Package 'joineR'

Title: Joint Modelling of Repeated Measurements and Time-to-Event Data
Description: Analysis of repeated measurements and time-to-event data via random effects joint models. Fits the joint models proposed by Henderson and colleagues <doi:10.1093/biostatistics/1.4.465> (single event time) and by Williamson and colleagues (2008) <doi:10.1002/sim.3451> (competing risks events time) to a single continuous repeated measure. The time-to-event data is modelled using a (cause-specific) Cox proportional hazards regression model with time-varying covariates. The longitudinal outcome is modelled using a linear mixed effects model. The association is captured by a latent Gaussian process. The model is estimated using am Expectation Maximization algorithm. Some plotting functions and the variogram are also included. This project is funded by the Medical Research Council (Grant numbers G0400615 and MR/M013227/1).
Authors: Pete Philipson [aut] , Ines Sousa [aut] , Peter J. Diggle [aut] , Paula Williamson [aut] , Ruwanthi Kolamunnage-Dona [aut] , Robin Henderson [aut], Graeme L. Hickey [aut, cre] , Maria Sudell [ctb], Medical Research Council [fnd] (Grant numbers: G0400615 and MR/M013227/1)
Maintainer: Graeme L. Hickey <[email protected]>
License: GPL-3 | file LICENSE
Version: 1.2.8
Built: 2024-10-03 04:00:10 UTC
Source: https://github.com/graemeleehickey/joiner

Help Index

AIDS drug trial data

Description

This dataset describes a randomized clinical trial (Goldman et al., 1996) in which both survival and longitudinal data were collected to compare the efficacy and safety of two antiretroviral drugs, namely ddI (didanosine) and ddC (zalcitabine), in treating HIV-infected patients intolerant or failing zidovudine (AZT) therapy.

Usage

data(aids)

Format

A data.frame in the unbalanced format with 1405 longitudinal observations from 467 subjects. The columns are:

id

integer: number for patient identification.

time

numeric: time to death (or censoring).

death

integer: event indicator. Coded as 0 = right-censoring, and 1 = death.

obstime

numeric: measurement times for the repeated CD4 count measurements.

CD4

numeric: CD4 cell counts measured at obstime.

drug

factor: drug indicator. Coded as ddI = didanosine and ddC = zalcitabine.

gender

factor: gender indicator. Coded as male and female.

prevOI

factor: opportunistic infection indicator. Coded as AIDS = AIDS diagnosis at study entry, and noAIDS = no previous infection.

AZT

factor: AZT intolerance/failure indicator. Coded as intolerance or failure.

Source

Guo X, Carlin B. Separate and joint modeling of longitudinal and event time data using standard computer packages. The American Statistician. 2004; 58: 16-24

References

Goldman A, Carlin B, Crane L, Launer C, Korvick J, Deyton L, Abrams D. Response of CD4 and clinical consequences to treatment using ddI or ddC in patients with advanced HIV infection. Journal of Acquired Immune Deficiency Syndromes and Human Retrovirology. 1996; 11: 161-169 URL: http://www.biostat.umn.edu/~brad/data.html.

See Also

heart.valve, epileptic, mental, liver.

Dose calibration of anti-epileptic drugs data

Description

The SANAD (Standard and New Anti-epileptic Drugs) study (Marson et al., 2007) is a randomized control trial of standard and new anti-epileptic drugs, comparing effects on longer term clinical outcomes. The data consists of longitudinal measurements of calibrated dose for the groups randomized to a standard drug (CBZ) and a new drug (LTG). The objective of the analysis is to investigate the effect of drug titration on the relative effects of LTG and CBZ on treatment failure (withdrawal of the randomized drug). There are several baseline covariates available, and also data on the time to withdrawal from randomized drug.

Usage

data(epileptic)

Format

This is a data frame in the unbalanced format, that is, with one row per observation. The data consists of columns for patient identifier, time of measurement, calibrated dose, baseline covariates, and survival data. The column names are identified as follows:

id

integer: patient identifier.

dose

numeric: calibrated dose.

time

integer: timing of clinic visit at which dose recorded (days).

with.time

integer: time of drug withdrawal/maximum follow up time (days).

with.status

censoring indicator (1 = withdrawal of randomized drug and 0 = not withdrawn from randomized drug/lost to follow up).

with.status2

censoring indicator (1 = withdrawal of randomized drug due to inadequate seizure control, (2 = withdrawal of randomized drug due to unacceptable adverse effects, and 0 = not withdrawn from randomized drug/lost to follow up).

with.status.uae

1 = withdrawal due to unacceptable adverse effects, 0 = otherwise.

with.status.isc

1 = withdrawal due to inadequate seizure control, 0 = otherwise.

treat

factor: randomized treatment (CBZ or LTG).

age

numeric: age of patient at randomization (years).

gender

factor: gender of patient. F = female, M = male.

learn.dis

factor: learning disability.

Source

SANAD Trial Group, University of Liverpool

References

Marson AG, Appleton R, Baker GA, et al. A randomised controlled trial examining longer-term outcomes of standard versus new antiepileptic drugs. The SANAD Trial. Health Tech Assess. 2007; 11(37).

Marson AG, Al-Kharusi AM, Alwaidh M, et al. The SANAD study of effectiveness of carbamazepine, gabapentin, lamotrigine, oxcarbazepine, or topiramate for treatment of partial epilepsy: an unblinded randomised controlled trial. Lancet. 2007; 365: 2007-2013.

Williamson PR, Kolamunnage-Dona R, Philipson P, Marson AG. Joint modelling of longitudinal and competing risks data. Stats Med. 2008; 27(30): 6426-6438.

See Also

heart.valve, liver, mental, aids.

Aortic valve replacement surgery data

Description

This is longitudinal data on an observational study on detecting effects of different heart valves, differing on type of tissue, implanted in the aortic position. The data consists of longitudinal measurements on three different heart function outcomes, after surgery occurred. There are several baseline covariates available, and also survival data.

