subgroup_detect {subdetect}

Test for and Identify a Subgroup with an Enhanced Treatment Effect.

Description

Tests for the existence of a subgroup with an enhanced treatment effect. The subgroup of interest is represented by \{\theta:\theta^T X\ge 0\}. The test returns a p-value for H_0:\tau=0, where \tau is the treatment effect in this subgroup. If H_0 is rejected, estimates for \theta can be used to obtain the estimated subgroup.

Usage

subgroup_detect(outcome, propen, data, 
                K = 1000L, M = 1000L, seed = NULL)

Arguments

outcome

A formula object. The linear model for the outcome regression. The left-hand-side variable must be the response. R function lm will be used to estimate model parameters. The response must be continuous.

propen

A formula object. The model for the propensity score. The left-hand-side variable must be the treatment variable. R function glm will be used with input option family = binomial(link="logit") to estimate model parameters. The treatment must be binary.

data

A data.frame object. All covariates, treatment, and response variables. Note that the treatment must be binary and that the response must be continuous.

K

An integer object. The number of random sampled points on the unit ball surface \{\theta:||\theta||^2=1\}. These randomly sampled points are used for approximating the Gaussian process in the null and local alternative distributions of the test statistic with multivariate normal distributions. It is recommended that K be set to 10^p, where p is the number of parameters in the outcome model. Note that it is recommended that the number of covariates be less than 10 for this implementation. Default value is 1000.

M

An integer object. The number of resamplings of the perturbed test statistic. This sample is used to calculate the critical value of the test. Default and minimum values are 1000.

seed

An integer object or NULL. If integer, the seed for random number generation, set at the onset of the calculation. If NULL, current seed in R environment is used.

Details

In this function, a linear model with least squares estimate is used for fitting the baseline model \mu(X), and a logistic model with maximum likelihood estimate is used for fitting the propensity score model P(a=1|X). These settings cannot be changed by the user.

Value

A list consisting of

outcome

An lm object. The object returned by the lm fit of the outcome.

propen

A glm object. The object returned by the glm fit of the propensity.

p_value

A numeric object. The p-value of the test.

theta

A named numeric vector. The change-plane parameter estimates for subgroup.

prop

A numeric object. The proportion of sampled points on \theta unit ball surface that are used for calculating test statistic. For some values of theta, the subgroup contains no samples or all samples. These are discarded.

seed

If seed was provided as input, the user specified integer seed. If seed was not provided, not present.

References

Ailin Fan, Rui Song, and Wenbin Lu, (2016). Change-plane analysis for subgroup detection and sample size calculation, Journal of the American Statistical Association, in press.

Examples

#set parameters
tau <- 0.5
theta_t <- c(-0.15,0.3,sqrt(1-(-0.15)^2-(0.3)^2))
beta <- c(1,1,1)
sigma <- 0.5
n <- 50
p <- 2

#generate data
x1 <- rbinom(n,size=1,prob=0.5)
x2 <- runif(n,min=-1,max=1)
X <- cbind(1,x1,x2)
a <- rbinom(n,1,prob=0.5)
y <- drop(X%*%beta) + tau*a*(drop(X%*%theta_t)>=0) + rnorm(n,0,sigma)

data <- data.frame(X[,2:3], a, y)

subgroup_detect(outcome = y~x1+x2,
                propen = a~x1+x2,
                data = data)