ci.cum: Compute cumulative sum of estimates.

Description

Computes the cumulative sum of parameter functions and the standard error of it. Optionally the exponential is applied to the parameter functions before it is cumulated.

Usage

ci.cum( obj,
    ctr.mat = NULL,
     subset = NULL,
       intl = 1,
      alpha = 0.05,
        Exp = TRUE,
     ci.Exp = FALSE,
     sample = FALSE )

Arguments

obj

A model object (of class lm, glm, coxph, survreg, lme,mer,nls,gnlm, MIresult or polr).

ctr.mat

Contrast matrix defining the parameter functions from the parameters of the model.

subset

Subset of the parameters of the model to which ctr.mat should be applied.

intl

Interval length for the cumulation. Either a constant or a numerical vector of length nrow(ctr.mat).

alpha

Significance level used when computing confidence limits.

Exp

Should the parameter function be exponentiated before it is cumulated?

ci.Exp

Should the confidence limits for the cumulative rate be computed on the log-scale, thus ensuring that exp(-cum.rate) is always in [0,1]?

sample

Should a sample of the original parameters be used to compute a cumulative rate?

Value

A matrix with 4 columns: Estimate, lower and upper c.i. and standard error. If sample is TRUE, a sampled vector is reurned, if sample is numeric a matrix with sample columns is returned, each column a cumulative rate based on a random sample from the distribution of the parameter estimates.

Details

The purpose of this function is to the compute cumulative rate (integrated intensity) at a set of points based on a model for the rates. ctr.mat is a matrix which, when premultiplied to the parameters of the model reurn the (log)rates at a set of increasing time points. If log-rates are returned from the model, the they should be exponentiated before cumulated, and the variances computed accordingly. Since the primary use is for log-linear Poisson models the Exp parameter defaults to TRUE.

The ci.Exp argument ensures that the confidence intervals for the cumulaive rates are alwys positive, so that exp(-cum.rate) is always in [0,1].

Examples

Run this code

# NOT RUN {
# Packages required for this example
library( splines )
library( survival )
data( lung )
par( mfrow=c(1,2) )

# Plot the Kaplan-meier-estimator
plot( survfit( Surv( time, status==2 ) ~ 1, data=lung ) )

# Declare data as Lexis
lungL <- Lexis( exit=list("tfd"=time),
                exit.status=(status==2)*1, data=lung )
summary( lungL )

# Cut the follow-up every 10 days
sL <- splitLexis( lungL, "tfd", breaks=seq(0,1100,10) )
str( sL )
summary( sL )

# Fit a Poisson model with a natural spline for the effect of time.
# Extract the variables needed
D <- status(sL, "exit")
Y <- dur(sL)
tB <- timeBand( sL, "tfd", "left" )
MM <- ns( tB, knots=c(50,100,200,400,700), intercept=TRUE )
mp <- glm( D ~ MM - 1 + offset(log(Y)),
           family=poisson, eps=10^-8, maxit=25 )

# mp is now a model for the rates along the time scale tB

# Contrast matrix to extract effects, i.e. matrix to multiply with the
# coefficients to produce the log-rates: unique rows of MM, in time order.
T.pt <- sort( unique( tB ) )
T.wh <- match( T.pt, tB )

# ctr.mat=MM[T.wh,] selects the rates as evaluated at times T.pt:
Lambda <- ci.cum( mp, ctr.mat=MM[T.wh,], intl=diff(c(0,T.pt)) )

# Put the estimated survival function on top of the KM-estimator
matlines( c(0,T.pt[-1]), exp(-Lambda[,1:3]), lwd=c(3,1,1), lty=1, col="Red" )

# Extract and plot the fitted intensity function
lambda <- ci.lin( mp, ctr.mat=MM[T.wh,], Exp=TRUE )
matplot( T.pt, lambda[,5:7]*10^3, type="l", lwd=c(3,1,1), col="black", lty=1,
         log="y", ylim=c(0.2,20) )
# }