pIndex function

Probability Index for Survival Time Difference

{pIndex} is a function to estimate and test differce of survival time among groups. It is defined as p = Pr{T_1 < T_2 }, where $T_1$ is survival time for subjects in group 1 and $T_2$ is surval time in group 2.

pIndex(x, ...)

## S3 method for class 'formula'
pIndex(formula, data, control = list(...),...)
###To estimate probability index for treatment and control groups (define by trt):
#
# fit = pIndex(Surv(time, status) ~ trt)
#
###To estimate probability index difference for treatment and control 
###groups (define by trt) between biomarker postive and biomarker negative
###subjects(i.e. Treatment-biomarker interaction):
#
# fit = pIndex(Surv(time, status) ~ trt+biomarker)
#

Arguments

• formula: an object of class "formula"(or one that can be coerced to that class): a sy mbolic description of the model to be fitted. The details of model specification are given under 'Details'.
• data: an optional data frame, list or environment (or object coercible by 'as.data.frame' to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the enviro nment from which pIndex is called.
• x: Here covariate x is a design matrix of dimension n * 1 (for two sample test) or dimension n * 2 (for treatment * biomarker interaction).
• control: a list of parameters for controlling the fitting process. See 'pIndexControl' for details
• ...: additional arguments to be passed to the low level regression fitting functions (see below).

Details

pIndex(yx) will estimate probability index of two groups (eg. treatment vs control) define by x. pIndex(yx1 + x2) will estimate the difference of probability index of x1 (eg. treatment vs control) between biomarker positive and biomarker negative groups (x2). Function print(x) can be used to print a summary of pIndex results.

Returns

pIndex returns an object of class inheriting from "pIndex". When B > 0, an object of class "pIndex" is a list containing at least the following components: - theta: the estimated probability index

• theta.b: Bootstrap or Jackknife sample of the probability index

• sd: standard deviation of theta based on resampling

• ci: (1-alpha) percent confidence interval based on resampling

References

Jiang, S., Chen, B. E. and Tu, D.(2016). Inference on treatment-covariate interaction based on a nonparametric measure of treatment effects and censored survival data. Statistics in Medicine. 35, 2715-2725.

Author(s)

Bingshu E. Chen (bingshu.chen@queensu.ca)

Note

This function is part of the bhm package.

See Also

bhm, pIndexControl,

Examples

##
## Generate a random data set
n = 50
b = c(0.5, 1, 1.5)
data = gendat.surv(n, c0 = 0.40, beta = b, type='brm')
age = runif(n, 0, 1)*100
tm = data[, 1]
status = data[, 2]
trt = data[, 3]
ki67 = data[, 4]
#
### No run
# 
# fit = pIndex(Surv(tm, status) ~ trt + ki67) 
#