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

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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,…,k is equal to 1 if group i was randomized to strategy α_{1} and 0 if randomized to strategy α_{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

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

m.a1

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

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.

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

Author(s)

Joseph Rigdon jrigdon@bios.unc.edu

References

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

Examples

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#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)