function.
`state`	List containing the parameter vector 'theta'.

Value

List containing the updated parameter vector 'theta' and the objective increment 'delta'.

Restricted Mean Survival Time

Description

Calculates the RMST as the area under a fitted parametric survival distribution.

Usage

ParaRMST(fit, tau, sig = 0.05)
ParaRMST(fit, tau, sig = 0.05)

Arguments

`fit`	Fitted parametric survival distribution.
`tau`	Numeric vector of truncation times.
`sig`	Significance level, for CIs.

Value

Data.frame containing the estimated RMST at each truncation time.

Examples

# Generate Weibull data with 20% censoring.
data <- GenData(n = 1e3, dist = "weibull", theta = c(2, 0.5), p = 0.2)

# Fit Weibull distribution.
fit <- FitParaSurv(data, dist = "weibull")

# Calculate RMSTs.
rmst <- ParaRMST(fit = fit, tau = c(0.5, 1.0, 1.5, 2.0))

# Generate gamma data with 10% censoring.
data <- GenData(n = 1e3, dist = "gamma", theta = c(2, 2), p = 0.10)

# Fit gamma distribution.
fit <- FitParaSurv(data, dist = "gamma")

# Calculate RMSTs.
rmst <- ParaRMST(fit = fit, tau = c(0.5, 1.0, 1.5, 2.0))
# Generate Weibull data with 20% censoring.
data <- GenData(n = 1e3, dist = "weibull", theta = c(2, 0.5), p = 0.2)

# Fit Weibull distribution.
fit <- FitParaSurv(data, dist = "weibull")

# Calculate RMSTs.
rmst <- ParaRMST(fit = fit, tau = c(0.5, 1.0, 1.5, 2.0))

# Generate gamma data with 10% censoring.
data <- GenData(n = 1e3, dist = "gamma", theta = c(2, 2), p = 0.10)

# Fit gamma distribution.
fit <- FitParaSurv(data, dist = "gamma")

# Calculate RMSTs.
rmst <- ParaRMST(fit = fit, tau = c(0.5, 1.0, 1.5, 2.0))

Permutation P Value

Description

Calculates permutation p-values for location and RMST estimates.

Usage

PermP(df1, df0, fit0, fit1, eps, init1, init0, maxit, reps, tau)
PermP(df1, df0, fit0, fit1, eps, init1, init0, maxit, reps, tau)

Arguments

`df1`	Target data.frame containing time and status.
`df0`	Reference data.frame containing time and status.
`fit0`	Fitted parametric survival distribution for arm 0.
`fit1`	Fitted parametric survival distribution for arm 1.
`eps`	Tolerance for Newton-Raphson iterations.
`init1`	Initial parameter values for the target group.
`init0`	Initial parameter values for the reference group.
`maxit`	Maximum number of Newton-Raphson iterations.
`reps`	Number of permutation replicates.
`tau`	Optional truncation times for calculating RMST.

Value

Numeric vector of permutation p-values.

Print Method for a Contrast of Survival Distributions.

Description

Print method for an object of class contrast.

Usage

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

Arguments

`x`	A `contrast` object.
`...`	Unused.

Print Method for Fitted Survival Distributions

Description

Print method for objects of class fit.

Usage

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

Arguments

`x`	An object of class `fit`.
`...`	Unused.

Quadratic Form

Description

Quadratic Form

Usage

QF(x, A)
QF(x, A)

Arguments

`x`	Numeric vector.
`A`	Numeric matrix.

Value

Numeric scalar.

Quantile Function for the Weibull Distribution

Description

Quantile function for the Weibull distribution. See FitWeibull for the parameterization.

Usage

qWeibull(p, a = 1, l = 1)
qWeibull(p, a = 1, l = 1)

Arguments

`p`	Probability.
`a`	Shape.
`l`	Rate.

Value

Scalar quantile.

Simulation from the Gamma Distribution

Description

Generates gamma event times with shape parameter $\alpha$ and rate parameter $\lambda$ . See FitGamma for the parameterization. If a censoring proportion $p$ is provided, the event times are subject to non-informative random right censoring.