Usage

data(heart.valve)

Format

This is a data frame in the unbalanced format, that is, with one row per observation. The data consists in columns for patient identification, time of measurements, longitudinal multiple longitudinal measurements, baseline covariates, and survival data. The column names are identified as follows:

num

number for patient identification.

sex

gender of patient (0 = Male and 1 = Female).

age

age of patient at day of surgery (years).

time

observed time point, with surgery date as the time origin (years).

fuyrs

maximum follow up time, with surgery date as the time origin (years).

status

censoring indicator (1 = died and 0 = lost at follow up).

grad

valve gradient at follow-up visit.

log.grad

natural log transformation of grad.

lvmi

left ventricular mass index (standardised) at follow-up visit.

log.lvmi

natural log transformation of lvmi.

ef

ejection fraction at follow-up visit.

bsa

preoperative body surface area.

lvh

preoperative left ventricular hypertrophy.

prenyha

preoperative New York Heart Association (NYHA) classification (1 = I/II and 3 = III/IV).

redo

previous cardiac surgery.

size

size of the valve (millimeters).

con.cabg

concomitant coronary artery bypass graft.

creat

preoperative serum creatinine (μ\mumol/mL).

dm

preoperative diabetes.

acei

preoperative use of ace inhibitor.

lv

preoperative left ventricular ejection fraction (LVEF) (1 = good, 2 = moderate, and 3 = poor).

emergenc

operative urgency (0 = elective, 1 = urgent, and 3 = emergency).

hc

preoperative high cholesterol (0 = absent, 1 = present treated, and 2 = present untreated).

sten.reg.mix

aortic valve haemodynamics (1 = stenosis, 2 = regurgitation, 3 = mixed).

hs

implanted aortic prosthesis type (1 = homograft and 0 = stentless porcine tissue).

References

Lim E, Ali A, Theodorou P, Sousa I, Ashrafian H, Chamageorgakis T, Duncan M, Diggle P, Pepper J. A longitudinal study of the profile and predictors of left ventricular mass regression after stentless aortic valve replacement. Ann Thorac Surg. 2008; 85(6): 2026-2029.

See Also

mental, liver, epileptic, aids.

joineR

Description

The joineR package implements methods for analyzing data from longitudinal studies in which the response from each subject consists of a time-sequence of repeated measurements and a possibly censored time-to-event outcome. The modelling framework for the repeated measurements is the linear model with random effects and/or correlated error structure (Laird and Ware, 1982). The model for the time-to-event outcome is a: Cox proportional hazards model with log-Gaussian frailty (Cox, 1972). A cause-specific hazards model is used when competing risks are present. Stochastic dependence is captured by allowing the Gaussian random effects of the linear model to be correlated with the frailty term of the Cox proportional hazards model. The methodology used to fit the model is described in Henderson et al. (2002) in the case of a single event time, and by Williamson et al. (2008) in the case of competing risks data. Both models exploit the general methodology proposed by Wulfsohn and Tsiatis (1997).

The package offers several types of functions for the analysis of joint data.

Data manipulation functions

There are several functions, including jointdata, sample.jointdata, subset.jointdata, to.balanced, to.unbalanced, and UniqueVariables, which offer the ability to construct a joint model dataset and manipulate it, e.g. take a sample according to a baseline covariate or outcome.

Plot functions

The plot function can be applied to jointdata and vargm (variogram) objects. In addition, points and lines can also be used with jointplot objects.

Model fitting functions

The primary function for fitting a joint model is joint. Standard errors can be estimated using jointSE.

Note

Further details on the package are given in the vignette. To access this, run vignette("joineR").

References

Wulfsohn MS, Tsiatis AA. A joint model for survival and longitudinal data measured with error. Biometrics. 1997; 53(1): 330-339.

Henderson R, Diggle PJ, Dobson A. Joint modelling of longitudinal measurements and event time data. Biostatistics. 2000; 1(4): 465-480.

Cox DR. Regression models and life-tables. J R Stat Soc Ser B Stat Methodol. 1972; 34(2): 187-220.

Laird NM, Ware JH. Random-effects models for longitudinal data. Biometrics. 1982; 38(4): 963-974.

Williamson PR, Kolamunnage-Dona R, Philipson P, Marson AG. Joint modelling of longitudinal and competing risks data. Stat Med. 2008; 27: 6426-6438.

Fit joint model for survival and longitudinal data measured with error

Description

This generic function fits a joint model with random latent association, building on the formulation described in Wulfsohn and Tsiatis (1997) while allowing for the presence of longitudinal and survival covariates, and three choices for the latent process. The link between the longitudinal and survival processes can be proportional or separate. When failure is attributable to 2 separate causes, a competing risks joint model is fitted as per Williamson et al. (2008).

Usage

joint(
  data,
  long.formula,
  surv.formula,
  model = c("intslope", "int", "quad"),
  sepassoc = FALSE,
  longsep = FALSE,
  survsep = FALSE,
  gpt,
  lgpt,
  max.it,
  tol,
  verbose = FALSE
)

Arguments

data

an object of class jointdata containing the variables named in the formulae arguments.
long.formula

a formula object with the response variable, and the covariates to include in the longitudinal sub-model.
surv.formula

a formula object with the survival time, censoring indicator and the covariates to include in the survival sub-model. The response must be a survival object as returned by the Surv function.
model

a character string specifying the type of latent association. This defaults to the intercept and slope version as seen in Wulfsohn and Tsiatis (1997). For association via the random intercept only, choose model = "int", whereas for a quadratic association, use model = "quad". Computing times are commensurate with the type of association structure chosen.
sepassoc

logical value: if TRUE then the joint model is fitted with separate association, see Details.
longsep

logical value: if TRUE, parameter estimates and log-likelihood from a separate linear mixed model analysis of the longitudinal data (see the lme function for details) are returned.
survsep

if TRUE, parameter estimates and log-likelihood from a separate analysis of the survival data using the Cox proportional hazards model are returned (see coxph function for details).
gpt

the number of quadrature points across which the integration with respect to the random effects will be performed. Defaults to gpt = 3 which produces stable estimates in most datasets.
lgpt

the number of quadrature points which the log-likelihood is evaluated over following a model fit. This defaults to lgpt = 10, though lgpt = 3 is often sufficient.
max.it

the maximum number of iterations of the EM algorithm that the function will perform. Defaults to max.it = 200, though more iterations may be necessary for large, complex data.
tol

the tolerance level before convergence of the algorithm is deemed to have occurred. Default value is tol = 0.001.
verbose

if TRUE, the parameter estimates at each iteration of the EM algorithm are printed. Default is verbose = FALSE.

Details

The joint function fits a joint model to survival and longitudinal data. The formulation is similar to Wulfsohn and Tsiatis (1997). A linear mixed effects model is assumed for the longitudinal data, namely

Yi=Xi1(ti)Tβ1+Di(ti)TUi+ϵi,Y_i = X_{i1}(t_i)^T\beta_1 + D_i(t_i)^T U_i + \epsilon_i,

where UiU_i is a vector of random effects, (U0i,…Uqi)(U_{0i}, \ldots U_{qi}) whose length depends on the model chosen, i.e. q=1q = 1 for the random intercept model. DiD_i is the random effects covariate matrix, which will be time-dependent for all but the random intercept model. Xi1X_{i1} is the longitudinal design matrix for unit ii, and tit_i is the vector of measurement times for subject ii. Measurement error is represented by ϵi\epsilon_i.

