cci {currentSurvival}

Estimates Current Cumulative Incidence (CCI) and Common Cumulative Incidence (comCI) Functions

Description

This function estimates the current cumulative incidence (CCI), i.e. the probability that a patient is alive and in any disease remission (e.g. complete cytogenetic remission in chronic myeloid leukaemia) after initiating his or her therapy (e.g. tyrosine kinase therapy for chronic myeloid leukaemia). Optionally, this function estimates the common cumulative incidence (comCI), i.e. the probability that a patient is alive and in the first disease remission after therapy initiation. The CCI and comCI curves can also be stratified by risk factors. Moreover, statistical test can be applied to compare the risk groups.

Usage

cci(data, maxx = NULL, com.est = TRUE, conf.int = FALSE, 
    conf.int.level = NULL, no.iter = NULL, points = NULL, 
    fig = TRUE, strat = FALSE, pvals = FALSE, pval.test = NULL)

Arguments

data

a matrix with ascending times from therapy initiation to occurrence of individual events (in days, i.e. positive integer values), total follow-up times from therapy initiation to data cut-off date (in days), and censoring indicators; moreover, a vector for stratification factor may be included;
if no stratification factor is included, the size of the data matrix is n times (2*r+2), where n is the number of patients and r is the maximum number of disease remissions achieved by patients;
if the data contain a stratification factor, the size of the data matrix is n times (2*r+3), where n is the number of patients and r is the maximum number of disease remissions achieved by patients;
the data matrix consists of the following columns:
data[,1] is the time from therapy initiation to achievement of the first disease remission
data[,2] is the time from therapy initiation to loss of the first disease remission
data[,3] is the time from therapy initiation to achievement of the second disease remission
...
data[,2*r-1] is the time from therapy initiation to achievement of the rth disease remission
data[,2*r] is the time from therapy initiation to loss of the rth disease remission
data[,2*r+1] is the follow-up time (time from the therapy initiation to death or to the date of last contact with a patient)
data[,2*r+2] is the censoring indicator (1..patient died, 0..patient is censored)
(data[,2*r+3] is the stratification factor (maximum number of stratification levels is 8 because of figure clarity))

maxx

maximum follow-up time calculated from therapy initiation in years (defining time period for which the point estimates will be computed and curves will be plotted). Setting maxx smaller than the maximum follow-up time enables creating plots without fluctuating curve ends that may be caused by small number of patients. The default value is the maximum follow-up time (i.e. max(data[,2*r+1])/365).

com.est

a logical value indicating whether common cumulative incidence function should be estimated. The default value is TRUE.

conf.int

a logical value indicating whether confidence interval for the function(s) should be estimated. The default value is FALSE.

conf.int.level

two-sided confidence interval level (must be in range 0.9 and 0.99). The default value is 0.95.

no.iter

a number of bootstrap iterations for confidence interval computation (must be in range between 10 and 10,000). The default value is 100.

points

time points in which the point estimates will be computed (in months). The default values are 0, 12, 24, ..., floor(maxx/(365/12)).

fig

a logical value indicating whether a figure should be plotted. The default value is TRUE.

strat

a logical value indicating whether a stratification factor is included. The default value is FALSE.

pvals

a logical value indicating whether p-values for the comparison of stratified curves at pre-defined time points should be computed. The default value is FALSE.

pval.test

a type of a test that will be used for the computation of p-values. Possible values are “naive”, “log”, “loglog”. The default value is “loglog”.

Value

a list containing the following elements:

no.risk

numbers of patients at risk at the defined time points

pest

a matrix of point estimates (accompanied with confidence intervals) at the defined time points

pest.day

a matrix of point estimates (accompanied with confidence intervals) at each day of the follow-up time

pval

p-values for the comparison of point estimates at the defined time points

summary

summary of input data

Author(s)

Eva Janousova, Tomas Pavlik
Institute of Biostatistics and Analyses
Masaryk University, Brno, Czech Republic
[e-mail]

References

Pavlik T., Janousova E., Pospisil Z., et al. (2011). Estimation of current cumulative incidence of leukaemia-free patients and current leukaemia-free survival in chronic myeloid leukaemia in the era of modern pharmacotherapy. BMC Med Res Methodol 11:140.

