hetsurr.fun {hetsurr}

Assess and test for heterogeneity in the utility of a surrogate

Description

This function assesses and tests for heterogeneity in the utility of a surrogate with respect to a continuous or discrete baseline covariate. The method is nonparametric and focuses on estimation of the proportion of the treatment effect that is explained by the surrogate marker. Inference information is provided including a confidence band for the proportion and results from formal testing for heterogeneity. When the baseline covariate is continuous, two tests are performed - an omnibus test and a trend test; when the baseline covariate is discrete, only one test is performed - an omnibus test.

Usage

hetsurr.fun(y1, y0, s1, s0, w1, w0, wf.grd = NULL, h0 = NULL, h1 = NULL, h2 = NULL, 
h3 = NULL, h4 = NULL, var.want = FALSE, type = "cont", test.want = FALSE, c.adj = 1)

Arguments

y1

the primary outcome in the treatment group

y0

the primary outcome in the control group

s1

the surrogate marker in the treatment group

s0

the surrogate marker in the control group

w1

the baseline covariate of interest in the treatment group

w0

the baseline covariate of interest in the control group

wf.grd

the grid of the baseline covariate where estimates are wanted; if this is not specified, this will bet set equal to 50 equally spaced points between the 10th and 90th percentile of the union of w1 and w0 values (if continuous) or the set of unique categories (if discrete)

h0

bandwidth; if not specific, this is set to a value of appropriate order

h1

bandwidth; if not specific, this is set to a value of appropriate order

h2

bandwidth; if not specific, this is set to a value of appropriate order

h3

bandwidth; if not specific, this is set to a value of appropriate order

h4

bandwidth; if not specific, this is set to a value of appropriate order

var.want

TRUE or FALSE; indicates whether variance estimate are wanted, default is FALSE

type

"cont" or "discrete"; indicates the form of the baseline covariate w, default is "cont"

test.want

TRUE or FALSE; indicates whether testing results are wanted, default is FALSE

c.adj

a multiplicative adjustment for the bandwidth; default is 1

Details

This function calculates the treatment effect, Delta, the residual treatment effect, Delta_S, and the proportion of treatment effect explained R_S, as a function of the baseline covariate (if continuous) or stratified by category (if discrete). The estimation approach is nonparametric. Variance estimates can be requested including a confidence band for R_S. Results from formal testing for heterogeneity can also be requested. When the baseline covariate is continuous, two tests are performed - an omnibus test and a trend test; when the baseline covariate is discrete, only one test is performed - an omnibus test.

Value

w.values

values of the baseline covariate at which estimates are provided

delta.w

estimated treatment effect, Delta, at each w value

delta.w.s

estimated residual treatment effect, Delta_S, at each w value

R.w.s

estimated proportion of treatment effect explained, R_S, at each w value

se.delta.w

estimated standard error of Delta

se.delta.w.s

estimated standard error of Delta.S

se.R.w.s

estimated standard error of R.S

conf.delta.w.lower

lower bound of the confidence intervals for Delta

conf.delta.w.upper

upper bound of the confidence intervals for Delta

conf.delta.w.s.lower

lower bound of the confidence intervals for Delta.S

conf.delta.w.s.upper

upper bound of the confidence intervals for Delta.S

conf.R.w.s.lower

lower bound of the confidence intervals for R.S

conf.R.w.s.upper

upper bound of the confidence intervals for R.S

band.R.w.s.lower

lower bound of the confidence band for R.S

band.R.w.s.upper

upper bound of the confidence band for R.S

omnibus.test.statistic

test statistic from omnibus test; for a continuous baseline covariate only

omnibus.p.value

p-value from omnibus test, testing for evidence of heterogeneity; for a continuous baseline covariate only

trend.test.statistic

test statistic from the trend test; for a continuous baseline covariate only

trend.p.value

p-value from trend test, testing for evidence of heterogeneity; for a continuous baseline covariate only

test.statistic

p-value from the test testing for evidence of heterogeneity; for a discrete baseline covariate only

p.value

p-value from the test testing for evidence of heterogeneity; for a discrete baseline covariate only

Author(s)

Layla Parast

References

Parast, L., Cai, T., Tian L (2021). Testing for Heterogeneity in the Utility of a Surrogate Marker. Biometrics, In press.

Examples

	data(example.data)
	names(example.data)
	#computationally intensive
	
	het.ob = hetsurr.fun(y1=example.data$y1, y0=example.data$y0, s1=example.data$s1, 
	s0=example.data$s0, w1=example.data$w1, w0=example.data$w0, wf.grd = seq(0.25, 1.75, 
	length=50), var.want =FALSE, type = "cont")
	het.ob = hetsurr.fun(y1=example.data$y1, y0=example.data$y0, s1=example.data$s1, 
	s0=example.data$s0, w1=example.data$w1, w0=example.data$w0, wf.grd = seq(0.25, 1.75, 
	length=50), var.want =TRUE,  test.want = TRUE, type = "cont")
	
	#reducing dimension of example data to provide a computationally faster example
	het.ob = hetsurr.fun(y1=example.data$y1[1:500], y0=example.data$y0[1:500],
	s1=example.data$s1[1:500], s0=example.data$s0[1:500], w1=example.data$w1[1:500],
	w0=example.data$w0[1:500], wf.grd = seq(0.25, 1.75, length=5), var.want =FALSE, 
	type = "cont")