Package 'event'

Title:	Event History Procedures and Models
Description:	Functions for setting up and analyzing event history data.
Authors:	Bruce Swihart [cre, aut], Jim Lindsey [aut] (Jim created this package, Bruce is maintaining the CRAN version)
Maintainer:	Bruce Swihart <[email protected]>
License:	GPL-2
Version:	1.1.0
Built:	2025-01-10 04:16:00 UTC
Source:	https://github.com/swihart/event

Help Index

Plot Autointensity Function of a Point Process
Create a Vector of Cumulative Numbers of Previous Events for a Point Process (Birth Processes)
Cox Proportional Hazards Model with Random Effect
Plot Counting Process Data
Regression Models for Event History Intensity Functions
Event History Analysis Library
Log Hazard Function for a Box-Cox Process
Log Hazard Function for a Burr Process
Log Hazard Function for a Cauchy Process
Log Hazard Function for a Poisson Process
Log Hazard Function for a Gamma Process
Log Hazard Function for an Extreme Value Process
Log Hazard Function for a Generalized Gamma Process
Log Hazard Function for a Generalized Logistic Process
Log Hazard Function for a Generalized Weibull Process
Log Hazard Function for a Hjorth Process
Log Hazard Function for a Inverse Gauss Process
Log Hazard Function for a Laplace Process
Log Hazard Function for a Log Normal Process
Log Hazard Function for a Logistic Process
Log Hazard Function for a Normal Process
Log Hazard Function for a Pareto Process
Log Hazard Function for a Skew Laplace Process
Log Hazard Function for a Student t Process
Log Hazard Function for a Weibull Process
Create an Individual Identification Vector for a Point Process
Repeated Events Models with Frailty or Serial Dependence
Kaplan-Meier Survivor Curves
Fit Overdispersed Count Data as a Birth Process
Plot Intensity Functions
Create a Point Process Vector from Times between Events
Weibull and Cox Models with Random Effects
Create a Vector of Time-constant Covariates for a Point Process
Create a Vector of Times Past since Previous Events for a Point Process
Create a Vector of Total Time Elapsed for each Individual for a Point Process
Create a Vector of Time-varying Covariates for a Point Process

Plot Autointensity Function of a Point Process

Description

autointensity plots the autointensity function of a point process, including a solid horizontal line indicating the constant intensity of a Poisson process.

Usage

autointensity(times, window=NULL, maxlag=max(times),
	ylab="Conditional probability", xlab="Lag",
	main="Autointensity function", xlim=c(0,max(times)),
	ylim=c(0,if(plotse)max(se1)else max(z$density)),
	lty=1, plot=TRUE, plotse=TRUE, add=FALSE, ...)
autointensity(times, window=NULL, maxlag=max(times),
	ylab="Conditional probability", xlab="Lag",
	main="Autointensity function", xlim=c(0,max(times)),
	ylim=c(0,if(plotse)max(se1)else max(z$density)),
	lty=1, plot=TRUE, plotse=TRUE, add=FALSE, ...)

Arguments

`times`	Vector of times between events.
`window`	Width of grouping interval.
`maxlag`	Maximum lag to be calculated, by default the maximum interevent time.
`plot`	If FALSE, values are returned but the function is not plotted.
`plotse`	If TRUE, plots pointwise two-standard error bands around the curve.
`add`	If TRUE, add curve to an existing plot.
`ylab`	Plotting control options.
`xlab`	Plotting control options.
`main`	Plotting control options.
`xlim`	Plotting control options.
`ylim`	Plotting control options.
`lty`	Plotting control options.
`...`	Plotting control options.

Value

A list containing the coordinates of the plotted function and the standard error bands.

Author(s)

J.K. Lindsey

References

Guttorp, P. (1995) Stochastic Modeling of Scientific Data. Chapman & Hall, pp. 229, 238-240.

Examples

times <- rgamma(100,2,scale=4)
autointensity(times, window=3)
times <- rgamma(100,2,scale=4)
autointensity(times, window=3)

Create a Vector of Cumulative Numbers of Previous Events for a Point Process (Birth Processes)

Description

bp creates a vector of length sum(y) of cumulative numbers of previous events for each individual for use in fitting birth processes with ehr. Add one if the process starts at an event.

Usage

bp(y, id, censor=1)
bp(y, id, censor=1)

Arguments

`y`	Vector of times.
`id`	Vector of corresponding individual identifiers for who had which sequence of times.
`censor`	Vector of censoring indicators.

Value

bp creates a vector of length sum(y) of cumulative numbers of previous events for each individual for use in fitting birth processes with ehr. Add one if the process starts at an event.

Author(s)

J.K. Lindsey

Examples

y <- c(5,3,2,4)
i <- c(1,1,2,2)
birth <- bp(y, i)
birth
y <- c(5,3,2,4)
i <- c(1,1,2,2)
birth <- bp(y, i)
birth

Cox Proportional Hazards Model with Random Effect

Description

coxre fits a Cox proportional hazards model to event history data using a gamma distribution random effect. The parameter, gamma, is the variance of this mixing distribution.

If a matrix of response times is supplied, the model can be stratified by columns, i.e. a different intensity function is fitted for each column. To fit identical intensity functions to all response types, give the times as a vector.

Usage

coxre(response, censor, nest=NULL, cov=NULL, stratified=FALSE,
	cumul=FALSE,estimate=1, iter=10, print.level=0, ndigit=10,
	gradtol=0.00001, steptol=0.00001, iterlim=100, fscale=1,
	typsize=abs(estimate), stepmax=estimate)
coxre(response, censor, nest=NULL, cov=NULL, stratified=FALSE,
	cumul=FALSE,estimate=1, iter=10, print.level=0, ndigit=10,
	gradtol=0.00001, steptol=0.00001, iterlim=100, fscale=1,
	typsize=abs(estimate), stepmax=estimate)

Arguments

`response`	Vector or matrix of times to events, with one column per type of response (or subunit).
`censor`	Corresponding vector or matrix of censoring indicators. If NULL all values are set to one.
`nest`	Vector indicating to which unit each observation belongs.
`cov`	One covariate
`stratified`	If TRUE, a model stratified on type of response (the columns of response) is fitted instead of proportional intensities.
`cumul`	Set to TRUE if response times are from a common origin instead of times to (or between) events.
`estimate`	Initial estimate of the frailty parameter.
`iter`	Maximum number of iterations allowed for the inner EM loop.
`print.level`	`nlm` control options.
`ndigit`	`nlm` control options.
`gradtol`	`nlm` control options.
`steptol`	`nlm` control options.
`iterlim`	`nlm` control options.
`fscale`	`nlm` control options.
`typsize`	`nlm` control options.
`stepmax`	`nlm` control options.

Author(s)

D.G. Clayton and J.K. Lindsey

References

Clayton, D. (1987) The analysis of event history data: a review of progress and outstanding problems. Statistics in Medicine 7: 819-841

Examples

# 11 individuals, each with 5 responses
y <- matrix(c(51,36,50,35,42,
	27,20,26,17,27,
	37,22,41,37,30,
	42,36,32,34,27,
	27,18,33,14,29,
	43,32,43,35,40,
	41,22,36,25,38,
	38,21,31,20,16,
	36,23,27,25,28,
	26,31,31,32,36,
	29,20,25,26,25),ncol=5,byrow=TRUE)
# Different intensity functions
coxre(response=y, censor=matrix(rep(1,55),ncol=5), nest=1:11,
	est=0.7, stratified=TRUE)
# Proportional intensity functions for the five responses
coxre(response=y, censor=matrix(rep(1,55),ncol=5), nest=1:11,
	est=0.7, stratified=FALSE)
# Identical intensity functions
coxre(response=as.vector(t(y)), censor=rep(1,55),
	nest=rep(1:11,rep(5,11)), est=0.7)
# 11 individuals, each with 5 responses
y <- matrix(c(51,36,50,35,42,
	27,20,26,17,27,
	37,22,41,37,30,
	42,36,32,34,27,
	27,18,33,14,29,
	43,32,43,35,40,
	41,22,36,25,38,
	38,21,31,20,16,
	36,23,27,25,28,
	26,31,31,32,36,
	29,20,25,26,25),ncol=5,byrow=TRUE)
# Different intensity functions
coxre(response=y, censor=matrix(rep(1,55),ncol=5), nest=1:11,
	est=0.7, stratified=TRUE)
# Proportional intensity functions for the five responses
coxre(response=y, censor=matrix(rep(1,55),ncol=5), nest=1:11,
	est=0.7, stratified=FALSE)
# Identical intensity functions
coxre(response=as.vector(t(y)), censor=rep(1,55),
	nest=rep(1:11,rep(5,11)), est=0.7)

Plot Counting Process Data

Description

cprocess plots the cumulative number of events (the counting process) over time for each vector in the list. One or both of times and events can be supplied.

