repeated (version 1.1.9)

kalseries: Repeated Measurements Models for Continuous Variables with Frailty or Serial Dependence

Description

kalseries is designed to handle repeated measurements 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 among observations on a unit can be through gamma or power variance family frailties (a type of random effect), with or without autoregression, or one of two types of serial dependence over time.

Usage

kalseries(
  response = NULL,
  times = NULL,
  intensity = "exponential",
  depend = "independence",
  mu = NULL,
  shape = NULL,
  density = FALSE,
  ccov = NULL,
  tvcov = NULL,
  torder = 0,
  interaction = NULL,
  preg = NULL,
  ptvc = NULL,
  pintercept = NULL,
  pshape = NULL,
  pinitial = 1,
  pdepend = NULL,
  pfamily = NULL,
  delta = NULL,
  transform = "identity",
  link = "identity",
  envir = parent.frame(),
  print.level = 0,
  ndigit = 10,
  gradtol = 1e-05,
  steptol = 1e-05,
  fscale = 1,
  iterlim = 100,
  typsize = abs(p),
  stepmax = 10 * sqrt(p %*% p)
)

Value

A list of classes kalseries and recursive is returned.

Arguments

response

A list of two column matrices with responses and corresponding times for each individual, one matrix or dataframe of response values, 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.

times

When response is a matrix, a vector of possibly unequally spaced times when they are the same for all individuals or a matrix of times. Not necessary if equally spaced. Ignored if response has class, response or repeated.

intensity

The form of function to be put in the Pareto distribution. Choices are exponential, Weibull, gamma, normal, logistic, Cauchy, log normal, log logistic, log Cauchy, log Student, inverse Gauss, and gen(eralized) logistic. (For definitions of distributions, see the corresponding [dpqr]distribution help.)

depend

Type of dependence. Choices are independence, Markov, serial, and frailty.

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.

density

If TRUE, the density of the function specified in intensity is used instead of the intensity.

ccov

A vector or matrix containing time-constant baseline covariates with one row 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 a time-varying covariate is observed at arbitrary time, gettvc can be used to find the most recent values for each response and create a suitable list. 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.

torder

The order of the polynomial in time to be fitted.

interaction

Vector of length equal to the number of time-constant covariates, giving the levels of interactions between them and the polynomial in time in the linear model.

preg

Initial parameter estimates for the regression model: intercept, one for each covariate in ccov, and torder plus sum(interaction). 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.

pintercept

The initial estimate of the intercept for the generalized logistic intensity.

pshape

An initial estimate for the shape parameter of the intensity function (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. With 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.

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 jacobian is calculated automatically for the transform option. Ignored if response has class, response or repeated.

transform

Transformation of the response variable: identity, exp, square, sqrt, or log.

link

Link function for the mean: identity, exp, square, sqrt, or log.

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

Arguments for nlm.

ndigit

Arguments for nlm.

gradtol

Arguments for nlm.

steptol

Arguments for nlm.

fscale

Arguments for nlm.

iterlim

Arguments for nlm.

typsize

Arguments for nlm.

stepmax

Arguments for nlm.

Author

J.K. Lindsey

Details

By default, a gamma mixture of the distribution specified in intensity is used, as the conditional distribution in the Markov and 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.