The Cox proportional hazards model is adopted for the survival data, namely

λ(t)=λ0(t)exp⁡{Xi2(t)Tβ2+Di(t)(γTUi)}.\lambda(t) = \lambda_0(t) \exp\{{X_{i2}(t)^T \beta_2 + D_i(t)(\gamma^T U_i)}\}.

The parameter γ\gamma determines the level of association between the two processes. For the intercept and slope model with separate association we have

Di(t)(γTUi)=γ0U0i+γ1U1it,D_i(t) (\gamma^T U_i) = \gamma_0 U_{0i} + \gamma_1 U_{1i} t,

whereas under proportional association

Di(t)(γTUi)=γ(U0i+U1it).D_i(t)(\gamma^T U_i) = \gamma (U_{0i} + U_{1i} t).

Xi2X_{i2} is the vector of survival covariates for unit ii. The baseline hazard function is λ0(t)\lambda_0(t).

The function uses an EM algorithm to estimate parameters in the joint model. Starting values are provided by calls to standard R functions lme and coxph for the longitudinal and survival components, respectively.

Value

A list containing the parameter estimates from the joint model and, if required, from either or both of the separate analyses. The combined log-likelihood from a separate analysis and the log-likelihood from the joint model are also produced as part of the fit.

Competing risks

If failure can be attributed to 2 causes, i.e. so-called competing risks events data, then a cause-specific hazards model is adopted, namely

λg(t)=λ0g(t)exp⁡{Xi2(t)Tβ2(g)+Di(t)(γTUi)},\lambda_g(t) = \lambda_{0g}(t) \exp\{{X_{i2}(t)^T \beta_2^{(g)} + D_i(t)(\gamma^T U_i)}\},

where g=1,2g = 1,2 denotes the failure type, β2(g)\beta_2^{(g)} (g=1,2g = 1,2) are cause-specific hazard parameters corresponding to the same covariates, and λ0g(t)\lambda_{0g}(t) are cause-specific baseline hazard functions. For this data, a proportional association structure is assumed (i.e. sepassoc = FALSE) and a random-intercepts and random-slopes model must be used (i.e. model = "intslope"). Note that the function only permits 2 failure types. The model is specified in full by Williamson et al. (2008). The function joint() automatically detects whether competing risks are present by counting the number of unique components in the event column on the event time data.

Separate models

Both longsep and survsep ignore any latent association (i.e. γ=0\gamma = 0) between the longitudinal and survival processes but their output can be used to compare with the results from the joint model. If interest is solely in the individual processes then the user should instead make use of the functions lme and coxph mentioned above. Furthermore, if interest is in the separate effect of each random effect (this is for intercept and slope or quadratic models only) upon the survival data, the user should set sepassoc = TRUE.

Note

Since numerical integration is required, it is advisable to check the stability of the maximum likelihood estimates with an increasing number of Gauss-Hermite quadrature points. joint() uses gpt = 3 by default, as this has been adequate for many datasets. However, for certain datasets and models, this might be too small.

Author(s)

Pete Philipson

References

Wulfsohn MS, Tsiatis AA. A joint model for survival and longitudinal data measured with error. Biometrics. 1997; 53(1): 330-339.

Henderson R, Diggle PJ, Dobson A. Joint modelling of longitudinal measurements and event time data. Biostatistics. 2000; 1(4): 465-480.

Williamson PR, Kolamunnage-Dona R, Philipson P, Marson AG. Joint modelling of longitudinal and competing risks data. Stat Med. 2008; 27: 6426-6438.

See Also

lme, coxph, jointdata, jointplot.

Examples

## Standard joint model

data(heart.valve)
heart.surv <- UniqueVariables(heart.valve,
                              var.col = c("fuyrs", "status"),
                              id.col = "num")
heart.long <- heart.valve[, c("num", "time", "log.lvmi")]
heart.cov <- UniqueVariables(heart.valve,
                             c("age", "hs", "sex"),
                             id.col = "num")
heart.valve.jd <- jointdata(longitudinal = heart.long,
                            baseline = heart.cov,
                            survival = heart.surv,
                            id.col = "num",
                            time.col = "time")
fit <- joint(data = heart.valve.jd,
             long.formula = log.lvmi ~ 1 + time + hs,
             surv.formula = Surv(fuyrs, status) ~ hs,
             model = "intslope")
             
## Competing risks joint model (same data as Williamson et al. 2008)

## Not run: 
data(epileptic)
epileptic$interaction <- with(epileptic, time * (treat == "LTG"))
longitudinal <- epileptic[, c(1:3, 13)]
survival <- UniqueVariables(epileptic, c(4, 6), "id")
baseline <- UniqueVariables(epileptic, "treat", "id")
data <- jointdata(longitudinal = longitudinal,
                  survival = survival,
                  baseline = baseline,
                  id.col = "id",
                  time.col = "time")
                  
fit2 <- joint(data = data,
              long.formula = dose ~ time + treat + interaction,
              surv.formula = Surv(with.time, with.status2) ~ treat,
              longsep = FALSE, survsep = FALSE,
              gpt = 3)
summary(fit2)

## End(Not run)

Fitted joint object

Description

An object returned by the joint function, inheriting from class joint and representing a fitted joint model for longitudinal and time-to-event (or competing risks) data.

Usage

joint.object

Format

An object of class NULL of length 0.

Value

A list with the following components.

coefficients

a list with the estimated coefficients. The components of this list are:

fixed

longitudinal and survival sub-model fixed effects.

random

the BLUPs of the random effects.

latent

the latent association parameter(s) from the time-to-event sub-model.

sigama.z

a numeric double for the residual standard error.

sigma.u

the variance-covariance matrix of the random effects.

hazard

a vector of the (centered) baseline hazards at each unique failure time.

log.lik

the log-likelihood from the joint model fit and sub-model contributions.

numIter

the number of EM algorithm iterations.

convergence

a logical value of whether convergence was achieved or not.

model

see joint for details.

sepassoc

see joint for details.

sepests

see joint for details.

compRisk

a logical value indicating whether competing risks were detected or not.

sep.loglike

the log-likelihood from the joint model fit (with association set to zero) and separately fitted sub-model contributions.

formulae

a list of model formulae. See joint for details.

data

a jointdata object. See joint for details.

call

the model call. Can be used by update.

Author(s)

Graeme L. Hickey

See Also

joint.

Creates an object of class jointdata

Description

This function creates an object of class jointdata. This is an object with information on at least one of, longitudinal data or survival data. Moreover, it can also have data on baseline covariates.

