Temporal Process Regression

Description

Fit regression models for temporal process responses with time-varying and time-independent coefficients.

Details

An overview of how to use the package, including the most important functions

Author(s)

Jun Yan <jun.yan@uconn.edu>

References

Fine, Yan, and Kosorok (2004): Temporal Process Regression. Biometrika.

Confidence Interval Plot

Description

Plotting time-varying coefficient with pointwise confidence.

Usage

ci.plot(x, y, se, level = 0.95, ylim = NULL, newplot = TRUE,
        fun = gaussian()$linkinv, dfun = gaussian()$mu.eta, ...)

Arguments

Author(s)

Jun Yan jun.yan@uconn.edu

rhDNase Data

Description

Randomized trial of rhDNase for treatment of cystic fibrosis

Usage

data(dnase)

Format

A data frame with 767 observations on the following 6 variables.

id

subject id

rx

treatment arm: 0 = placebo, 1 = rhDNase

fev

forced expirotary volume, a measure of lung capacity

futime

follow time

iv1

IV start time

iv2

IV stop time

Details

During an exacerbation, patients received intravenous (IV) antibiotics and were considered unsusceptible until seven exacerbation-free days beyond the end of IV therapy.

A few subjects were infected at the time of enrollment, for instance a subject has a first infection interval of -21 to 7. We do not count this first infection as an "event", and the subject first enters the risk set at day 7.

Source

Therneau and Grambsch (2000). Modeling Survival Data: Extending the Cox model. Springer. http://www.mayo.edu/hsr/people/therneau/book/data/dnase.html

References

Yan and Fine (2008). Analysis of Episodic Data with Application to Recurrent Pulmonary Exacerbations in Cystic Fibrosis Patients. JASA.

Examples

## This example steps through how to set up for the tpr function.
## Three objects are needed:
##     1) response process (an object of "lgtdl")
##     2) data availability process (an object of "lgtdl")
##     3) a time-independent covariate matrix

data(dnase)

## extracting the unique id and subject level information
dat <- unique(dnase[,c("id", "futime", "fev", "rx")])

## construct temporal process response for recurrent enent
rec <- lapply(split(dnase[,c("id", "iv1", "futime")], dnase$id),
              function(x) {
                v <- x$iv1
                maxfu <- max(x$futime)
                ## iv1 may be negative!!!
                if (is.na(v[1])) c(0, maxfu + 1.0)
                else if (v[1] < 0) c(v[1] - 1, v[!is.na(v)], maxfu + 1.0)
                else c(0, v[!is.na(v)], maxfu + 1.0)
              })

yrec <- lapply(rec,
               function(x) {
                 dat <- data.frame(time=x, cov=1:length(x)-1)
                 len <- length(x)
                 dat$cov[len] <- dat$cov[len - 1]
                 as.lgtdl(dat)
               })

## construct temporal process response for accumulative days exacerbation
do1.acc <- function(x) {
  gap <- x$iv2 - x$iv1 + 1
  if (all(is.na(gap))) yy <- tt <- NULL
  else {
    gap <- na.omit(gap)
    yy <- cumsum(rep(1, sum(gap)))
    tt <- unlist(sapply(1:length(gap), function(i)
                        seq(x$iv1[i], x$iv2[i], by=1.0)))
  }
  yy <- c(0, yy, rev(yy)[1])
  if (!is.null(tt[1]) && tt[1] < 0)
    tt <- c(tt[1] - 1, tt, max(x$futime) + 1.0)
  else tt <- c(0, tt, max(x$futime) + 1.0)
  as.lgtdl(data.frame(time=tt, cov=yy))
}

yacc <- lapply(split(dnase[,c("id", "iv1", "iv2", "futime")], dnase$id),
              do1.acc)

## construct data availability (or at risk) indicator process
tu <- max(dat$futime) + 0.001
rt <- lapply(1:nrow(dat),
             function(i) {
               x <- dat[i, "futime"]
               time <- c(0, x, tu)
               cov <- c(1, 0, 0)
               as.lgtdl(data.frame(time=time, cov=cov))
             })

