analyze.CumInc.stepp: Analyze competing risks data using Cumulative Incidence method

Description

This method will be deprecated in the future. Please use the constructor function stepp.CI to create a STEPP Cumulative Incidence model for future development.

A method to explore the treatment-effect interactions in competing risks data arising from two treatment arms of a clinical trial. A permutation distribution approach to inference is implemented that permutes covariate values within a treatment group. The statistical significance of observed heterogeneity of treatment effects is calculated using permutation tests: 1) for the maximum difference between each subpopulation effect and the overall population treatment effect or supremum based test statistic; 2) for the difference between each subpopulation effect and the overall population treatment effect, which resembles the chi-square statistic.

Usage

analyze.CumInc.stepp(coltrt, coltime, coltype, covar, trts, patspop, minpatspop, 
    timest, noperm=2500, ncex = 0.7, legendy = 30, pline = -2.5, 
    color = c("red", "black"), 
    xlabel = "Subpopulations by Median Covariate", 
    ylabel = "?-year Disease-Free Survival", 
    tlegend = c("1st Treatment", "2nd Treatment"),  
    nlas = 3, pointwise = FALSE)

Value

analyze.CumInc.stepp generates a Subpopulation Treatment Effect Pattern Plot (STEPP) displaying the p-value from the test for interaction. Descriptive summaries of the dataset and the estimated variance-covariance matrix are returned through the steppes object. See documentation on steppes object for details on how you can use it.

Arguments

coltrt: the treatment variable
coltime: the time to event variable
coltype: variable with distinct codes for different causes of failure where coltype=0 for censored observations; coltype=1 for event of interest; coltype=2 for other causes of failure
covar: the covariate of interest
trts: a vector containing the codes for the 2 treatment arms, 1st and 2nd treatment arms, respectively
patspop: larger parameter(r2) for subpopulation construction that determines how many patients are in each subpopulation
minpatspop: smaller parameter(r1) for subpopulation construction that determines the largest number of patients in common among consecutive subpopulations
timest: timepoint to estimate survival
noperm: the desired number of permutations; must be 0 or above
ncex: optional - specify the size of the text for the sample size annotation, that is, the character expansion factor
legendy: optional - the vertical location of the legend according to the units on the y-axis
pline: optional - specify the vertical location of the p-value, that is, on which margin line, starting at 0 counting outwards
color: optional - a vector containing the line colors for the 1st and 2nd treatment, respectively
ylabel: optional - specify the label for the y-axis
xlabel: optional - specify the label for the x-axis
tlegend: optional - a vector containing the treatment labels, 1st and 2nd treatment, respectively
nlas: optional - specify the las parameter (0,1,2,3) to determine the orientation of the sample size annotation
pointwise: optional -specify pointwise confidence intervals (pointwise=TRUE), or confidence bands (pointwise=FALSE, default) to be displayed

Author

Ann Lazar, Wai-ki Yip, David Zahrieh, Bernard Cole, Marco Bonetti, Richard Gelber

Warning

This function together with other old functions will be depreciated in the future. A new set of S4 classes are implemented to replace old interfaces. Please use them for future development.

A few tips to keep in mind:

The variables coltrt, coltime, coltype, and covar must be numeric. No formatting allowed.

If you receive the error "Error in solve.default(sigma): system is computationally singular; reciprocal condition number = 0" then we recommend changing the seed by re-running analyze.KM.stepp. If this error persists after several runs, then the program cannot provide reliable results. Please try modifying your choices of the two parameters minpatspop(r1) and patspop(r2) that define the subpopulation.

The number of permutations specified in noperm, the sample size, and the number of subpopulations generated will affect how long analyze.CumInc.stepp takes to execute. The results are stable if 2500 or more permutations are specified. Furthermore, varying the number of subpopulations will affect inference.

The time point selected to estimate survival in timest must be in the same units (e.g., months) as the coltime variable.

The order of the treatments in the vector trts must be in the same order in the vector tlegend.

Details

A statistical method to explore treatment by covariate interactions in competing risks data arising from two treatment arms of a clinical trial. The method is based on constructing overlapping subpopulations of patients with respect to a covariate of interest, and in observing the pattern of the treatment effects estimated across subpopulations. A plot of these treatment effects is called STEPP, or Subpopulation Treatment Effect Pattern Plot. STEPP uses the permutation distribution based approach for inference.

One can explore the window parameters without invoking the permutation analysis by setting noperm to 0. In that case, pvalue and the covarance matrix will not be available.

We acknowledge Robert J. Gray for permitting us to use the cmprsk package.

References

Bonetti M, Gelber RD. Patterns of treatment effects in subsets of patients in clinical trials. Biostatistics 2004; 5(3):465-481.

Bonetti M, Zahrieh D, Cole BF, Gelber RD. A small sample study of the STEPP approach to assessing treatment-covariate interactions in survival data. Statistics in Medicine 2009; 28(8):1255-68.

Lazar AA, Cole BF, Bonetti M, Gelber RD. Evaluation of treatment-effect heterogeneity usiing biomarkers measured on a continuous scale: subpopulation treatment effect pattern plot. Journal of Clinical Oncology, 2010; 28(29): 4539-4544.

Examples

Run this code

#GENERATE TREATMENT VARIABLE:
n <- 1000		# set the sample size
mu <- 0			# set the mean and sd of the covariate
sigma <- 1

beta0 <- log(-log(0.5)) # set the intercept for the log hazard
beta1 <- -0.2		# set the slope on the covariate
beta2 <- 0.5		# set the slope on the treatment indicator
beta3 <- 0.7		# set the slope on the interaction

prob2 <- 0.2		# set the proportion type 2 events
cprob <- 0.3		# set the proportion censored

set.seed(7775432) 	# set the random number seed
covariate <- rnorm(n,mean=mu,sd=sigma)	# generate the covariate values
Txassign <- rbinom(n,1,0.5)		# generate the treatment indicator
x3 <- covariate*Txassign		# compute interaction term
					# compute the hazard for type 1 event
lambda1 <- exp(beta0+beta1*covariate+beta2*Txassign+beta3*x3)
lambda2 <- prob2*lambda1/(1-prob2)	# compute the hazard for the type 2 event
					# compute the hazard for censoring time
lambda0 <- cprob*(lambda1+lambda2)/(1-cprob)
t1 <- rexp(n,rate=lambda1)		# generate the survival time for type 1 event
t2 <- rexp(n,rate=lambda2)		# generate the survival time for type 2 event
t0 <- rexp(n,rate=lambda0)		# generate the censoring time
time <- pmin(t0,t1,t2)			# compute the observed survival time
type <- rep(0,n)
type[(t1 < t0)&(t1 < t2)] <- 1
type[(t2 < t0)&(t2 < t1)] <- 2

# Call analyze.CumInc.stepp to analyze the data
# Warning: In this example, the permutations have been set to 0 to allow the stepp function
# to finish in a short amount of time.  IT IS RECOMMEND TO USE AT LEAST 2500 PERMUTATIONS TO 
# PROVIDE STABLE RESULTS.
analyze.CumInc.stepp(coltrt=Txassign, trts=c(0,1), coltime=time, coltype=type, covar=covariate,
  patspop=300, minpatspop=200, timest=1.0, noperm=0,
  ncex=0.70,legendy=30,pline=-2.5,color=c("red", "black"),
  xlabel="Subpopulations by Median Age",ylabel="4-year Cancer Relapse",
  tlegend=c("Treatment A", "Treatment B"), nlas=3,pointwise=FALSE)

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