Usage

cprocess(times=NULL, events=NULL, number=FALSE, lty=NULL, xlim=NULL,
	ylim=NULL, xlab="Time", ylab="Counts", ...)
cprocess(times=NULL, events=NULL, number=FALSE, lty=NULL, xlim=NULL,
	ylim=NULL, xlab="Time", ylab="Counts", ...)

Arguments

`times`	Vector of times between events, a list of such vectors, or a `repeated` object.
`events`	Vector of counts of events, a list of such vectors, or a `repeated` object.
`number`	If TRUE, the counting processes are numbered consecutively on the graph.
`ylab`	Plotting control options.
`xlab`	Plotting control options.
`xlim`	Plotting control options.
`ylim`	Plotting control options.
`lty`	Plotting control options.
`...`	Plotting control options.

Author(s)

J.K. Lindsey

Examples

times <- rgamma(20,2,scale=4)
cprocess(times)
times <- rgamma(20,2,scale=4)
cprocess(times)

Regression Models for Event History Intensity Functions

Description

ehr fits an intensity function to event histories, where point is produced by point <- pp(y) and lambda is the user-defined log intensity function.

Nonlinear regression models for lambda can be supplied as formulae where parameters are unknowns. Factor variables cannot be used and parameters must be scalars. (See finterp.)

Usage

ehr(point, lambda=NULL, linear=NULL, plambda=NULL, delta=1,
	envir=parent.frame(), print.level=0, typsize=rep(1,length(plambda)),
	ndigit=10, gradtol=0.00001, iterlim=100, fscale=1,
	stepmax=max(10*sqrt(plambda%*%plambda),10), steptol=0.0004)
ehr(point, lambda=NULL, linear=NULL, plambda=NULL, delta=1,
	envir=parent.frame(), print.level=0, typsize=rep(1,length(plambda)),
	ndigit=10, gradtol=0.00001, iterlim=100, fscale=1,
	stepmax=max(10*sqrt(plambda%*%plambda),10), steptol=0.0004)

Arguments

`point`	A point process vector produced by `pp`.
`lambda`	User-specified function of `p`, and possibly `linear`, giving the regression equation for the intensity or a formula beginning with ~, specifying either a linear regression function in the Wilkinson and Rogers notation or a general function with named unknown parameters. The function may contain a linear part that must simply be given the name, `linear`, in the function. If no function is supplied, the intensity is taken to be constant (a homogeneous Poisson process).
`linear`	A formula beginning with ~ specifying the linear part of the regression function.
`plambda`	Vector of initial parameter estimates. If `lambda` is a formula with unknown parameters, their estimates must be supplied either in their order of appearance in the expression or in a named list.
`delta`	If any time intervals are different from unity, a vector of time intervals.
`envir`	Environment in which model formulae are to be interpreted or a data object of class, repeated, tccov, or tvcov. If `point` has class `repeated`, it is used as the environment.
`print.level`	`nlm` control options.
`ndigit`	`nlm` control options.
`gradtol`	`nlm` control options.
`steptol`	`nlm` control options.
`iterlim`	`nlm` control options.
`fscale`	`nlm` control options.
`typsize`	`nlm` control options.
`stepmax`	`nlm` control options.

Author(s)

J.K. Lindsey

References

Lindsey, J.K. (1995) Fitting parametric counting processes by using log linear models. Journal of the Royal Statistical Society C44, 201-212.

Examples

y <- c(5,3,2,4)
# event indicator
py <- pp(y)
# time since previous event
ptime <- tpast(y)
# individual ID
i <- c(1,1,2,2)
id <- ident(y, i)
# times and corresponding covariate values
tx <- c(2,3,1,2,2,2,2)
x <- c(1,2,2,1,2,2,1)
zcov <- tvcov(y, x, tx)
# Poisson process
ehr(py, plambda=1)
# Weibull process
lambda1 <- function(p) p[1]+p[2]*log(ptime)
ehr(py, lambda=lambda1, plambda=c(1,1))
# or
ehr(py, lambda=~log(ptime), plambda=c(1,1))
# or
ehr(py, lambda=~b0+b1*log(ptime), plambda=list(b0=1,b1=1))
# Poisson process with time-varying covariate
lambda2 <- function(p) p[1]+p[2]*zcov
ehr(py, lambda=lambda2, plambda=c(1,1))
# or
ehr(py, lambda=~zcov, plambda=c(1,1))
# or
ehr(py, lambda=~c0+c1*zcov, plambda=list(c0=1,c1=1))
# Weibull process with time-varying covariate
lambda3 <- function(p) p[1]+p[2]*log(ptime)+p[3]*zcov
ehr(py, lambda=lambda3, plambda=c(1,1,1))
# or
ehr(py, lambda=~log(ptime)+zcov, plambda=c(1,1,1))
# or
ehr(py, lambda=~c0+b1*log(ptime)+c1*zcov, plambda=list(c0=1,c1=1,b1=1))
# gamma process with time-varying covariate
lambda4 <- function(p) hgamma(ptime, p[1], exp(p[2]+p[3]*zcov))
ehr(py, lambda=lambda4, plambda=c(1,1,1))
# or
ehr(py, lambda=~hgamma(ptime, b1, exp(c0+c1*zcov)),
	plambda=list(c0=1,c1=1,b1=1))
# or
lambda5 <- function(p, linear) hgamma(ptime, p[1], exp(linear))
ehr(py, lambda=lambda5, linear=~zcov, plambda=c(1,1,1))
y <- c(5,3,2,4)
# event indicator
py <- pp(y)
# time since previous event
ptime <- tpast(y)
# individual ID
i <- c(1,1,2,2)
id <- ident(y, i)
# times and corresponding covariate values
tx <- c(2,3,1,2,2,2,2)
x <- c(1,2,2,1,2,2,1)
zcov <- tvcov(y, x, tx)
# Poisson process
ehr(py, plambda=1)
# Weibull process
lambda1 <- function(p) p[1]+p[2]*log(ptime)
ehr(py, lambda=lambda1, plambda=c(1,1))
# or
ehr(py, lambda=~log(ptime), plambda=c(1,1))
# or
ehr(py, lambda=~b0+b1*log(ptime), plambda=list(b0=1,b1=1))
# Poisson process with time-varying covariate
lambda2 <- function(p) p[1]+p[2]*zcov
ehr(py, lambda=lambda2, plambda=c(1,1))
# or
ehr(py, lambda=~zcov, plambda=c(1,1))
# or
ehr(py, lambda=~c0+c1*zcov, plambda=list(c0=1,c1=1))
# Weibull process with time-varying covariate
lambda3 <- function(p) p[1]+p[2]*log(ptime)+p[3]*zcov
ehr(py, lambda=lambda3, plambda=c(1,1,1))
# or
ehr(py, lambda=~log(ptime)+zcov, plambda=c(1,1,1))
# or
ehr(py, lambda=~c0+b1*log(ptime)+c1*zcov, plambda=list(c0=1,c1=1,b1=1))
# gamma process with time-varying covariate
lambda4 <- function(p) hgamma(ptime, p[1], exp(p[2]+p[3]*zcov))
ehr(py, lambda=lambda4, plambda=c(1,1,1))
# or
ehr(py, lambda=~hgamma(ptime, b1, exp(c0+c1*zcov)),
	plambda=list(c0=1,c1=1,b1=1))
# or
lambda5 <- function(p, linear) hgamma(ptime, p[1], exp(linear))
ehr(py, lambda=lambda5, linear=~zcov, plambda=c(1,1,1))