Usage

jointdata(
  longitudinal = NA,
  survival = NA,
  baseline = NA,
  id.col = "ID",
  time.col = NA
)

Arguments

longitudinal

a data frame or matrix in the unbalanced format (one row per observation), with subject identification, time of measurements, and longitudinal measurements and/or time dependent covariates. This must be given if no survival argument is.
survival

a data frame or matrix with survival data for all the subjects. This must be given if no longitudinal argument is.
baseline

a data frame or matrix with baseline covariates, or non-time dependent covariates, for the same subjects as in survival and/or longitudinal. This has to be in the balanced format (one row per subject). By default an object of this class does not include baseline covariates.
id.col

an element of class character with the name identification of subject. This is to identify the subject identification in the data frames.
time.col

an element of class character with the time measurements identification. This is to identify the time column in the data frames.

Details

This function creates an object of class jointdata. This is a list with elements used in joint modelling, mainly longitudinal and/or survival data. The output has to have at least one of the data sets, longitudinal or survival. However, for joint modelling is necessary to have both data sets. Moreover, a third data frame is possible to be given as input, for the baseline (non-time dependent) covariates. The subject identification and time measurement column names are necessary.

Value

A list of length six. The first element is the vector of subjects identification. The second is, if exists a data frame of the longitudinal data. The third element of the list is, if exists a data frame of the survival data. The fourth element of the list is, if exists a data frame on the baseline covariates. The fifth is, if longitudinal data is given, the column name identification of longitudinal times. And the sixth and last element of the list is the column name identification of subjects.

Author(s)

Ines Sousa

Examples

data(heart.valve)
heart.surv <- UniqueVariables(heart.valve,
                              var.col = c("fuyrs", "status"), 
                              id.col = "num")
heart.valve.jd <- jointdata(survival = heart.surv, 
                            id.col = "num",
                            time.col = "time")

Joint plot of longitudinal and survival data

Description

This function views the longitudinal profile of each unit with the last longitudinal measurement prior to event-time (censored or not) taken as the end-point, referred to as time zero. In doing so, the shape of the profile prior to event-time can be inspected. This can be done over a user-specified number of time units.

Usage

jointplot(
  object,
  Y.col,
  Cens.col,
  lag,
  split = TRUE,
  col1,
  col2,
  xlab,
  ylab,
  gp1lab,
  gp2lab,
  smooth = 2/3,
  mean.profile = FALSE,
  mcol1,
  mcol2
)

Arguments

object

an object of class jointdata.
Y.col

an element of class character identifying the longitudinal response part of the jointdata object.
Cens.col

an element of class character identifying the survival status or censoring indicator part of the jointdata object.
lag

argument which specifies how many units in time we look back through. Defaults to the maximum observation time across all units.
split

logical argument which allows the profiles of units which fail and those which are censored to be viewed in separate panels of the same graph. This is the default option. Using split = FALSE will plot all profiles overlaid on a single plot.
col1

argument to choose the colour for the profiles of the censored units.
col2

argument to choose the colour for the profiles of the failed units.
xlab

an element of class character indicating the title for the x-axis.
ylab

an element of class character indicating the title for the x-axis.
gp1lab

an element of class character for the group corresponding to a censoring indicator of zero. Typically, the censored group.
gp2lab

an element of class character for the group corresponding to a censoring indicator of one. Typically, the group experiencing the event of interest.
smooth

the smoother span. This gives the proportion of points in the plot which influence the smooth at each value. Defaults to a value of 2/3. Larger values give more smoothness. See lowess for further details.
mean.profile

draw mean profiles if TRUE. Only applies to the split = TRUE case.
mcol1

argument to choose the colour for the mean profile of the units with a censoring indicator of zero.
mcol2

argument to choose the colour for the mean profile of the units with a censoring indicator of one.

Details

The function tailors the xyplot function to produce a representation of joint data with longitudinal and survival components.

Value

A lattice plot.

Note

If more than one cause of failure is present (i.e. competing risks data), then all failures are pooled together into a single failure type.

Author(s)

Pete Philipson

References

Wulfsohn MS, Tsiatis AA. A joint model for survival and longitudinal data measured with error. Biometrics. 1997; 53(1): 330-339.

See Also

xyplot, joint, jointdata.

Examples

data(heart.valve)
heart.surv <- UniqueVariables(heart.valve, 
                              var.col = c("fuyrs", "status"),
                              id.col = "num")
heart.long <- heart.valve[, c("num", "time", "log.lvmi")]
heart.cov <- UniqueVariables(heart.valve, 
                             c("age", "sex"), 
                             id.col = "num")
heart.valve.jd <- jointdata(longitudinal = heart.long, 
                            baseline = heart.cov, 
                            survival = heart.surv,
                            id.col = "num",
                            time.col = "time")
jointplot(heart.valve.jd, Y.col = "log.lvmi", 
          Cens.col = "status", lag = 5)

Standard errors via bootstrap for a joint model fit

Description

This function takes a model fit from a joint model and calculates standard errors, with optional confidence intervals, for the main longitudinal and survival covariates.

Usage

jointSE(fitted, n.boot, gpt, lgpt, max.it, tol, print.detail = FALSE)

Arguments

fitted

a list containing as components the parameter estimates obtained by fitting a joint model along with the respective formulae for the longitudinal and survival sub-models and the model chosen, see joint for further details.
n.boot

argument specifying the number of bootstrap samples to use in order to obtain the standard error estimates and confidence intervals. Note that at least n.boot = 100 is required in order for the function to return non-zero confidence intervals.
gpt

the number of quadrature points across which the integration with respect to the random effects will be performed. Defaults to gpt = 3 which produces stable estimates in most datasets.
lgpt

the number of quadrature points which the log-likelihood is evaluated over following a model fit. This defaults to lgpt = 10, though lgpt = 3 is often sufficient.
max.it

the maximum number of iterations of the EM algorithm that the function will perform. Defaults to max.it = 200, though more iterations may be necessary for large, complex data.
tol

the tolerance level before convergence of the algorithm is deemed to have occurred. Default value is tol = 0.001.
print.detail

This argument determines the level of printing that is done during the bootstrapping. If TRUE then the parameter estimates from each bootstrap sample are output.

Details

Standard errors and confidence intervals are obtained by repeated fitting of the requisite joint model to bootstrap samples of the original longitudinal and survival data. It is rare that more than 200 bootstrap samples are needed for estimating a standard error. The number of bootstrap samples needed for accurate confidence intervals can be as large as 1000.

Value

An object of class data.frame.

Author(s)

Ruwanthi Kolamunnage-Dona and Pete Philipson

References

Wulfsohn MS, Tsiatis AA. A joint model for survival and longitudinal data measured with error. Biometrics. 1997; 53(1): 330-339.