Usage

rGamma(n, a = 1, l = 1, p = 0)
rGamma(n, a = 1, l = 1, p = 0)

Arguments

`n`	Sample size.
`a`	Shape.
`l`	Rate.
`p`	Expected censoring proportion.

Value

Data.frame including the observation times and status.

Simulation from the Generalized Gamma Distribution

Description

Generates generalized gamma event times with shape parameters $(\alpha,\beta)$ , and rate parameter $\lambda$ . See FitGenGamma for the parameterization. If a censoring proportion $p$ is provided, the event times are subject to non-informative random right censoring.

Usage

rGenGamma(n, a = 1, b = 1, l = 1, p = 0)
rGenGamma(n, a = 1, b = 1, l = 1, p = 0)

Arguments

`n`	Sample size.
`a`	First shape parameter, $\alpha$ .
`b`	Second shape parameter, $\beta$ . For the standard gamma distribution, set $\beta=1$ .
`l`	Rate.
`p`	Expected censoring proportion.

Value

Data.frame including the observation times and status indicators.

Simulation from the Log-Normal Distribution

Description

Generates log-normal event times with location parameter $\mu$ and scale parameter $\sigma$ . See FitLogNormal for the parameterization. If a censoring proportion $p$ is provided, the event times are subject to non-informative random right censoring.

Usage

rLogNormal(n, m = 0, s = 1, p = 0)
rLogNormal(n, m = 0, s = 1, p = 0)

Arguments

`n`	Sample size.
`m`	Location.
`s`	Scale.
`p`	Expected censoring proportion.

Value

Data.frame including the observation time and status.

Round Data Frames

Description

Round Data Frames

Usage

RoundDF(df, digits = 3)
RoundDF(df, digits = 3)

Arguments

`df`	Data.frame.
`digits`	Integer.

Value

Data.frame.

Simulation from the Weibull Distribution

Description

Generates Weibull event times with shape parameter $\alpha$ and rate parameter $\lambda$ . See FitWeibull for the parameterization. If a censoring proportion $p$ is provided, the deviates are subject to non-informative random right censoring.

Usage

rWeibull(n, a = 1, l = 1, p = 0)
rWeibull(n, a = 1, l = 1, p = 0)

Arguments

`n`	Sample size.
`a`	Shape.
`l`	Rate.
`p`	Expected censoring proportion.

Value

Data.frame including the observation time and status.

Show Method for a Contrast of Survival Distributions.

Description

Show Method for a Contrast of Survival Distributions.

Usage

## S4 method for signature 'contrast'
show(object)
## S4 method for signature 'contrast'
show(object)

Arguments

object

An object of class contrast.

Show Method for Fitted Survival Distributions

Description

Show Method for Fitted Survival Distributions

Usage

## S4 method for signature 'fit'
show(object)
## S4 method for signature 'fit'
show(object)

Arguments

object

An object of class fit.

Survival Functions

Description

Constructs the survival function for a parameter distribution.

Usage

SurvFunc(dist, theta)
SurvFunc(dist, theta)

Arguments

`dist`	String, distribution name.
`theta`	Numeric parameter vector.

Details

The parameter vector theta should contain the following elements, in order, according to the distribution:

Exponential: Rate $\lambda$ .
Gamma: Shape $\alpha$ , rate $\lambda$ .
Generalized Gamma: Shape 1 $\alpha$ , shape 2 $\beta$ , rate $\lambda$ .
Log-Normal: Locaion $\mu$ , scale $\sigma$ .
Weibull: Shape $\alpha$ , rate $\lambda$ .

Value

Survival function.

Examples

# Survival function for the generalized gamma.
surv <- SurvFunc(dist = "gen-gamma", theta = c(2, 2, 2))

# Evaluation.
surv(1.0)
# Survival function for the generalized gamma.
surv <- SurvFunc(dist = "gen-gamma", theta = c(2, 2, 2))

# Evaluation.
surv(1.0)

Log Likelihood

Description

Evaluates the log-likelihood for a parametric survival distribution.

