resboot function

Rresidual Bootstrap Test (RBT) for treatment-biomarker interaction

{resboot} is a function to test the existance of treatment-biomarker interaction in biomarker threshold model

g(Y) = b0+b1I(w>c) + b2z + b3*I(w>c)*z.

resboot(x, ...)

## S3 method for class 'formula'
resboot(formula, family, data=list(...), B = 100, epsilon = 0.01, ...)
#
###To test the null hypothesis of interaction between treatment variable  
###(define by z) and biomarker variables (define by w) for survival dataa, 
###use:
#
# fit = resboot(Surv(time, status) ~ w + z + w:z)
#

Arguments

• formula: an object of class "formula"(or one that can be coerced to that class): a symbolic description of the model to be fitted. The details of model specification are given under 'Details'.
• family: default is family = 'Surv' for survival data.
• 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 resboot 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).
• B: Number of bootstraps, default is B = 100
• epsilon: Biomarker (transformed) step length for profile likelihood method, default is epsilon = 0.01
• ...: additional arguments to be passed to the low level regression fitting functions (see below).

Details

resboot(y~w + z + w:z) will give residual bootstrap p-value for interaction between biomarker variable (w) and treatment variable (z). The null hypothesis is given by H0: b3 = 0, where b3 is the regression coefficient for the interaction term I(w>c)*z. Function print(x) can be used to print a summary of resboot results.

Returns

resboot returns an object of class inheriting from "resboot". When B > 0, an object of class "resboot" is a list containing at least the following components: - theta: the estimated maximum of likelihood ratio statistics

• theta.b: Bootstrap sample of theta

• sd: standard deviation of theta based on resampling

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

References

Gavanji, P., Chen, B. E. and Jiang, W.(2018). Residual Bootstrap test for interactions in biomarker threshold models with survival data. Statistics in Biosciences.

Author(s)

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

Note

Based on code from Parisa Gavanji.

See Also

bhm

coxph

Examples

##
## Generate a random data set
n = 30
b = c(0.5, 1, 1.5)
data = gendat.surv(n, c0 = 0.40, beta = b)
tm = data[, 1]
status = data[, 2]
trt = data[, 3]
ki67 = data[, 4]
#
### No run
# 
# fit = resboot(Surv(tm, status) ~ ki67+trt+ki67:trt) 
#