Efron B, Tibshirani R. An Introduction to the Bootstrap. 2000; Boca Raton, FL: Chapman & Hall/CRC.

See Also

lme, coxph, joint, jointdata.

Examples

data(heart.valve)
heart.surv <- UniqueVariables(heart.valve, 
                              var.col = c("fuyrs", "status"), 
                              id.col = "num")
heart.long <- heart.valve[, c("num", "time", "log.lvmi")]
heart.cov <- UniqueVariables(heart.valve, 
                             c("age", "hs", "sex"), 
                             id.col = "num")
heart.valve.jd <- jointdata(longitudinal = heart.long, 
                            baseline = heart.cov, 
                            survival = heart.surv, 
                            id.col = "num", 
                            time.col = "time")
fit <- joint(heart.valve.jd, 
             long.formula = log.lvmi ~ 1 + time + hs, 
             surv.formula = Surv(fuyrs, status) ~ hs, 
             model = "int")
jointSE(fitted = fit, n.boot = 1)

Add lines to an existing jointdata plot

Description

Add lines to an existing plot of an object of class jointdata, for a longitudinal variable. It is possible to plot all the subjects in the data set, or just a selected subset. See subset.jointdata.

Usage

## S3 method for class 'jointdata'
lines(x, Y.col, ...)

Arguments

x

object of class jointdata.
Y.col

column number, or column name, of longitudinal variable to be plotted. Defaults to Y.col = NA, plotting all longitudinal variables.
...

other graphical arguments; see plot.

Value

A graphical device with a plot for longitudinal data.

Author(s)

Ines Sousa

See Also

Other functions are useful to be used with this such as plot and points.

Examples

data(heart.valve)
heart.surv <- UniqueVariables(heart.valve, 
                              var.col = c("fuyrs", "status"), 
                              id.col = "num")
heart.long <- heart.valve[, c(1, 4, 5, 7, 8, 9, 10, 11)]
heart.jd <- jointdata(longitudinal = heart.long, 
                      survival = heart.surv,
                      id.col = "num",
                      time.col = "time")
                      
# Randomly select a pair of subjects to plot profiles of
take <- sample(1:max(heart.jd$survival$num), 2)
heart.jd.1 <- subset(heart.jd, take[1])
heart.jd.2 <- subset(heart.jd, take[2])

plot(heart.jd.1, Y.col = 4)
lines(heart.jd.2, Y.col = 4, lty = 2)

Liver cirrhosis drug trial data

Description

This dataset gives the longitudinal observations of prothrombin index, a measure of liver function, for patients from a controlled trial into prednisone treatment of liver cirrhosis. Time-to-event information in the form of the event time and associated censoring indicator are also recorded along with a solitary baseline covariate - the allocated treatment arm in this instance. The data are taken from Andersen et al. (1993, p. 19) and were analyzed in Henderson et al. (2002). This is a subset of the full data where a number of variables were recorded both at entry and during the course of the trial.

Usage

data(liver)

Format

A data.frame in the unbalanced format with longitudinal observations from 488 subjects. The columns are:

id

integer: number for patient identification.

prothrombin

integer: prothrombin index measurement (%).

time

numeric: time of prothrombin index measurement (years).

treatment

integer: patient treatment indicator. Coded as 0 = placebo; 1 = prednisone.

survival

numeric: patient survival time (years).

cens

integer: censoring indicator. Coded as 1 = died; 0 = censored.

Source

Skrondal A, Rabe-Hesketh S. Generalized Latent Variable Modeling: Multilevel, Longitudinal and Structural Equation Models. Chapman & Hall/CRC. 2004. URL: http://www.gllamm.org/books/readme.html#14.6.

References

Andersen PK, Borgan O, Gill RD, Kieding N. Statistical Models Based on Counting Processes. New York: Springer. 2003.

Henderson R, Diggle PJ, Dobson A. Identification and efficacy of longitudinal markers for survival. Biostatistics 2002; 3: 33-50.

See Also

heart.valve, epileptic, mental, aids.

Mental health trial data

Description

The data is obtained from a trial in which chronically ill mental health patients were randomized across two treatments: placebo and an active drug. A questionnaire instrument was used to assess each patient's mental state at weeks 0, 1, 2, 4, 6 and 8 post-randomisation, a high recorded score implying a severe condition. Some of the 100 patients dropped out of the study for reasons that were thought to be related to their mental state, and therefore potentially informative; others dropped out for reasons unrelated to their mental state.

Usage

data(mental)

Format

A balanced data set with respect to the times at which observations recorded. The data consists of the following variables on each patient:

id

integer: patient identifier.

Y.t0

integer: mental state assessment in week 0. Coded NA if missing.

Y.t1

integer: mental state assessment in week 1. Coded NA if missing.

Y.t2

integer: mental state assessment in week 2. Coded NA if missing.

Y.t4

integer: mental state assessment in week 4. Coded NA if missing.

Y.t6

integer: mental state assessment in week 6. Coded NA if missing.

Y.t8

integer: mental state assessment in week 8. Coded NA if missing.

treat

integer: treatment allocation. Coded as 0 = placebo; 1 = active drug.

n.obs

integer: number of non-missing mental state assessments.

surv.time

numeric: imputed dropout time in weeks. Coded as surv.time = 8.002 for completers.

cens.ind

integer: censoring indicator. Coded as 0 = completer or non-informative dropout; 1 = potentially informative dropout.

Source

Peter J. Diggle ([email protected])

References

Henderson R, Diggle PJ, Dobson A. Joint modelling of longitudinal measurements and event time data. Biostatistics. 2000; 1(4): 465-480.

Diggle PJ, Farewell D, Henderson R. Longitudinal data with dropout: objectives, assumptions and a proposal (with Discussion). Applied Statistics. 2007; 56: 499-550.

See Also

heart.valve, liver, epileptic.

Plot longitudinal data

Description

Plot longitudinal data of an object of class jointdata, for a longitudinal variable. It is possible to plot all the subjects in the data set, or just a selected subset. See subset.jointdata.

Usage

## S3 method for class 'jointdata'
plot(x, Y.col, type, xlab, xlim = NULL, ylim = NULL, main = NA, pty, ...)

Arguments

x

object of class jointdata.
Y.col

column number, or column name, of longitudinal variable to be plotted. Defaults to Y.col = NA, plotting all longitudinal variables.
type

the type of line to be plotted, see plot for further details.
xlab

a title for the x-axis, see title.
xlim, ylim

numeric vectors of length 2, giving the x and y coordinates ranges, see plot.window for further details.
main

an overall title for the plot; see title.
pty

a character specifying the type of plot region to be used, see par for details.
...

other graphical arguments; see plot.

Value

A graphical device with a plot for longitudinal data.