Usage

SurvLogLik(
  data,
  dist,
  theta,
  log_scale = FALSE,
  status_name = "status",
  time_name = "time"
)
SurvLogLik(
  data,
  dist,
  theta,
  log_scale = FALSE,
  status_name = "status",
  time_name = "time"
)

Arguments

`data`	Data.frame
`dist`	Distribution, from among: "exp","gamma","gen-gamma","log-normal","weibull".
`theta`	Parameters, which will vary according to the distribution.
`log_scale`	Are strictly positive parameters on log-scale?
`status_name`	Status indicator, coded as 1 if an event was observed, 0 if censored.
`time_name`	Name of column containing the time to event.

Details

The parameter vector theta should contain the following elements, in order, depending on the distribution:

Exponential: Rate $\lambda$ .
Gamma: Shape $\alpha$ , rate $\lambda$ .
Generalized Gamma: Shape 1 $\alpha$ , shape 2 $\beta$ , rate $\lambda$ .
Log-Normal: Location $\mu$ , scale $\sigma$ .
Weibull: Shape $\alpha$ , rate $\lambda$ .

Value

Scalar value of the log likelihood.

Examples

# Generate gamma event time data with 10% censoring.
data <- GenData(n = 1e3, dist = "gamma", theta = c(2, 2), p = 0.1)

# Evaluate log likelihood.
ll <- SurvLogLik(data, dist = "gamma", theta = c(2, 2))

# Generate Weibull event time data with 20% censoring.
data <- GenData(n = 1e3, dist = "weibull", theta = c(2, 2), p = 0.2)

# Evaluate log likelihood.
ll <- SurvLogLik(data, dist = "weibull", theta = c(2, 2))
# Generate gamma event time data with 10% censoring.
data <- GenData(n = 1e3, dist = "gamma", theta = c(2, 2), p = 0.1)

# Evaluate log likelihood.
ll <- SurvLogLik(data, dist = "gamma", theta = c(2, 2))

# Generate Weibull event time data with 20% censoring.
data <- GenData(n = 1e3, dist = "weibull", theta = c(2, 2), p = 0.2)

# Evaluate log likelihood.
ll <- SurvLogLik(data, dist = "weibull", theta = c(2, 2))

Weibull Information Matrix.

Description

Information matrix for the Weibull shape and rate parameters.

Usage

WeiInfo(data, shape, rate)
WeiInfo(data, shape, rate)

Arguments

`data`	Data.frame.
`shape`	Shape parameter, alpha.
`rate`	Rate parameter, lambda.

Value

Numeric information matrix.

Weibull Initialization.

Description

Weibull Initialization.

Usage

WeiInit(data, init)
WeiInit(data, init)

Arguments

`data`	Data.frame.
`init`	Initialization list.

Value

Numeric initial value for shape.

Weibull Rate MLE

Description

Profile MLE of the Weibull rate as a function of the shape.

Usage

WeiRate(data, shape)
WeiRate(data, shape)

Arguments

`data`	Data.frame.
`shape`	Shape parameter.

Value

Numeric rate.

Weibull Profile Score for Shape

Description

Profile score equation for the Weibull shape parameter.

Usage

WeiScore(data, shape)
WeiScore(data, shape)

Arguments

`data`	Data.frame.
`shape`	Shape parameter.

Value

Numeric score.

`dist`	String, distribution.
`theta`	Numeric, parameter vector.

Package 'Temporal'

Help Index

Check Arm

Description

Usage

Arguments

Value

Check Distribution

Description

Usage

Arguments

Value

Check Initialization

Description

Usage

Arguments

Value

Status Check

Description

Usage

Arguments

Value

Check Theta

Description

Usage

Arguments

Value

Compare Parametric Survival Distribution

Description

Usage

Arguments

Details

Value

Examples

Contrast of Survival Distributions.

Description

Slots

Contrast Locations

Description

Usage

Arguments

Value

Contrast RMSTs

Description

Usage

Arguments

Value

Set Default Parameters

Description

Usage

Arguments

Value

Distributions

Description

Usage

Arguments

Value

Difference of Estimates

Description

Usage

Arguments

Value

Ratio of Estimates

Description

Usage

Arguments

Value

Extract Observed Estimates

Description

Usage

Arguments

Value

Fitted Survival Distribution

Description

Slots

Exponential Distribution Parameter Estimation

Description

Usage

Arguments

Value