Examples

treat <- c(0,0,1,1)
tr <- tcctomat(treat)
dose <- matrix(rpois(20,10), ncol=5)
dd <- tvctomat(dose)
y <- restovec(matrix(rnorm(20), ncol=5), name="y")
reps <- rmna(y, ccov=tr, tvcov=dd)
#
# normal intensity, independence model
kalseries(y, intensity="normal", dep="independence", preg=1, pshape=5)
if (FALSE) {
# random effect
kalseries(y, intensity="normal", dep="frailty", preg=1, pinitial=1, psh=5)
# serial dependence
kalseries(y, intensity="normal", dep="serial", preg=1, pinitial=1,
	pdep=0.1, psh=5)
# random effect and autoregression
kalseries(y, intensity="normal", dep="frailty", preg=1, pinitial=1,
	pdep=0.1, psh=5)
#
# add time-constant variable
kalseries(y, intensity="normal", dep="serial", pinitial=1,
	pdep=0.1, psh=5, preg=c(1,0), ccov=treat)
# or equivalently
kalseries(y, intensity="normal", mu=~treat, dep="serial", pinitial=1,
	pdep=0.1, psh=5, preg=c(1,0))
# or
kalseries(y, intensity="normal", mu=~b0+b1*treat, dep="serial",
	pinitial=1, pdep=0.1, psh=5, preg=c(1,0), envir=reps)
#
# add time-varying variable
kalseries(y, intensity="normal", dep="serial", pinitial=1, pdep=0.1,
	psh=5, preg=c(1,0), ccov=treat, ptvc=0, tvc=dose)
# or equivalently, from the environment
dosev <- as.vector(t(dose))
kalseries(y, intensity="normal",
	mu=~b0+b1*rep(treat,rep(5,4))+b2*dosev,
	dep="serial", pinitial=1, pdep=0.1, psh=5, ptvc=c(1,0,0))
# or from the reps data object
kalseries(y, intensity="normal", mu=~b0+b1*treat+b2*dose,
	dep="serial", pinitial=1, pdep=0.1, psh=5, ptvc=c(1,0,0),
	envir=reps)
# try power variance family instead of gamma distribution for mixture
kalseries(y, intensity="normal", mu=~b0+b1*treat+b2*dose,
	dep="serial", pinitial=1, pdep=0.1, psh=5, ptvc=c(1,0,0),
	pfamily=0.1, envir=reps)
# first-order one-compartment model
# data objects for formulae
dose <- c(2,5)
dd <- tcctomat(dose)
times <- matrix(rep(1:20,2), nrow=2, byrow=TRUE)
tt <- tvctomat(times)
# vector covariates for functions
dose <- c(rep(2,20),rep(5,20))
times <- rep(1:20,2)
# functions
mu <- function(p) exp(p[1]-p[3])*(dose/(exp(p[1])-exp(p[2]))*
	(exp(-exp(p[2])*times)-exp(-exp(p[1])*times)))
shape <- function(p) exp(p[1]-p[2])*times*dose*exp(-exp(p[1])*times)
# response
conc <- matrix(rgamma(40,shape(log(c(0.01,1))),
	scale=mu(log(c(1,0.3,0.2))))/shape(log(c(0.1,0.4))),ncol=20,byrow=TRUE)
conc[,2:20] <- conc[,2:20]+0.5*(conc[,1:19]-matrix(mu(log(c(1,0.3,0.2))),
	ncol=20,byrow=TRUE)[,1:19])
conc <- restovec(ifelse(conc>0,conc,0.01))
reps <- rmna(conc, ccov=dd, tvcov=tt)
#
# constant shape parameter
kalseries(reps, intensity="gamma", dep="independence", mu=mu,
	ptvc=c(-1,-1.1,-1), pshape=1.5)
# or
kalseries(reps, intensity="gamma", dep="independence",
	mu=~exp(absorption-volume)*
	dose/(exp(absorption)-exp(elimination))*
	(exp(-exp(elimination)*times)-exp(-exp(absorption)*times)),
	ptvc=list(absorption=-1,elimination=-1.1,volume=-1),
	pshape=1.2)
# add serial dependence
kalseries(reps, intensity="gamma", dep="serial", pdep=0.9,
	mu=~exp(absorption-volume)*
	dose/(exp(absorption)-exp(elimination))*
	(exp(-exp(elimination)*times)-exp(-exp(absorption)*times)),
	ptvc=list(absorption=-1,elimination=-1.1,volume=-1),
	pshape=0.2)
# time dependent shape parameter
kalseries(reps, intensity="gamma", dep="independence", mu=mu,
	shape=shape, ptvc=c(-1,-1.1,-1), pshape=c(-3,0))
# or
kalseries(reps, intensity="gamma", dep="independence",
	mu=~exp(absorption-volume)*
	dose/(exp(absorption)-exp(elimination))*
	(exp(-exp(elimination)*times)-exp(-exp(absorption)*times)),
	ptvc=list(absorption=-1,elimination=-1.1,volume=-1),
	shape=~exp(b1-b2)*times*dose*exp(-exp(b1)*times),
	pshape=list(b1=-3,b2=0))
# add serial dependence
kalseries(reps, intensity="gamma", dep="serial", pdep=0.5,
	mu=~exp(absorption-volume)*
	dose/(exp(absorption)-exp(elimination))*
	(exp(-exp(elimination)*times)-exp(-exp(absorption)*times)),
	ptvc=list(absorption=-1,elimination=-1.1,volume=-1),
	shape=~exp(b1-b2)*times*dose*exp(-exp(b1)*times),
	pshape=list(b1=-3,b2=0))
}