Author(s)

Ines Sousa

See Also

lines and points.

Examples

data(heart.valve)
heart.surv <- UniqueVariables(heart.valve,
                              var.col = c("fuyrs", "status"),
                              id.col = "num")
heart.long <- heart.valve[, c(1, 4, 5, 7, 8, 9, 10, 11)]
heart.jd <- jointdata(longitudinal = heart.long, 
                      survival = heart.surv,
                      id.col = "num",
                      time.col = "time")
plot(heart.jd, Y.col = "grad", col = "grey")

Plots the empirical variogram for longitudinal data

Description

Plots the empirical variogram for observed measurements, of an object of class vargm, obtained by using function variogram.

Usage

## S3 method for class 'vargm'
plot(x, smooth = FALSE, bdw = NULL, follow.time = NULL, points = TRUE, ...)

Arguments

x

object of class vargm obtained by using function. variogram
smooth

logical value to use a non-parametric estimator to calculate the variogram of all vijkv_ijk. The default is FALSE, as it uses time averages.
bdw

bandwidth to use in the time averages. The default is NULL, because this is calculated automatically.
follow.time

the interval of time we want to construct the variogram for. When NULL this is the maximum of the data.
points

logical value if the points vijkv_ijk should be plotted.
...

other graphical options as in par.

Value

A graphical device with the plot of empirical variogram.

Author(s)

Ines Sousa

Examples

data(mental)
mental.unbalanced <- to.unbalanced(mental, id.col = 1, 
                                   times = c(0, 1, 2, 4, 6, 8),
                                   Y.col = 2:7, 
                                   other.col = c(8, 10, 11))
names(mental.unbalanced)[3] <- "Y"
vgm <- variogram(indv = tail(mental.unbalanced[, 1], 30),
                 time = tail(mental.unbalanced[, 2], 30),
                 Y = tail(mental.unbalanced[, 3], 30))
plot(vgm)

Add points to an existing jointdata plot

Description

Add points to an existing plot of an object of class jointdata, for a longitudinal variable. It is possible plot all the subjects in the data set, or just a selected subset. See subset.jointdata.

Usage

## S3 method for class 'jointdata'
points(x, Y.col, ...)

Arguments

x

object of class jointdata.
Y.col

column number, or column name, of longitudinal variable to be plotted. Defaults to Y.col = NA, plotting all longitudinal variables.
...

other graphical arguments; see plot.

Value

A graphical device with a plot for longitudinal data. Other functions are useful to be used with this as plot and lines.

Author(s)

Ines Sousa

Examples

data(heart.valve)
heart.surv <- UniqueVariables(heart.valve,
                              var.col = c("fuyrs", "status"),
                              id.col = "num")
heart.long <- heart.valve[, c(1, 4, 5, 7, 8, 9, 10, 11)]
heart.jd <- jointdata(longitudinal = heart.long,
                      survival = heart.surv,
                      id.col = "num",
                      time.col = "time")
                      
# Randomly select a pair of subjects to plot profiles of
take <- sample(1 : max(heart.jd$survival$num), 2)
heart.jd.1 <- subset(heart.jd, take[1])
heart.jd.2 <- subset(heart.jd, take[2])

plot(heart.jd.1, Y.col = "grad", type = "p")
points(heart.jd.2, Y.col = "grad", col = "blue", pch = 20)

Sample from a jointdata x

Description

Generic function used to sampling a subset of data from an x of class jointdata, with a specific size of number of subjects.

Usage

sample.jointdata(x, size, replace = FALSE)

Arguments

x

an object of class jointdata.
size

number of subjects to include in the sampled subset.
replace

should sampling be with replacement? Default is replace = TRUE.

Value

An object of class jointdata, with data only on the subjects sampled.

Author(s)

Ines Sousa

See Also

sample, jointdata, UniqueVariables.

Examples

data(heart.valve)
heart.surv <- UniqueVariables(heart.valve, 
                              var.col = c("fuyrs", "status"), 
                              id.col = "num")
heart.valve.jd <- jointdata(survival = heart.surv, 
                            id.col = "num", 
                            time.col = "time")
sample.jointdata(heart.valve.jd, size = 10)

Simulate data from a joint model

Description

This function simulates longitudinal and time-to-event data from a joint model.

Usage

simjoint(
  n = 500,
  model = c("intslope", "int", "quad"),
  sepassoc = FALSE,
  ntms = 5,
  b1 = c(1, 1, 1, 1),
  b2 = c(1, 1),
  gamma = c(1, 0.1),
  sigu,
  vare = 0.01,
  theta0 = -3,
  theta1 = 1,
  censoring = TRUE,
  censlam = exp(-3),
  truncation = FALSE,
  trunctime = max(ntms),
  gridstep = 0.01
)

Arguments

n

the number of subjects to simulate data for.
model

a character string specifying the type of latent association. This defaults to the intercept and slope version as seen in Wulfsohn and Tsiatis (1997). For association via the random intercept only, choose model = "int", whereas for a quadratic association, use model = "quad". Computing times are commensurate with the type of association structure chosen.
sepassoc

logical value: if TRUE then the joint model is fitted with separate association, see Details.
ntms

the maximum number of (discrete) time points to simulate repeated longitudinal measurements at.
b1

a vector specifying the coefficients of the fixed effects in the longitudinal sub-model. The order in each row is intercept, a continuous covariate, covariate, a binary covariate, the measurement time.
b2

a vector of length = 2 specifying the coefficients for the time-to-event baseline covariates, in the order of a continuous covariate and a binary covariate.
gamma

a vector of specifying the latent association parameter(s) for the longitudinal outcome. It must be of length 1 if sepassoc = FALSE.
sigu

a positive-definite matrix specifying the variance-covariance matrix. If model = "int", the matrix has dimension dim = c(1, 1); if model = "intslope", the matrix has dimension dim = c(2, 2); else if model = "quad", the matrix has dimension dim = c(3, 3). If D = NULL (default), an identity matrix is assumed.
vare

a numeric value specifying the residual standard error.
theta0, theta1

parameters controlling the failure rate. See Details.
censoring

logical: if TRUE, includes an independent censoring time.
censlam

a scale (>0>0) parameter for an exponential distribution used to simulate random censoring times for when censoring = TRUE.
truncation

logical: if TRUE, adds a truncation time for a maximum event time in the case of model = "int" or model = "intslope".
trunctime

a truncation time for use when truncation = TRUE. For model = "quad", trunctime is required, and defaults to max(ntms) if not specified.
gridstep

the step-size for the grid used to simulate event times when model = "quad". Default is gridstep = 0.01. See Details.