Event History Analysis Library

Description

autointensity Plot Autointensity Function of a Point Process

bp Create a Vector of Cumulative Numbers of Previous Events for a Point Process

coxre Cox Proportional Hazards Model with Random Effect

cprocess Counting Process Plot

ehr Fit an Intensity Function to Event Histories

hboxcox Log Hazard Function for a Box-Cox Process

hburr Log Hazard Function for a Burr Process

hcauchy Log Hazard Function for a Cauchy Process

hexp Log Hazard Function for an Exponential (Poisson) Process

hgamma Log Hazard Function for a Gamma Process

hgextval Log Hazard Function for an Extreme Value Process

hggamma Log Hazard Function for a Generalized Gamma Process

hglogis Log Hazard Function for a Generalized Logistic Process

hgweibull Log Hazard Function for a Generalized Weibull Process

hhjorth Log Hazard Function for a Hjorth Process

hinvgauss Log Hazard Function for a Inverse Gauss Process

hlaplace Log Hazard Function for a Laplace Process

hlnorm Log Hazard Function for a Log Normal Process

hlogis Log Hazard Function for a Logistic Process

hnorm Log Hazard Function for a Normal Process

hpareto Log Hazard Function for a Pareto Process

hskewlaplace Log Hazard Function for a Skew Laplace Process

hstudent Log Hazard Function for a Student Process

hweibull Log Hazard Function for a Weibull Process

ident Create an Individual Identification Vector for a Point Process

kalsurv Generalized Repeated Measurements Models for Event Histories

km Kaplan-Meier Survival Curves

pbirth Fit Overdispersed Count Data as a Birth Process

pp Create a Point Process Vector from Times between Events

read.list Read a List of Matrices of Unbalanced Repeated Measurements from a File

read.surv Read a List of Vectors of Event Histories from a File

survkit Weibull and Cox Models with Random Effects

tccov Create a Vector of Time-constant Covariates for a Point Process

tpast Create a Vector of Times Past since Previous Events for a Point Process

ttime Create a Vector of Total Time Elapsed for each Individual for a Point Process

tvcov Create a Vector of Time-varying Covariates for a Point Process

Log Hazard Function for a Box-Cox Process

Description

This function provides information about the Box-Cox distribution with location parameter equal to m, dispersion equal to s, and power transformation equal to f: log hazard. (See 'rmutil' for the d/p/q/r boxcox functions density, cumulative distribution, quantiles, and random generation).

The Box-Cox distribution has density

$f(y) = \frac{1}{\sqrt{2 \pi \sigma^2}} \exp(-((y^\nu/\nu-\mu)^2/(2 \sigma^2)))/ (1-I(\nu<0)-sign(\nu)*pnorm(0,\mu,sqrt(\sigma)))$

where $\mu$ is the location parameter of the distribution, $\sigma$ is the dispersion, $\nu$ is the family parameter, $I()$ is the indicator function, and $y>0$ .

$\nu=1$ gives a truncated normal distribution.

Usage

hboxcox(y, m, s, f)
hboxcox(y, m, s, f)

Arguments

`y`	vector of responses.
`m`	vector of location parameters.
`s`	vector of dispersion parameters.
`f`	vector of power parameters.

Author(s)

J.K. Lindsey

Examples

hboxcox(2, 5, 5, 2)
hboxcox(2, 5, 5, 2)

Log Hazard Function for a Burr Process

Description

These functions provide information about the Burr distribution with location parameter equal to m, dispersion equal to s, and family parameter equal to f: log hazard. (See 'rmutil' for the d/p/q/r boxcox functions density, cumulative distribution, quantiles, and random generation).

The Burr distribution has density

$f(y) = \frac{\nu \sigma (y / \mu)^{\sigma-1}} {\mu (1+(y/\mu)^\sigma)^{\nu+1}}$

where $\mu$ is the location parameter of the distribution, $\sigma$ is the dispersion, and $\nu$ is the family parameter.

Usage

hburr(y, m, s, f)
hburr(y, m, s, f)

Arguments

`y`	vector of responses.
`m`	vector of location parameters.
`s`	vector of dispersion parameters.
`f`	vector of family parameters.

Author(s)

J.K. Lindsey

Examples

hburr(2, 5, 1, 2)
hburr(2, 5, 1, 2)

Log Hazard Function for a Cauchy Process

Description

Log Hazard Function for a Cauchy Process

Usage

hcauchy(y, m, s)
hcauchy(y, m, s)

Arguments

`y`	Vector of times.
`m`	Location parameter.
`s`	Dispersion parameter.

Value

hcauchy returns the log hazard function for a Cauchy process with the given parameter values.

Author(s)

J.K. Lindsey

Examples

hcauchy(1:10, 3, 2)
hcauchy(1:10, 3, 2)

Log Hazard Function for a Poisson Process

Description

Log Hazard Function for a Poisson Process

Usage

hexp(y, rate)
hexp(y, rate)

Arguments

`y`	Vector of times.
`rate`	Vector of rates.

Value

hexp returns the log hazard function for a Poisson process with the given parameter value.

Author(s)

J.K. Lindsey

Examples

hexp(1:10, 3)
hexp(1:10, 3)

Log Hazard Function for a Gamma Process

Description

Log Hazard Function for a Gamma Process

Usage

hgamma(y, shape, rate=1, scale=1/rate)
hgamma(y, shape, rate=1, scale=1/rate)

Arguments

`y`	Vector of times.
`shape`	Shape parameter.
`rate`	Rate parameter.
`scale`	Scale parameter.

Value

hgamma returns the log hazard function for a gamma process with the given parameter values.

Author(s)

J.K. Lindsey

Examples

hgamma(1:10, 3, 2)
hgamma(1:10, 3, 2)

Log Hazard Function for an Extreme Value Process

Description

These functions provide information about the generalized extreme value distribution with location parameter equal to m, dispersion equal to s, and family parameter equal to f:log hazard. (See 'rmutil' for the d/p/q/r boxcox functions density, cumulative distribution, quantiles, and random generation).

The generalized extreme value distribution has density

$f(y) = y^{\nu-1} \exp(y^\nu/\nu) \frac{\sigma}{\mu} \frac{\exp(y^\nu/\nu)}{\mu^{\sigma-1}/(1-I(\nu>0)+sign(\nu) exp(-\mu^-\sigma))}\exp(-(\exp(y^\nu\nu)/\mu)^\sigma)$

where $\mu$ is the location parameter of the distribution, $\sigma$ is the dispersion, $\nu$ is the family parameter, $I()$ is the indicator function, and $y>0$ .

$\nu=1$ a truncated extreme value distribution.

Usage

hgextval(y, s, m, f)
hgextval(y, s, m, f)

Arguments

`y`	vector of responses.
`m`	vector of location parameters.
`s`	vector of dispersion parameters.
`f`	vector of family parameters.

Author(s)

J.K. Lindsey

Examples

hgextval(1, 2, 1, 2)
hgextval(1, 2, 1, 2)

Log Hazard Function for a Generalized Gamma Process

Description

These functions provide information about the generalized gamma distribution with scale parameter equal to m, shape equal to s, and family parameter equal to f: log hazard. (See 'rmutil' for the d/p/q/r boxcox functions density, cumulative distribution, quantiles, and random generation).

The generalized gamma distribution has density

$f(y) = \frac{\nu y^{\nu-1}} {(\mu/\sigma)^{\nu\sigma} Gamma(\sigma)} y^{\nu(\sigma-1)} \exp(-(y \sigma/\mu)^\nu)$

where $\mu$ is the scale parameter of the distribution, $\sigma$ is the shape, and $\nu$ is the family parameter.

$\nu=1$ yields a gamma distribution, $\sigma=1$ a Weibull distribution, and $\sigma=\infty$ a log normal distribution.

Usage

hggamma(y, s, m, f)
hggamma(y, s, m, f)

Arguments

`y`	vector of responses.
`m`	vector of location parameters.
`s`	vector of dispersion parameters.
`f`	vector of family parameters.

Author(s)

J.K. Lindsey

Examples

hggamma(2, 5, 4, 2)
hggamma(2, 5, 4, 2)

Log Hazard Function for a Generalized Logistic Process

Description

These functions provide information about the generalized logistic distribution with location parameter equal to m, dispersion equal to s, and family parameter equal to f: log hazard. (See 'rmutil' for the d/p/q/r boxcox functions density, cumulative distribution, quantiles, and random generation).

The generalized logistic distribution has density

$f(y) = \frac{\nu \sqrt{3} \exp(-\sqrt{3} (y-\mu)/(\sigma \pi))}{ \sigma \pi (1+\exp(-\sqrt{3} (y-\mu)/(\sigma \pi)))^{\nu+1}}$

where $\mu$ is the location parameter of the distribution, $\sigma$ is the dispersion, and $\nu$ is the family parameter.

$\nu=1$ gives a logistic distribution.

Usage

hglogis(y, m, s, f)
hglogis(y, m, s, f)

Arguments

`y`	vector of responses.
`m`	vector of location parameters.
`s`	vector of dispersion parameters.
`f`	vector of family parameters.

