interferenceCI (version 1.1)

exactCI: Exact confidence intervals for treatment effects on a binary outcome in a two-stage randomized experiment with interference

Description

Finds exact confidence intervals for treatment effects on a binary outcome in a two-stage randomized experiment with interference. See Section 4.2 of Rigdon and Hudgens (2014) for details.

Usage

exactCI(eff, g, data, m.a0, m.a1, B2, C2, level)

Arguments

eff

treatment effect of interest; either ``DEa0'', ``DEa1'', ``IE'', ``TE'', or ``OE''

g

1st stage of randomization vector where element $i=1,\ldots,k$ is equal to 1 if group $i$ was randomized to strategy $\alpha_{1}$ and 0 if randomized to strategy $\alpha_{0}$

data

$2 \times 2\times k$ array of $2 \times 2$ table data where row 1 is treatment=yes, row 2 is treatment=no, column 1 is outcome=yes, and column 2 is outcome=no

m.a0

$\alpha_{0}$ randomization vector where element $i=1,\ldots,k$ is equal to the number of subjects in group $i$ who would receive treatment if group $i$ was randomized to strategy $\alpha_{0}$

m.a1

$\alpha_{0}$ randomization vector where element $i=1,\ldots,k$ is equal to the number of subjects in group $i$ who would receive treatment if group $i$ was randomized to strategy $\alpha_{1}$

B2

number of sharp nulls to test in the targeted sampling algorithm

C2

number of re-randomizations (experiments) to conduct in computing the null distribution of the estimator

level

significance level of hypothesis tests, i.e., method yields a 1-level confidence interval

Value

B1

total number of hypotheses that could be tested

C1

total number of re-randomizations (experiments) that could be performed

frac.NA

fraction of hypothesized sharp nulls that are not tested

prob1

final value of targeting parameter $q_{p_{l}}$ in finding lower confidence limit

prob2

final value of targeting parameter $q_{p_{u}}$ in finding upper confidence limit

effect

vector of sharp null hypotheses

p

vector of p-values corresponding to the sharp null hypotheses

lower

lower limit to confidence interval

upper

upper limit to confidence interval

Details

See Section 4.2 of Rigdon and Hudgens (2014) for detailed description. Please plot the p-values against the effect as a check of targeted sampling algorithm performance.

References

Rigdon, J. and Hudgens, M.G. ``Exact confidence intervals in the presence of interference.'' Submitted to Statistics and Probability Letters 2014.

Examples

#Made up example with 10 groups of 10 where half are randomized to a0 and half to a1
#a0 is assign 3 of 10 to treatment and half to a1 is assign 6 of 10 to treatment
d = c(1,1,5,3,0,6,3,1,0,4,3,3,0,5,3,2,1,1,5,3,2,2,4,2,1,5,2,2,2,3,4,1,1,1,5,3,1,5,2,2)
data.ex = array(d,c(2,2,10))
assign.ex = c(1,0,0,0,1,1,0,1,1,0)

#Inference for overall effect
l1 = exactCI('OE',assign.ex,data.ex,rep(3,10),rep(6,10),100,100,0.05)

#Check algorithm using a plot
plot(l1$effect,l1$p)