Details

The function simjoint simulates data from a joint model, similar to that performed in Henderson et al. (2000). It works by first simulating longitudinal data for all possible follow-up times using random draws for the multivariate Gaussian random effects and residual error terms. Data can be simulated assuming either random-intercepts only (model = "int") in each of the longitudinal sub-models; random-intercepts and random-slopes (model = "intslope"); or quadratic random effects structures (model = "quad"). The failure times are simulated from proportional hazards time-to-event models, using the following methodologies:

model = "int"

The baseline hazard function is specified to be an exponential distribution with

λ0(t)=exp⁡θ0.\lambda_0(t) = \exp{\theta_0}.

Simulation is conditional on known time-independent effects, and the methodology of Bender et al. (2005) is used to simulate the failure time.

model = "intslope"

The baseline hazard function is specified to be a Gompertz distribution with

λ0(t)=exp⁡θ0+θ1t.\lambda_0(t) = \exp{\theta_0 + \theta_1 t}.

In the usual representation of the Gompertz distribution, θ1\theta_1 is the shape parameter, and the scale parameter is equivalent to exp⁡(θ0)\exp(\theta_0). Simulation is conditional on on a predictable (linear) time-varying process, and the methodology of Austin (2012) is used to simulate the failure time.

model="quad"

The baseline hazard function is specified as per model="intslope". The integration technique used for the above two cases is complex in quadratic (and higher order) models, therefore we use a different approach. We note that hazard function can be written as

lim⁡dt→0λ(t)dt=lim⁡dt→0P[t≤T≤t+dt∣T≥t].\lim_{dt \rightarrow 0} \lambda(t) dt = \lim_{dt \rightarrow 0} P[t \le T \le t + dt | T \ge t].

In the simulation routine the parameter gridstep acts as dtdt in that we choose a nominally small value, which multiplies the hazard and this scaled hazard is equivalent to the probability of having an event in the interval (t,t+dt)(t, t + dt), or equivalently (t,t+(t, t +gridstep)). A vector of possible times is set up for each individual, ranging from 0 to trunctime in increments of dtdt (or gridstep). The failure probability at each time is compared to an independent U(0,1)U(0, 1) draw, and if the probability does not exceed the random draw then the survival time is set as trunctime, otherwise it is the generated time from the vector of candidate times. The minimum of these candidate times (i.e. when we deem the event to have first happened) is taken as the survival time.

Value

A list of 2 data.frames: one recording the requisite longitudinal outcomes data, and one recording the time-to-event data.

Author(s)

Pete Philipson

References

Austin PC. Generating survival times to simulate Cox proportional hazards models with time-varying covariates. Stat Med. 2012; 31(29): 3946-3958.

Bender R, Augustin T, Blettner M. Generating survival times to simulate Cox proportional hazards models. Stat Med. 2005; 24: 1713-1723.

Henderson R, Diggle PJ, Dobson A. Joint modelling of longitudinal measurements and event time data. Biostatistics. 2000; 1(4): 465-480.

Examples

simjoint(10, sepassoc = TRUE)

Subsetting object of class jointdata

Description

Returns an object of class jointdata which is a subset of an original object of class jointdata.

Usage

## S3 method for class 'jointdata'
subset(x, subj.subset, ...)

Arguments

x

an object of class jointdata.
subj.subset

vector of subject identifiers, to include in the data subset. This must be a unique vector of patient identifiers.
...

further arguments to be passed to or from other methods.

Value

An object of class jointdata, with data only on a subset of subjects.

Author(s)

Ines Sousa

Examples

data(heart.valve)
heart.surv <- UniqueVariables(heart.valve,
                              var.col = c("fuyrs", "status"),
                              id.col = "num")
heart.long <- heart.valve[, c(1, 4, 5, 7, 8, 9, 10, 11)]
heart.jd <- jointdata(longitudinal = heart.long, 
                      survival = heart.surv,
                      id.col = "num",
                      time.col = "time")
take <- heart.jd$survival$num[heart.jd$survival$status == 0]
heart.jd.cens <- subset(heart.jd, take)

Summarise a random effects joint model fit

Description

Generic function used to produce summary information from a fitted random effects joint model as represented by object of class joint.

Usage

## S3 method for class 'joint'
summary(object, variance = TRUE, ...)

Arguments

object

an object of class joint.
variance

should the variance components be output as variances or standard deviations? Defaults to variance = TRUE.
...

further arguments for the summary.

Value

An object inheriting from class summary.joint with all components included in object (see joint for a full description of the components) plus the following components:

nobs

the total number of (typically longitudinal) observations (i.e. rows in an unbalanced data set).
ngrps

the number of groups in the analyzed dataset, often individual subjects.

Author(s)

Pete Philipson

Examples

data(heart.valve)
heart.surv <- UniqueVariables(heart.valve,
                              var.col = c("fuyrs","status"),
                              id.col = "num")
heart.long <- heart.valve[, c("num", "time", "log.lvmi")]
heart.cov <- UniqueVariables(heart.valve,
                             c("age", "hs", "sex"),
                             id.col = "num")
heart.valve.jd <- jointdata(longitudinal = heart.long,
                            baseline = heart.cov,
                            survival = heart.surv,
                            id.col = "num",
                            time.col = "time")
fit <- joint(data = heart.valve.jd,
             long.formula = log.lvmi ~ 1 + time + hs,
             surv.formula = Surv(fuyrs,status) ~ hs,
             model = "intslope")
summary(fit)

Summarise a jointdata object

Description

Generic function used to produce summaries of objects of class jointdata.

Usage

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

Arguments

object

an object of class joint.
...

further arguments for the summary.

Value

A list with five elements. Each summarises an element of the jointdata object:

subjects

Gives the number of subjects in the data set.
longitudinal

If longitudinal data is available, it gives the names and class, of the longitudinal variables.
survival

If survival data is available, it gives the number of subjects with failure and censored survival times.
baseline

If baseline covariates is available, it gives the names and class, of the baseline covariates.
times

If longitudinal data is available, it gives the unique longitudinal time measurements, if it is a balanced study. In case of unbalanced study, it will only state it is an unbalanced study.

Author(s)

Ines Sousa

See Also

jointdata, UniqueVariables.

Examples

data(heart.valve)
heart.surv <- UniqueVariables(heart.valve,
                              var.col = c("fuyrs", "status"), 
                              id.col = "num")
heart.valve.jd <- jointdata(survival = heart.surv, 
                            id.col = "num",
                            time.col = "time")
summary(heart.valve.jd)

Summary of a balanced longitudinal data set

Description

For a balanced longitudinal data set a vector of the mean response and variances at defined time points is returned along with the correlation matrix of the responses across the time points.

Usage

summarybal(object, Y.col, times, use = "all.obs", na.rm, ...)