Author(s)

J.K. Lindsey

Examples

hglogis(5, 5, 1, 2)
hglogis(5, 5, 1, 2)

Log Hazard Function for a Generalized Weibull Process

Description

These functions provide information about the generalized Weibull distribution, also called the exponentiated Weibull, with scale parameter equal to m, shape equal to s, and family parameter equal to f: log hazard. (See 'rmutil' for the d/p/q/r boxcox functions density, cumulative distribution, quantiles, and random generation).

The generalized Weibull distribution has density

$f(y) = \frac{\sigma \nu y^{\sigma-1} (1-\exp(-(y/\mu)^\sigma))^{\nu-1} \exp(-(y/\mu)^\sigma)}{\mu^\sigma}$

where $\mu$ is the scale parameter of the distribution, $\sigma$ is the shape, and $\nu$ is the family parameter.

$\nu=1$ gives a Weibull distribution, for $\sigma=1$ , $\nu<0$ a generalized F distribution, and for $\sigma>0$ , $\nu\leq0$ a Burr type XII distribution.

Usage

hgweibull(y, s, m, f)
hgweibull(y, s, m, f)

Arguments

`y`	vector of responses.
`m`	vector of location parameters.
`s`	vector of dispersion parameters.
`f`	vector of family parameters.

Author(s)

J.K. Lindsey

Examples

hgweibull(5, 1, 3, 2)
hgweibull(5, 1, 3, 2)

Log Hazard Function for a Hjorth Process

Description

These functions provide information about the Hjorth distribution with location parameter equal to m, dispersion equal to s, and family parameter equal to f: log hazard. (See 'rmutil' for the d/p/q/r boxcox functions density, cumulative distribution, quantiles, and random generation).

The Hjorth distribution has density

$f(y) = (1+\sigma y)^{-\nu/\sigma} \exp(-(y/\mu)^2/2) (\frac{y}{\mu^2}+\frac{\nu}{1+\sigma y})$

where $\mu$ is the location parameter of the distribution, $\sigma$ is the dispersion, and $\nu$ is the family parameter.

Usage

hhjorth(y, m, s, f)
hhjorth(y, m, s, f)

Arguments

`y`	vector of responses.
`m`	vector of location parameters.
`s`	vector of dispersion parameters.
`f`	vector of family parameters.

Author(s)

J.K. Lindsey

Examples

hhjorth(5, 5, 5, 2)
hhjorth(5, 5, 5, 2)

Log Hazard Function for a Inverse Gauss Process

Description

These functions provide information about the inverse Gaussian distribution with mean equal to m and dispersion equal to s: log hazard. (See 'rmutil' for the d/p/q/r boxcox functions density, cumulative distribution, quantiles, and random generation).

The inverse Gaussian distribution has density

$f(y) = \frac{1}{\sqrt{2\pi\sigma y^3}} e^{-(y-\mu)^2/(2 y \sigma m^2)}$

where $\mu$ is the mean of the distribution and $\sigma$ is the dispersion.

Usage

hinvgauss(y, m, s)
hinvgauss(y, m, s)

Arguments

`y`	vector of responses.
`m`	vector of means.
`s`	vector of dispersion parameters.

Author(s)

J.K. Lindsey

Examples

hinvgauss(5, 5, 1)
hinvgauss(5, 5, 1)

Log Hazard Function for a Laplace Process

Description

These functions provide information about the Laplace distribution with location parameter equal to m and dispersion equal to s: log hazard. (See 'rmutil' for the d/p/q/r boxcox functions density, cumulative distribution, quantiles, and random generation).

The Laplace distribution has density

$f(y) = \frac{\exp(-abs(y-\mu)/\sigma)}{(2\sigma)}$

where $\mu$ is the location parameter of the distribution and $\sigma$ is the dispersion.

Usage

hlaplace(y, m=0, s=1)
hlaplace(y, m=0, s=1)

Arguments

`y`	vector of responses.
`m`	vector of location parameters.
`s`	vector of dispersion parameters.

Author(s)

J.K. Lindsey

Examples

hlaplace(5, 2, 1)
hlaplace(5, 2, 1)

Log Hazard Function for a Log Normal Process

Description

Log Hazard Function for a Log Normal Process

Usage

hlnorm(y, m, s)
hlnorm(y, m, s)

Arguments

`y`	Vector of times.
`m`	Mean parameter.
`s`	Variance parameter.

Value

hlnorm returns the log hazard function for a log normal process with the given parameter values.

Author(s)

J.K. Lindsey

Examples

hlnorm(1:10, 3, 2)
hlnorm(1:10, 3, 2)

Log Hazard Function for a Logistic Process

Description

Log Hazard Function for a Logistic Process

Usage

hlogis(y, m, s)
hlogis(y, m, s)

Arguments

`y`	Vector of times.
`m`	Location parameter.
`s`	Scale parameter.

Value

hlogis returns the log hazard function for a logistic process with the given parameter values.

Author(s)

J.K. Lindsey

Examples

hlogis(1:10, 3, 2)
hlogis(1:10, 3, 2)

Log Hazard Function for a Normal Process

Description

Log Hazard Function for a Normal Process

Usage

hnorm(y, m, s)
hnorm(y, m, s)

Arguments

`y`	Vector of times.
`m`	Mean parameter.
`s`	Variance parameter.

Value

hnorm returns the log hazard function for a normal process with the given parameter values.

Author(s)

J.K. Lindsey

Examples

hnorm(1:10, 3, 2)
hnorm(1:10, 3, 2)

Log Hazard Function for a Pareto Process

Description

These functions provide information about the Pareto distribution with location parameter equal to m and dispersion equal to s: log hazard. (See 'rmutil' for the d/p/q/r boxcox functions density, cumulative distribution, quantiles, and random generation).

The Pareto distribution has density

$f(y) = \frac{\sigma }{\mu (\sigma-1)(1 + y/(\mu (\sigma-1)))^{\sigma+1}}$

where $\mu$ is the mean parameter of the distribution and $\sigma$ is the dispersion.

This distribution can be obtained as a mixture distribution from the exponential distribution using a gamma mixing distribution.

Usage

hpareto(y, m, s)
hpareto(y, m, s)

Arguments

`y`	vector of responses.
`m`	vector of location parameters.
`s`	vector of dispersion parameters.

Author(s)

J.K. Lindsey

Examples

hpareto(5, 2, 2)
hpareto(5, 2, 2)

Log Hazard Function for a Skew Laplace Process

Description

These functions provide information about the skew Laplace distribution with location parameter equal to m, dispersion equal to s, and skew equal to f: log hazard. (See 'rmutil' for the d/p/q/r boxcox functions density, cumulative distribution, quantiles, and random generation). For f=1, this is an ordinary (symmetric) Laplace distribution.

The skew Laplace distribution has density

$f(y) = \frac{\nu\exp(-\nu(y-\mu)/\sigma)}{(1+\nu^2)\sigma}$

if $y\ge\mu$ and else

$f(y) = \frac{\nu\exp((y-\mu)/(\nu\sigma))}{(1+\nu^2)\sigma}$

where $\mu$ is the location parameter of the distribution, $\sigma$ is the dispersion, and $\nu$ is the skew.

The mean is given by $\mu+\frac{\sigma(1-\nu^2)}{\sqrt{2}\nu}$ and the variance by $\frac{\sigma^2(1+\nu^4)}{2\nu^2}$ .

Note that this parametrization of the skew (family) parameter is different than that used for the multivariate skew Laplace distribution in 'growth::elliptic'.

Usage

hskewlaplace(y, m=0, s=1, f=1)
hskewlaplace(y, m=0, s=1, f=1)

Arguments

`y`	vector of responses.
`m`	vector of location parameters.
`s`	vector of dispersion parameters.
`f`	vector of skew parameters.

Author(s)

J.K. Lindsey

Examples

hskewlaplace(5, 2, 1, 0.5)
hskewlaplace(5, 2, 1, 0.5)

Log Hazard Function for a Student t Process

Description

Log Hazard Function for a Student t Process

Usage

hstudent(y, m, s, f)
hstudent(y, m, s, f)

Arguments

`y`	Vector of times.
`m`	Location parameter.
`s`	Scale parameter.
`f`	Degrees of freedom.

Value

hstudent returns the log hazard function for a Student t process with the given parameter values.

Author(s)

J.K. Lindsey

Examples

hstudent(1:10, 3, 2, 5)
hstudent(1:10, 3, 2, 5)

Log Hazard Function for a Weibull Process

Description

Log Hazard Function for a Weibull Process

Usage

hweibull(y, s, m)
hweibull(y, s, m)

Arguments

`y`	Vector of times.
`s`	Shape parameter.
`m`	Scale parameter.

