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 )

Arguments

obj

A model object.

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?

Value

A matrix with 4 columns: Estimate, lower and upper c.i. and standard error. The numebr of rows equals nrow(ctr.mat) if zero if FALSE, otherwise nrow(ctr.mat)+1, because an initial row of 0s is added.

Details

The purpose of this function is to compute cumulative rate based on a model for the rates. If the model is a multiplicative model for the rates, the purpose of ctr.mat is to return a vector of rates or log-rates when applied to the coefficients of the model. If log-rates are returned, the they should be exponentiated before cumulated, and the variances computed accordingly. Since log-linear models are the most common the Exp parameter defaults to TRUE.

Examples

Run this code

# 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 ), data=lung ) )

# Cut the follow-up every 10 days
#
dx <- Lexis( exit=time, fail=(status==2), breaks=seq(0,1100,10), data=lung )
str( dx )

# Fit a Poisson model with a natural spline for the effect of time.
# Note that "Time" is the left endpoint of the interval in the dataframe dx.
#
MM <- ns( dx$Time, knots=c(50,100,200,400,700), intercept=TRUE )
mp <- glm( Fail ~ MM - 1 + offset(log(Exit-Entry)),
                  family=poisson, data=dx, eps=10^-8, maxit=25 )

# 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( dx$Time ) )
T.wh <- match( T.pt, dx$Time )
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) )