Arguments

object

a longitudinal data set in the balanced format.
Y.col

the column numbers of the longitudinal measurements at each design time point in the object. This does not have to be all of the longitudinal measurements taken and may be a subset instead.
times

a vector of unique time points of the longitudinal measurements. This does not have to be all of the study time points and may be a subset instead, but should match the columns defined in Y.col.
use

an optional character string giving a method for computing covariances in the presence of missing values. This must be (an abbreviation of) one of the strings "all.obs", "complete.obs" or "pairwise.complete.obs". Defaults to use = "all.obs".
na.rm

logical. Should missing values be removed? By default, na.rm = FALSE.
...

further arguments for the summary.

Value

A list with three elements:

mean.vect

a matrix with the time points in the first column and the mean response vector as the second column.
variance

The vector of variances for the response at the time points.
cor.mtx

Containing the correlation matrix of the responses between each pair of time points.

Author(s)

Ines Sousa

See Also

to.balanced.

Examples

data(mental)
summarybal(mental, Y.col = 2:7, times = c(0, 1, 2, 4, 6, 8), na.rm = TRUE)

Transform data to the longitudinal balanced format

Description

Transforms a longitudinal data set in the unbalanced format to the balanced format.

Usage

to.balanced(data, id.col, time.col, Y.col, other.col = NA)

Arguments

data

a data frame with longitudinal data in the unbalanced format. That is, in the format of 'one row per observation'.
id.col

a column number, or column name, in the data frame data, where the patient identifier is located.
time.col

a column number, or column name, in the data frame data, where the time measurements are.
Y.col

a vector of column numbers, or column names, of longitudinal variables, and/or time dependent covariates in the data frame data.
other.col

a vector of column numbers, or column names, of baseline covariates, and/or other subject level data, as for example, survival data. Default does not include other.col.

Value

A data frame with longitudinal data in the balanced format. The balanced format is considered in this context as the format where each row has data on each subject. Notice that in this format we will have multiple columns for the same longitudinal variable, each corresponding to the variable observed at each time point.

Author(s)

Ines Sousa

See Also

to.unbalanced.

Examples

simul <- data.frame(num = 1:10,
                    Y1.1 = rnorm(10), Y1.2 = rnorm(10),
                    Y2.1 = rnorm(10), Y2.2 = rnorm(10),
                    age = rnorm(10))
simul <- to.unbalanced(simul, id.col = 1, times = c(1, 2), 
                       Y.col = 2:5, other.col = 6)
simul <- to.balanced(simul, id.col = "num", time.col = "time",
                     Y.col = c("Y1.1", "Y2.1"), other.col = "age")

Transform data to the longitudinal unbalanced format

Description

Transforms a longitudinal data set in the balanced format to the unbalanced format.

Usage

to.unbalanced(data, id.col, times, Y.col, other.col = NA)

Arguments

data

a data frame with longitudinal data in the balanced format. That is, in the format of 'one row per subject'. data, where the patient identifications is.
id.col

a column number, or column name, in the data frame data, where the patient identifier is located.
times

a vector with the unique time points where the patients are observed. This is the study design time points in a balanced data set.
Y.col

a vector of column numbers, or column names, of longitudinal variables, and/or time dependent covariates in the data frame data.
other.col

a vector of column numbers, or column names, of baseline covariates, and/or other subject level data, as for example, survival data. Default does not include other.col.

Value

A data frame with longitudinal data in the unbalanced format. The unbalanced format is considered in this context as the format where each row has data on each subject observation.

Author(s)

Ines Sousa

See Also

to.balanced.

Examples

simul <- data.frame(num = 1:10,
                    Y1.1 = rnorm(10), Y1.2 = rnorm(10),
                    Y2.1 = rnorm(10), Y2.2 = rnorm(10), 
                    age = rnorm(10))
to.unbalanced(simul, id.col = 1, times = c(1, 2), Y.col = 2:5,
              other.col = 6)

Extracts the unique non-time dependent variables per patient, from an unbalanced data set

Description

This function extracts a set of unique variables within a patient, returning a data frame with columns, patient identification and variables selected. Each row corresponds to the data for each individual.

Usage

UniqueVariables(data, var.col, id.col = "ID")

Arguments

data

data frame, or matrix, with at least a column of patient identification and a covariate column.
var.col

vector of column names or column numbers, of the variables (non-time dependent). Cannot have mix of numbers and column names.
id.col

column name or column number of the patient identification.

Details

This function can be used, when longitudinal data is in the unbalanced format, and it is necessary, for example, to extract the set of unique baseline covariates, or any non-time dependent variables, that in the unbalanced format, are repeated for each observation row. Also, if the original data frame has survival data, this can also be used to extract the survival information from the original data set.

Value

A data frame with patient identification and covariates selected. Each row corresponds to the data for each individual. Note that, this can be only used for non-time dependent covariates. If extracting unique time dependent covariates, the function gives an error, because it can't select what is the unique covariate.

Author(s)

Ines Sousa

Examples

data(heart.valve)
heart.cov <- UniqueVariables(heart.valve,
                             c(2, 3, 5, 6, 12:25),
                             id.col = "num")

Empirical variogram for longitudinal data

Description

Calculates the variogram for observed measurements, with two components, the total variability in the data, and the variogram for all time lags in all individuals.

Usage

variogram(indv, time, Y)

Arguments

indv

vector of individual identification, as in the longitudinal data, repeated for each time point.
time

vector of observation time, as in the longitudinal data.
Y

vector of observed measurements. This can be a vector of longitudinal data, or residuals after fitting a model for the mean response.

Details

The empirical variogram in this function is calculated from observed half-squared-differences between pairs of measurements, vijk=0.5∗(rij−rik)2v_ijk = 0.5 * (r_ij-r_ik)^2 and the corresponding time differences uijk=tij−tiku_ijk=t_ij-t_ik. The variogram is plotted for averages of each time lag for the vijkv_ijk for all ii.

Value

An object of class vargm and list with two elements. The first svar is a matrix with columns for all values (uijk,vijk)(u_ijk,v_ijk), and the second sigma2 is the total variability in the data.

Note

There is a function plot.vargm which should be used to plot the empirical variogram.

Author(s)

Ines Sousa

Examples

data(mental)
mental.unbalanced <- to.unbalanced(mental, id.col = 1, 
                                   times = c(0, 1, 2, 4, 6, 8),
                                   Y.col = 2:7, 
                                   other.col = c(8, 10, 11))
names(mental.unbalanced)[3] <- "Y"

vgm <- variogram(indv = tail(mental.unbalanced[, 1], 30),
                 time = tail(mental.unbalanced[, 2], 30),
                 Y = tail(mental.unbalanced[, 3], 30))