Value

hweibull returns the log hazard function for a Weibull process with the given parameter values.

Author(s)

J.K. Lindsey

Examples

hweibull(1:10, 1.5, 2)
hweibull(1:10, 1.5, 2)

Create an Individual Identification Vector for a Point Process

Description

ident creates a vector of length sum(y) by repeating the values of individual identifiers for the times for use with ehr.

Usage

ident(y, id)
ident(y, id)

Arguments

`y`	Vector of times.
`id`	Vector of corresponding individual identifiers for who had which sequence of times.

Value

ident creates a vector of length sum(y) by repeating the values of individual identifiers for the times for use with ehr.

Author(s)

J.K. Lindsey

Examples

y <- c(5,3,2,4)
i <- c(1,1,2,2)
id <- ident(y, i)
id
y <- c(5,3,2,4)
i <- c(1,1,2,2)
id <- ident(y, i)
id

Repeated Events Models with Frailty or Serial Dependence

Description

kalsurv is designed to handle event history models with time-varying covariates. The distributions have two extra parameters as compared to the functions specified by intensity and are generally longer tailed than those distributions. Dependence of inter-event times can be through gamma frailties (a type of random effect), with or without autoregression, or several kinds of serial dependence by updating, as in Kalman filtering.

By default, a gamma mixture of the distribution specified in intensity is used, as the conditional distribution in the serial dependence models, and as a symmetric multivariate (random effect) model for frailty dependence. For example, with a Weibull intensity and frailty dependence, this yields a multivariate Burr distribution and with Markov or serial dependence, univariate Burr conditional distributions.

If a value for pfamily is used, the gamma mixture is replaced by a power variance family mixture.

Nonlinear regression models can be supplied as formulae where parameters are unknowns in which case factor variables cannot be used and parameters must be scalars. (See finterp.)

Marginal and individual profiles can be plotted using mprofile and iprofile and residuals with plot.residuals.

Usage

kalsurv(response, intensity="exponential", distribution="Pareto",
	depend="independence", update="Markov", mu=NULL, shape=NULL,
	renewal=TRUE, density=FALSE, censor=NULL, delta=NULL, ccov=NULL,
	tvcov=NULL, preg=NULL, ptvc=NULL, pbirth=NULL,
	pintercept=NULL, pshape=NULL, pinitial=1, pdepend=NULL,
	pfamily=NULL, envir=parent.frame(), print.level=0,
	ndigit=10, gradtol=0.00001, steptol=0.00001, iterlim=100,
	fscale=1, typsize=abs(p), stepmax=10*sqrt(p%*%p))
kalsurv(response, intensity="exponential", distribution="Pareto",
	depend="independence", update="Markov", mu=NULL, shape=NULL,
	renewal=TRUE, density=FALSE, censor=NULL, delta=NULL, ccov=NULL,
	tvcov=NULL, preg=NULL, ptvc=NULL, pbirth=NULL,
	pintercept=NULL, pshape=NULL, pinitial=1, pdepend=NULL,
	pfamily=NULL, envir=parent.frame(), print.level=0,
	ndigit=10, gradtol=0.00001, steptol=0.00001, iterlim=100,
	fscale=1, typsize=abs(p), stepmax=10*sqrt(p%*%p))

Arguments

`response`	A list of vectors with times between events for each individual, one matrix or dataframe of such times if all individuals have the same number of events, or an object of class, `response` (created by `restovec`) or `repeated` (created by `rmna` or `lvna`). If the `repeated` data object contains more than one response variable, give that object in `envir` and give the name of the response variable to be used here.
`intensity`	The form of intensity function to be put in the distribution given by dist. Choices are exponential, Weibull, gamma, log normal, log logistic, log Cauchy, log Student, and gen(eralized) logistic.
`distribution`	The outer distribution. Choices are Pareto, gamma, and Weibull.
`depend`	Type of dependence. Choices are `independence`, `frailty`, and `serial`.
`update`	Type of update for serial dependence. Choices are `Markov`, `elapsed Markov`, `serial`, `event`, `cumulated`, `count`, and `kalman`. With `frailty` dependence, weighting by length of observation time may be specified by setting update to `time`.
`mu`	A regression function for the location parameter or a formula beginning with ~, specifying either a linear regression function in the Wilkinson and Rogers notation or a general function with named unknown parameters. Give the initial estimates in `preg` if there are no time-varying covariates and in `ptvc` if there are.
`shape`	A regression function for the shape parameter or a formula beginning with ~, specifying either a linear regression function in the Wilkinson and Rogers notation or a general function with named unknown parameters. It must yield one value per observation.
`renewal`	IF TRUE, a renewal process is modelled, with time reinitialized after each event. Otherwise, time is cumulated from the origin of observations.
`density`	If TRUE, the density of the function specified in `intensity` is used instead of the intensity.
`censor`	A vector of the same length as the number of individuals containing a binary indicator, with a one indicating that the last time period in the series terminated with an event and zero that it was censored. For independence and frailty models, where response is matrix, censor may also be a matrix of the same size. Ignored if response has class, `response` or `repeated`.
`delta`	Scalar or vector giving the unit of measurement for each response value, set to unity by default. For example, if a response is measured to two decimals, delta=0.01. If the response has been pretransformed, this must be multiplied by the Jacobian. This transformation cannot contain unknown parameters. For example, with a log transformation, `delta=1/y`. (The delta values for the censored response are ignored.) Ignored if response has class, `response` or `repeated`.
`ccov`	A vector or matrix containing time-constant baseline covariates with one entry per individual, a model formula using vectors of the same size, or an object of class, `tccov` (created by `tcctomat`). If response has class, `repeated`, the covariates must be supplied as a Wilkinson and Rogers formula unless none are to be used or `mu` is given.
`tvcov`	A list of matrices with time-varying covariate values, observed at the event times in `response`, for each individual (one column per variable), one matrix or dataframe of such covariate values, or an object of class, `tvcov` (created by `tvctomat`). If response has class, `repeated`, the covariates must be supplied as a Wilkinson and Rogers formula unless none are to be used or `mu` is given.
`preg`	Initial parameter estimates for the regression model: intercept plus one for each covariate in `ccov`. If `mu` is a formula or function, the parameter estimates must be given here only if there are no time-varying covariates. If `mu` is a formula with unknown parameters, their estimates must be supplied either in their order of appearance in the expression or in a named list.
`ptvc`	Initial parameter estimates for the coefficients of the time-varying covariates, as many as in `tvcov`. If `mu` is a formula or function, the parameter estimates must be given here if there are time-varying covariates present.
`pbirth`	If supplied, this is the initial estimate for the coefficient of the birth model.
`pintercept`	The initial estimate of the intercept for the generalized logistic intensity.
`pshape`	An initial estimate for the shape parameter of the intensity (except exponential intensity). If `shape` is a function or formula, the corresponding initial estimates. If `shape` is a formula with unknown parameters, their estimates must be supplied either in their order of appearance in the expression or in a named list.
`pinitial`	An initial estimate for the initial parameter. In `frailty` dependence, this is the frailty parameter.
`pdepend`	An initial estimate for the serial dependence parameter. For `frailty` dependence, if a value is given here, an autoregression is fitted as well as the frailty.
`pfamily`	An optional initial estimate for the second parameter of a two-parameter power variance family mixture instead of the default gamma mixture. This yields a gamma mixture as `family -> 0`, an inverse Gauss mixture for `family = 0.5`, and a compound distribution of a Poisson-distributed number of gamma distributions for `-1 < family < 0`.
`envir`	Environment in which model formulae are to be interpreted or a data object of class, `repeated`, `tccov`, or `tvcov`; the name of the response variable should be given in `response`. If `response` has class `repeated`, it is used as the environment.
`print.level`	`nlm` control options.
`ndigit`	`nlm` control options.
`gradtol`	`nlm` control options.
`steptol`	`nlm` control options.
`iterlim`	`nlm` control options.
`fscale`	`nlm` control options.
`typsize`	`nlm` control options.
`stepmax`	`nlm` control options.

Value

A list of classes kalsurv and recursive is returned.