See Also

clfs

Examples

## 4 examples of CCI estimation without stratification (and 
## comCI estimation) with and without confidence intervals:
data(cml)  # load example data set
cml <- cml[,c(1:7)] # select event and follow-up times and death
           # (stratification factor is not included)
res <- cci(cml) # CCI + comCI without confidence intervals
res <- cci(cml, com.est=FALSE) # CCI without confidence intervals
## Not run: 
res <- cci(cml, conf.int=TRUE, no.iter=10) # CCI + comCI with 
           # confidence intervals
res <- cci(cml, com.est=FALSE, conf.int=TRUE, no.iter=10) # CCI 
           # with confidence intervals
## End(Not run)

## 4 examples of CCI estimation with stratification (and comCI 
## estimation) with and without confidence intervals:
data(cml)  # load example data set
cml <- cml[,c(1:7,10)] # select event and follow-up times, death,
           # and the EUTOS score as a stratification parameter
res <- cci(cml, strat=TRUE) # stratified CCI + comCI without 
           # confidence intervals
res <- cci(cml, com.est=FALSE, strat=TRUE) # stratified CCI 
           # without confidence intervals
## Not run: 
res <- cci(cml, conf.int=TRUE, no.iter=10, strat=TRUE, pvals=TRUE)
           # stratified CCI + comCI with confidence intervals
res <- cci(cml, com.est=FALSE, conf.int=TRUE, no.iter=10, 
           strat=TRUE, pvals=TRUE) # stratified CCI with 
           # confidence intervals
## End(Not run)

## Not run: 
## As the function does not allow setting plot option (e.g. line
## colour, width and type), you can create a plot using the 
## following commands:
data(cml)  # load example data set
cml <- cml[,c(1:7)] # select event and follow-up times and death
           # (stratification factor is not included)
res <- cci(cml, conf.int=TRUE, no.iter=10) # CCI + comCI with 
           # confidence intervals 
maxx <- max(res$pest.day[,1]) # maximum follow-up time in days
x=0:maxx
yrs <- floor(maxx/365) # maximum follow-up time in years
plot(0,0,pch='.',cex=0.01,xlab="Years after therapy initiation",
     ylab="Probability",axes=FALSE,xlim=c(0,maxx),ylim=c(0,1)) 
     # plot initialization
axis(2,at=seq(0,1,0.2)) # setting of points where tick-marks are
     # to be drawn on the y-axis
axis(1,at=seq(0,((yrs+1)*365),365),labels=seq(0,(yrs+1),1)) 
     # setting of points where tick-marks are to be drawn on the
     # x-axis
lines(x,res$pest.day[,2],type="S",lty=1,lwd=1) # lower confidence
     # interval for the CCI function estimate
lines(x,res$pest.day[,3],type="S",lty=1,lwd=2) # CCI estimate
lines(x,res$pest.day[,4],type="S",lty=1,lwd=1) # upper confidence
     # interval for the CCI function estimate
lines(x,res$pest.day[,5],type="S",lty=2,lwd=1) # lower confidence 
     # interval for the comCI function estimate
lines(x,res$pest.day[,6],type="S",lty=2,lwd=2) # comCI estimate
lines(x,res$pest.day[,7],type="S",lty=2,lwd=1) # upper confidence
     # interval for the comCI function estimate
legend("bottomright",legend=c("CCI","95% conf. int.","comCI",
       "95% conf. int."),lwd=c(2,1,2,1),lty=c(1,1,2,2),bty="n",
       cex=0.9) 
## End(Not run)