## time-independent covariate matrix
xmat <- model.matrix(~ rx + fev, data=dat)
## time-window in days
tlim <- c(10, 168)
good <- unlist(lapply(yrec, function(x) x$time[1] == 0))


## fully functional temporal process regression

## for recurrent event
m.rec <- tpr(yrec, rt, xmat[,1:3], list(), xmat[,-(1:3),drop=FALSE], list(),
             tis=10:160, w = rep(1, 151), family = poisson(),
             evstr = list(link = 5, v = 3))
par(mfrow=c(1,3), mgp=c(2,1,0), mar=c(4,2,1,0), oma=c(0,2,0,0))
for(i in 1:3) ci.plot(m.rec$tis, m.rec$alpha[,i], sqrt(m.rec$valpha[,i]))
## hypothesis test of significance
## integral test, covariate index 2 and 3
sig.test.int.ff(m.rec, idx=2:3, ncut=2)
sig.test.boots.ff(m.rec, idx=2:3, nsim=1000)
## constant fit
cfit <- cst.fit.ff(m.rec, idx=2:3)

## goodness-of-fit test for constant fit
gof.test.int.ff(m.rec, idx=2:3, ncut=2)
gof.test.boots.ff(m.rec, idx=2:3, nsim=1000)




## for cumulative days in exacerbation
m.acc <- tpr(yacc, rt, xmat[,1:3], list(), xmat[,-(1:3),drop=FALSE], list(),
             tis=10:160, w = rep(1, 151), family = gaussian(),
             evstr = list(link = 1, v = 1))
par(mfrow=c(1,3), mgp=c(2,1,0), mar=c(4,2,1,0), oma=c(0,2,0,0))
for(i in 1:3) ci.plot(m.acc$tis, m.acc$alpha[,i], sqrt(m.acc$valpha[,i]))

Temporal Process Regression

Description

Regression for temporal process responses and time-independent covariate. Some covariates have time-varying coefficients while others have time-independent coefficients.

Usage

tpr(y, delta, x, xtv=list(), z, ztv=list(), w, tis,
    family = poisson(),
    evstr = list(link = 5, v = 3),
    alpha = NULL, theta = NULL,
    tidx = 1:length(tis),
    kernstr = list(kern=1, poly=1, band=range(tis)/50),
    control = list(maxit=25, tol=0.0001, smooth=0, intsmooth=0))

Arguments

Details

This rapper function can be made more user-friendly in the future. For example, evstr can be determined from the family argument.

Value

An object of class "tpr":

Author(s)

Jun Yan <jun.yan@uconn.edu>

References

Fine, Yan, and Kosorok (2004). Temporal Process Regression. Biometrika.

Yan and Huang (2009). Partly Functional Temporal Process Regression with Semiparametric Profile Estimating Functions. Biometrics.

Constant fit of coefficients in a TPR model

Description

Weighted least square estimate of a constant model for time-varying coefficients in a TPR model.

Usage

cst.fit.ff(fit, idx)

Arguments

Value

The estimated constant fit, standard error, z-value and p-value.

Author(s)

Jun Yan jun.yan@uconn.edu

References

Fine, Yan, and Kosorok (2004). Temporal Process Regression. Biometrika.

See Also

tpr.test

Significance and Goodness-of-fit Test of TPR

Description

Two kinds of tests are provided for inference on the coefficients in a fully functional TRP model: integral test and bootstrap test.

Usage

sig.test.int.ff(fit, chypo = 0, idx, weight = TRUE, ncut = 2)
sig.test.boots.ff(fit, chypo = 0, idx, nsim = 1000, plot = FALSE)
gof.test.int.ff(fit, cfitList = NULL, idx, weight = TRUE, ncut = 2)
gof.test.boots.ff(fit, cfitList = NULL, idx, nsim = 1000, plot = FALSE)
gof.test.boots.pf(fit1, fit2, nsim, p = NULL, q = 1)

Arguments

Value

Test statistics and their p-values.

Author(s)

Jun Yan jun.yan@uconn.edu

References

Fine, Yan, and Kosorok (2004). Temporal Process Regression. Biometrika.

See Also

tpr

Examples

## see ?tpr