Author(s)

J.K. Lindsey

Examples

treat <- c(0,0,1,1)
tr <- tcctomat(treat)
cens <- matrix(rbinom(20,1,0.9),ncol=5)
times <- # matrix(rweibull(20,2,1+3*rep(treat,5)),ncol=5)
	matrix(c(1.36,0.18,0.84,0.65,1.44,1.79,1.04,0.43,1.35,1.63,2.15,1.15,
		1.21,5.46,1.58,3.44,4.40,2.75,4.78,2.44),ncol=5,byrow=TRUE)
times <- restovec(times, censor=cens)
reps <- rmna(times, ccov=tr)
# exponential intensity model with independence
kalsurv(times, pinitial=0.5, preg=1, dep="independence",
	intensity="exponential")
# Weibull intensity model with independence
kalsurv(times, pinitial=0.5, preg=1, pshape=1, dep="independence",
	intensity="Weibull")
# same model with serial update
kalsurv(times, pinitial=0.5, pdep=0.1, preg=1, pshape=1, dep="serial",
	intensity="Weibull")
# try power variance family instead of gamma distribution for mixture
kalsurv(times, pinitial=0.5, pdep=0.1, preg=1, pshape=1, dep="serial",
	intensity="Weibull", pfamily=0.1)
# treatment effect with log link
kalsurv(times, pinitial=0.5, preg=c(1,0), pshape=1, intensity="Weibull",
	ccov=treat)
# or equivalently
kalsurv(times, mu=~exp(a+b*treat), pinitial=0.1, preg=c(1,0), pshape=1,
	intensity="Weibull", envir=reps)
# with identity link instead
kalsurv(times, mu=~treat, pinitial=0.5, preg=c(1,0), pshape=1,
	intensity="Weibull")
# or equivalently
kalsurv(times, mu=~a+b*treat, pinitial=0.5, preg=c(1,0), pshape=1,
	intensity="Weibull", envir=reps)
# add the birth model
kalsurv(times, pinitial=0.5, preg=c(1,0), pshape=1,
	intensity="Weibull", ccov=treat, pbirth=0)
# try frailty dependence
kalsurv(times, pinitial=0.5, preg=c(1,0), pshape=1, dep="frailty",
	intensity="Weibull", ccov=treat)
# add autoregression
kalsurv(times, pinitial=0.5, preg=c(1,0), pshape=1, dep="frailty",
	pdep=0.1, intensity="Weibull", ccov=treat)
# switch to gamma intensity model
kalsurv(times, pinitial=0.5, preg=c(1,0), pshape=1, intensity="gamma",
	ccov=treat)
treat <- c(0,0,1,1)
tr <- tcctomat(treat)
cens <- matrix(rbinom(20,1,0.9),ncol=5)
times <- # matrix(rweibull(20,2,1+3*rep(treat,5)),ncol=5)
	matrix(c(1.36,0.18,0.84,0.65,1.44,1.79,1.04,0.43,1.35,1.63,2.15,1.15,
		1.21,5.46,1.58,3.44,4.40,2.75,4.78,2.44),ncol=5,byrow=TRUE)
times <- restovec(times, censor=cens)
reps <- rmna(times, ccov=tr)
# exponential intensity model with independence
kalsurv(times, pinitial=0.5, preg=1, dep="independence",
	intensity="exponential")
# Weibull intensity model with independence
kalsurv(times, pinitial=0.5, preg=1, pshape=1, dep="independence",
	intensity="Weibull")
# same model with serial update
kalsurv(times, pinitial=0.5, pdep=0.1, preg=1, pshape=1, dep="serial",
	intensity="Weibull")
# try power variance family instead of gamma distribution for mixture
kalsurv(times, pinitial=0.5, pdep=0.1, preg=1, pshape=1, dep="serial",
	intensity="Weibull", pfamily=0.1)
# treatment effect with log link
kalsurv(times, pinitial=0.5, preg=c(1,0), pshape=1, intensity="Weibull",
	ccov=treat)
# or equivalently
kalsurv(times, mu=~exp(a+b*treat), pinitial=0.1, preg=c(1,0), pshape=1,
	intensity="Weibull", envir=reps)
# with identity link instead
kalsurv(times, mu=~treat, pinitial=0.5, preg=c(1,0), pshape=1,
	intensity="Weibull")
# or equivalently
kalsurv(times, mu=~a+b*treat, pinitial=0.5, preg=c(1,0), pshape=1,
	intensity="Weibull", envir=reps)
# add the birth model
kalsurv(times, pinitial=0.5, preg=c(1,0), pshape=1,
	intensity="Weibull", ccov=treat, pbirth=0)
# try frailty dependence
kalsurv(times, pinitial=0.5, preg=c(1,0), pshape=1, dep="frailty",
	intensity="Weibull", ccov=treat)
# add autoregression
kalsurv(times, pinitial=0.5, preg=c(1,0), pshape=1, dep="frailty",
	pdep=0.1, intensity="Weibull", ccov=treat)
# switch to gamma intensity model
kalsurv(times, pinitial=0.5, preg=c(1,0), pshape=1, intensity="gamma",
	ccov=treat)

Kaplan-Meier Survivor Curves

Description

km calculates the Kaplan-Meier estimates for survival.

To plot the survivor curve, use plot(); for the empirical intensity curve, use plot.intensity(); for diagnostic curves to choose a distribution to which the data might belong, use plot.dist().

Usage

km(times, censor, group=1, freq=1, cdf=FALSE)
## S3 method for class 'km'
plot(x, add=FALSE, xlim=NULL, ylim=c(0,1), 
main=NULL, xlab="Time", ylab=NULL, lty=NULL, ...)
## S3 method for class 'km'
plot.intensity(x, add=FALSE, xlab="Time", ylab="Hazard", type="l", lty=NULL, ...)
## S3 method for class 'km'
plot.dist(x, ...)
km(times, censor, group=1, freq=1, cdf=FALSE)
## S3 method for class 'km'
plot(x, add=FALSE, xlim=NULL, ylim=c(0,1), 
main=NULL, xlab="Time", ylab=NULL, lty=NULL, ...)
## S3 method for class 'km'
plot.intensity(x, add=FALSE, xlab="Time", ylab="Hazard", type="l", lty=NULL, ...)
## S3 method for class 'km'
plot.dist(x, ...)

Arguments

`times`	Vector of times to events or a list of vectors of such times for different individuals.
`censor`	Vector of censoring indicators corresponding to the vector of times or to the last time in each vector of a list.
`group`	Vector indicating to which group each individual belongs.
`freq`	Vector of frequencies for grouped data.
`cdf`	If TRUE, calculate the cdf instead of the survivor curve.
`x`	An object produced by `km`.
`add`	Plotting control options.
`main`	Plotting control options.
`type`	Plotting control options.
`ylab`	Plotting control options.
`xlab`	Plotting control options.
`xlim`	Plotting control options.
`ylim`	Plotting control options.
`lty`	Plotting control options.
`...`	Plotting control options.

Value

A matrix with class, km, containing the Kaplan-Meier estimates is returned.

Author(s)

J.K. Lindsey

Examples

surv <- rgamma(40,2,scale=5)
cens <- rbinom(40,1,0.9)
treat <- gl(2,20)
plot(km(surv, cens, group=treat), main="",xlab="Months",
	ylab="Probability of deterioration")
plot.dist(km(surv, cens, group=treat))
plot.intensity(km(surv, cens, group=treat),ylab="Risk of deterioration")
surv <- rgamma(40,2,scale=5)
cens <- rbinom(40,1,0.9)
treat <- gl(2,20)
plot(km(surv, cens, group=treat), main="",xlab="Months",
	ylab="Probability of deterioration")
plot.dist(km(surv, cens, group=treat))
plot.intensity(km(surv, cens, group=treat),ylab="Risk of deterioration")

Fit Overdispersed Count Data as a Birth Process

Description

pbirth fits binomial, binomial exponential, binomial logistic, binomial total, Poisson, Poisson exponential, negative binomial, gen(eralized) negative binomial, and generalized negative binomial processes as a birth process.

Usage

pbirth(frequencies, p, intensity="negative binomial",
	type="spectral decomposition", print.level=0, ndigit=10,
	gradtol=0.00001, steptol=0.00001, fscale=1, iterlim=100,
	typsize=abs(p), stepmax=10*sqrt(p%*%p))
pbirth(frequencies, p, intensity="negative binomial",
	type="spectral decomposition", print.level=0, ndigit=10,
	gradtol=0.00001, steptol=0.00001, fscale=1, iterlim=100,
	typsize=abs(p), stepmax=10*sqrt(p%*%p))

Arguments

`frequencies`	Vector of frequencies or a matrix with each row a different series of frequencies.
`p`	Vector of initial estimates.
`intensity`	The intensity function of the process: binomial, binomial exdponential, binomial logistic, binomial total, Poisson, Poisson exponential, negative binomial, or gen(eralized) negative binomial.
`type`	Algorithm used for matrix exponentiation: spectral decomposition or series approximation.
`print.level`	`nlm` control options.
`ndigit`	`nlm` control options.
`gradtol`	`nlm` control options.
`steptol`	`nlm` control options.
`iterlim`	`nlm` control options.
`fscale`	`nlm` control options.
`typsize`	`nlm` control options.
`stepmax`	`nlm` control options.

