analyze.KM.stepp: Analyze survival data using Kaplan-Meier method

Description

This method will be deprecated in the future. Please use the constructor function stepp.KM to create a STEPP Kaplan-Meier model for future development.

A method to explore the treatment-covariate interactions in survival data arising from two treatment arms of a clinical trial. The treatment effects are measured using survival functions at a specified time point estimated from the Kaplan-Meier method and the hazard ratio based on observed-minus-expected estimation. A permutation distribution approach to inference is implemented, based on permuting the covariate values within each 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.KM.stepp(coltrt, coltime, colcens, 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.KM.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
colcens: the censoring variable
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

Wai-ki Yip, David Zahrieh, Marco Bonetti, Bernard Cole, Ann Lazar, 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, colcens, 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.KM.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-covariate interactions in survival data arising from two treatment arms of a clinical trial. The method is based on constructing overlapping subpopulations of patients with respect to one 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.

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.

Examples

Run this code

#GENERATE TREATMENT VARIABLE:
N <- 1000
Txassign <- sample(c(1,2), N, replace=TRUE, prob=c(1/2, 1/2))
n1 <- length(Txassign[Txassign==1])
n2 <- N - n1
#GENERATE A COVARIATE:
covariate <- rnorm(N, 55, 7)
#GENERATE SURVIVAL AND CENSORING VARIABLES ASSUMING A TREATMENT COVARIATE INTERACTION:
Entry <- sort( runif(N, 0, 5) )
SurvT1 <- .5
beta0 <-  -65 / 75
beta1 <- 2 / 75
Surv <- rep(0, N)
lambda1 <- -log(SurvT1) / 4
Surv[Txassign==1] <- rexp(n1, lambda1)
Surv[Txassign==2] <- rexp(n2, (lambda1*(beta0+beta1*covariate[Txassign==2])))
EventTimes <- rep(0, N)
EventTimes <- Entry + Surv
censor <- rep(0, N)
time <- rep(0,N)
for ( i in 1:N )
  {
   censor[i] <- ifelse( EventTimes[i] <= 7, 1, 0 )
   time[i] <- ifelse( EventTimes[i] < 7, Surv[i], 7 - Entry[i] ) 
  }

#CALL analyze.KM.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.
output <- analyze.KM.stepp ( coltrt=Txassign, coltime=time, 
  colcens=censor, covar=covariate, trts=c(1,2), patspop=300,
  minpatspop=200, timest=4, noperm=0, ncex=0.70, legendy=30,
  pline=-2.5, color=c("red", "black"),
  xlabel="Subpopulations by Median Age", ylabel="4-year Disease-Free Survival", 
  tlegend=c("Treatment A", "Treatment B"), nlas=3, pointwise=FALSE)

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