Author(s)

J.K. Lindsey

References

Faddy, M.J. and Fenlon, J.S. (1999) Stochastic modelling of the invasion process of nematodes in fly larvae. Applied Statistics 48: 31-37.

Examples

y <- rnbinom(100,2,0.6)
fr <- tabulate(y)
pbirth(fr, p=log(-log(0.7)), intensity="Poisson", type="series")
pbirth(fr, p=c(log(-log(0.7)),log(5)),
	intensity="negative binomial", type="series")
pbirth(fr, p=c(log(-log(0.7)),log(5),-1),
	intensity="gen negative binomial", type="series")
y <- rnbinom(100,2,0.6)
fr <- tabulate(y)
pbirth(fr, p=log(-log(0.7)), intensity="Poisson", type="series")
pbirth(fr, p=c(log(-log(0.7)),log(5)),
	intensity="negative binomial", type="series")
pbirth(fr, p=c(log(-log(0.7)),log(5),-1),
	intensity="gen negative binomial", type="series")

Plot Intensity Functions

Description

Plot the empirical intensity curve for given times between events.

Usage

## S3 method for class 'intensity'
plot(x, ...)
## Default S3 method:
plot.intensity(x, censor=1, group=1, colour=TRUE, mix=1,
	ylim=c(0,1), ylab="p", xlab="Time",
	main="Empirical Hazard Function(s)", ...)
## S3 method for class 'intensity'
plot(x, ...)
## Default S3 method:
plot.intensity(x, censor=1, group=1, colour=TRUE, mix=1,
	ylim=c(0,1), ylab="p", xlab="Time",
	main="Empirical Hazard Function(s)", ...)

Arguments

`censor`	Vector of censoring indicators corresponding to the vector of times or to the last time in each vector of a list.
`group`	Vector indicating to which group each individual belongs.
`colour`	Use a different colour for each curve.
`x`	An object produced by `km` for `plot.intensity`; for `plot.intensity.default` it is `times` (Vector of times to events or a list of vectors of such times for different individuals.) These changes were made for S3 methods compatability.
`mix`	...
`main`	Plotting control options.
`ylab`	Plotting control options.
`xlab`	Plotting control options.
`ylim`	Plotting control options.
`...`	Plotting control options.

Author(s)

J.K. Lindsey

Examples

surv <- rgamma(40,2,scale=5)
cens <- rbinom(40,1,0.9)
treat <- gl(2,20)
plot(km(surv, cens, group=treat), main="",xlab="Months",
	ylab="Probability of deterioration")
plot.dist(km(surv, cens, group=treat))
plot.intensity(km(surv, cens, group=treat),ylab="Risk of deterioration")
surv <- rgamma(40,2,scale=5)
cens <- rbinom(40,1,0.9)
treat <- gl(2,20)
plot(km(surv, cens, group=treat), main="",xlab="Months",
	ylab="Probability of deterioration")
plot.dist(km(surv, cens, group=treat))
plot.intensity(km(surv, cens, group=treat),ylab="Risk of deterioration")

Create a Point Process Vector from Times between Events

Description

pp creates a vector of length sum(y) of zeroes with a one at the end of each uncensored time interval for use with ehr.

Usage

pp(y, censor=1)
pp(y, censor=1)

Arguments

`y`	Vector of times.
`censor`	Vector of censoring indicators.

Value

pp creates a vector of length sum(y) of zeroes with a one at the end of each uncensored time interval for use with ehr.

Author(s)

J.K. Lindsey

Examples

y <- c(5,3,2,4)
py <- pp(y)
py
y <- c(5,3,2,4)
py <- pp(y)
py

Weibull and Cox Models with Random Effects

Description

survfit was written in Fortran by Dr. V. Ducrocq (INRA, France: [email protected]) and Dr. J. Soelkner (Vienna: [email protected]) to fit Weibull and Cox proportional hazards models with random effects for very large data sets. This is a cut-down version adapted to R. The full Survival Kit, including the manual, can be obtained from http://www.boku.ac.at/nuwi/popgen.

Usage

survkit(times, censor=NULL, ccov=NULL, tvcov=NULL,
	strata=NULL, id=NULL, model="Weibull", baseline=FALSE,
	residuals=FALSE, survival=NULL, svalues=NULL, valrho=NULL,
	constraints=NULL, impose=NULL, dist=NULL, random=NULL,
	estimate=NULL, moments=FALSE, rule=NULL, pedigree=NULL,
	integrate=NULL, jointmode=FALSE, within=NULL, converge=1.e-8,
	iterlim=100)
survkit(times, censor=NULL, ccov=NULL, tvcov=NULL,
	strata=NULL, id=NULL, model="Weibull", baseline=FALSE,
	residuals=FALSE, survival=NULL, svalues=NULL, valrho=NULL,
	constraints=NULL, impose=NULL, dist=NULL, random=NULL,
	estimate=NULL, moments=FALSE, rule=NULL, pedigree=NULL,
	integrate=NULL, jointmode=FALSE, within=NULL, converge=1.e-8,
	iterlim=100)

Arguments

`times`	Vector of times (events, right-censoring, change in time-varying covariate, left-truncation).
`censor`	Corresponding vector of censoring indicators. 1: event; 0: censored; -1: change of time-varying covariate; -2: left-truncation time.
`ccov`	Model formula for time-constant covariates. These may have one value per individual or one per time. Because of the way factor variables are handled, interactions must be coded as new variables.
`tvcov`	Model formula for time-varying covariates with one value per time. There can only be one change-point per individual. Again, interactions must be coded as new variables.
`strata`	A factor variable specifying stratification. With the Weibull model, different intercepts and power parameters are calculated for each stratum. For the Cox model, a different baseline curve is fitted.
`id`	A variable giving individual identification numbers (starting at one). If not supplied, all times are assumed to refer to different individuals.
`model`	Weibull or Cox model, or Kaplan-Meier estimates.
`baseline`	If TRUE, the baseline values are calculated for the Cox model.
`residuals`	If TRUE, calculate residuals (only for Cox model).
`survival`	Calculate values of the survival function at `quantiles`,or at `equal`ly-spaced, `specific`, or `all` observed times.
`svalues`	A vector of quantile values (between 0 and 100), spacing and maximum for equally-spaced, or specific times for `survival`.
`valrho`	A fixed value of the Weibull power parameter if it is not to be estimated.
`constraints`	By default, the category of each factor variable with the `largest` number of events is taken as baseline. Other options are `none` which gives values around the mean and `find`. See also, `impose`.
`impose`	A list of a vector of variable names and a corresponding vector of their baseline category numbers. Any factor variables not given will have their first category as baseline.
`dist`	The distribution of the random effect: loggamma, normal, or multivariate (normal).
`random`	A factor variable specifying the random effect.
`estimate`	One fixed value for the mode of the variance of the random effect or three values if the mode is to be estimated: lower and upper bounds, and precision.
`moments`	Estimate the first three moments of the random effect as well as the mode.
`rule`	For the multivariate normal random effect, the genetic relationships: `usual`, `mgs` (sire or father model), or `sire.dam` (father and mother).
`pedigree`	A matrix with four columns required for the multivariate normal random effect, containing the individual id, the sex, the father's category, and the mother's category.
`integrate`	A factor variable to integrate out as the log-gamma random effect in a Weibull model. (Not available for the Cox model.)
`jointmode`	If TRUE, the log-gamma variance parameter is estimated simultaneously with the other parameters using the information in `estimate`. Otherwise, a fixed value, given in `estimate` is assumed.
`within`	A second factor variable (within the `integrate` variable) to integrate out.
`converge`	The convergence criterion, by default 1.e-8.
`iterlim`	Maximum number of iterations.

Author(s)

V. Ducrocq, J. Soelkner, and J.K. Lindsey

Examples

# y <- trunc(rweibull(20,2,20))
y <- c(6,22,43,16,7,6,15,35,10,9,18,34,7,13,10,17,14,19,11,13)
# cens <- rbinom(20,1,0.9)
cens <- c(1,1,1,1,0,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1)
id <- gl(2,10)
# x <- rnorm(20)
x <- c(1.82881379,1.06606868,0.70877744,-0.09932880,-0.60626148,-0.75371046,
  0.23884069,0.51199483,-0.73060095,-0.93222151,2.27947539,-0.73855454,
 -0.36412735,-0.89122114,-0.05025962,-0.10001587,1.11460865,-1.87315971,
 -0.11280052,-1.6880509)
# Kaplan-Meier estimates
survkit(y, censor=cens, model="Kaplan")
# null Weibull model
survkit(y, censor=cens)
# one time-constant covariate
survkit(y, censor=cens, ccov=~x)
# stratify
survkit(y, censor=cens, ccov=~x, strata=id)
# estimate a normal random effect
survkit(y, censor=cens, ccov=~x, random=id, dist="normal",
	estimate=c(0.1,10,0.01), moments=TRUE)
# try a fixed value for the normal random effect
survkit(y, censor=cens, ccov=~x, random=id, dist="normal",
	estimate=1.3)
# estimate a log-gamma random effect
survkit(y, censor=cens, ccov=~x, random=id, dist="loggamma",
	estimate=c(0.1,10,0.01))
# estimate a log-gamma random effect by integrating it out
## Not run: 
survkit(y, censor=cens, ccov=~x, dist="loggamma", estimate=1.3,
	integ=id, jointmode=TRUE)
# try a fixed value of the log-gamma random effect, integrating it out
survkit(y, censor=cens, ccov=~x, dist="loggamma", estimate=1,
	integ=id)

## End(Not run)
#
# Cox model with one time-constant covariate
print(z <- survkit(y, censor=cens, ccov=~x, model="Cox", residuals=TRUE,
	baseline=TRUE))
residuals(z)
baseline(z)
# obtain the quantiles
print(z <- survkit(y, censor=cens, ccov=~x, model="Cox",
	survival="quantiles", svalues=seq(10,90,by=10)))
survival(z)
# estimate a log-gamma random effect
survkit(y, censor=cens, ccov=~x, model="Cox", random=id,
	dist="loggamma", estimate=c(0.1,10,0.01))
# y <- trunc(rweibull(20,2,20))
y <- c(6,22,43,16,7,6,15,35,10,9,18,34,7,13,10,17,14,19,11,13)
# cens <- rbinom(20,1,0.9)
cens <- c(1,1,1,1,0,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1)
id <- gl(2,10)
# x <- rnorm(20)
x <- c(1.82881379,1.06606868,0.70877744,-0.09932880,-0.60626148,-0.75371046,
  0.23884069,0.51199483,-0.73060095,-0.93222151,2.27947539,-0.73855454,
 -0.36412735,-0.89122114,-0.05025962,-0.10001587,1.11460865,-1.87315971,
 -0.11280052,-1.6880509)
# Kaplan-Meier estimates
survkit(y, censor=cens, model="Kaplan")
# null Weibull model
survkit(y, censor=cens)
# one time-constant covariate
survkit(y, censor=cens, ccov=~x)
# stratify
survkit(y, censor=cens, ccov=~x, strata=id)
# estimate a normal random effect
survkit(y, censor=cens, ccov=~x, random=id, dist="normal",
	estimate=c(0.1,10,0.01), moments=TRUE)
# try a fixed value for the normal random effect
survkit(y, censor=cens, ccov=~x, random=id, dist="normal",
	estimate=1.3)
# estimate a log-gamma random effect
survkit(y, censor=cens, ccov=~x, random=id, dist="loggamma",
	estimate=c(0.1,10,0.01))
# estimate a log-gamma random effect by integrating it out
## Not run: 
survkit(y, censor=cens, ccov=~x, dist="loggamma", estimate=1.3,
	integ=id, jointmode=TRUE)
# try a fixed value of the log-gamma random effect, integrating it out
survkit(y, censor=cens, ccov=~x, dist="loggamma", estimate=1,
	integ=id)

## End(Not run)
#
# Cox model with one time-constant covariate
print(z <- survkit(y, censor=cens, ccov=~x, model="Cox", residuals=TRUE,
	baseline=TRUE))
residuals(z)
baseline(z)
# obtain the quantiles
print(z <- survkit(y, censor=cens, ccov=~x, model="Cox",
	survival="quantiles", svalues=seq(10,90,by=10)))
survival(z)
# estimate a log-gamma random effect
survkit(y, censor=cens, ccov=~x, model="Cox", random=id,
	dist="loggamma", estimate=c(0.1,10,0.01))

Create a Vector of Time-constant Covariates for a Point Process

Description

tccov creates a vector of length sum(y) of time-constant covariates for use with ehr. id must be numbered consecutively. x must have one value for each distinct id,

Usage

tccov(y, x, id)
tccov(y, x, id)

Arguments

`y`	Vector of times.
`x`	Vector covariate.
`id`	Vector of corresponding individual identifiers for who had which sequence of times.

Value

tccov creates a vector of length sum(y) of time-constant covariates for use with ehr. id must be numbered consecutively. x must have one value for each distinct id,

Author(s)

J.K. Lindsey

Examples

y <- c(5,3,2,4)
id <- c(1,1,2,2)
x <- c(5.2,3.1)
xcov <- tccov(y, x, id)
xcov
y <- c(5,3,2,4)
id <- c(1,1,2,2)
x <- c(5.2,3.1)
xcov <- tccov(y, x, id)
xcov

Create a Vector of Times Past since Previous Events for a Point Process

Description

tpast creates a vector of length sum(y) of times since the immediately preceding event occurred for use with ehr.

Usage

tpast(y)
tpast(y)

Arguments

`y`	Vector of times.

Value

tpast creates a vector of length sum(y) of times since the immediately preceding event occurred for use with ehr.

Author(s)

J.K. Lindsey

Examples

y <- c(5,3,2,4)
ptime <- tpast(y)
ptime
y <- c(5,3,2,4)
ptime <- tpast(y)
ptime

Create a Vector of Total Time Elapsed for each Individual for a Point Process

Description

ttime creates a vector of length sum(y) of times since each individual began for use with ehr.

Usage

ttime(y, id)
ttime(y, id)

Arguments

`y`	Vector of times.
`id`	Vector of corresponding individual identifiers for who had which sequence of times.

Value

ttime creates a vector of length sum(y) of times since each individual began for use with ehr.

Author(s)

J.K. Lindsey

Examples

y <- c(5,3,2,4)
id <- c(1,1,2,2)
itime <- ttime(y, id)
itime
y <- c(5,3,2,4)
id <- c(1,1,2,2)
itime <- ttime(y, id)
itime

Create a Vector of Time-varying Covariates for a Point Process

Description

tvcov creates a vector of length sum(y) of time-varying covariates for use with ehr. It may also be used to create weight vectors.

Usage

tvcov(y, x, tx)
tvcov(y, x, tx)

Arguments

`y`	Vector of times.
`x`	Vector covariate.
`tx`	Vector of times at which x changes.

Value

tvcov creates a vector of length sum(y) of time-varying covariates for use with ehr. It may also be used to create weight vectors.

Author(s)

J.K. Lindsey

Examples

y <- c(5,3,2,4)
x <- c(1,2,2,1,2,2,1)
tx <- c(2,3,1,2,2,2,2)
zcov <- tvcov(y, x, tx)
zcov
y <- c(5,3,2,4)
x <- c(1,2,2,1,2,2,1)
tx <- c(2,3,1,2,2,2,2)
zcov <- tvcov(y, x, tx)
zcov

Package 'event'

Help Index

Plot Autointensity Function of a Point Process

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Create a Vector of Cumulative Numbers of Previous Events for a Point Process (Birth Processes)

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Cox Proportional Hazards Model with Random Effect

Description

Usage

Arguments

Author(s)

References

See Also

Examples

Plot Counting Process Data

Description

Usage

Arguments

Author(s)

See Also

Examples

Regression Models for Event History Intensity Functions

Description

Usage

Arguments

Author(s)

References

See Also

Examples

Event History Analysis Library

Description

Log Hazard Function for a Box-Cox Process

Description

Usage

Arguments

Author(s)

See Also

Examples

Log Hazard Function for a Burr Process

Description

Usage

Arguments

Author(s)

Examples

Log Hazard Function for a Cauchy Process

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Log Hazard Function for a Poisson Process

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Log Hazard Function for a Gamma Process

Description

Usage

Arguments

Value

Author(s)

See Also