Large sample confidence intervals for treatment effects on a binary outcome in a two-stage randomized experiment with interference

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Description

Computes the large sample confidence intervals of Liu and Hudgens (2014) for treatment effects on a binary outcome in a two-stage randomized experiment with interference

Usage

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HH(eff, g, data, m.a0, m.a1, 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_{1} 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}

level

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

Value

est

estimated treatment effect

v

estimated variance

lower.w

lower limit to Wald confidence interval

upper.w

upper limit to Wald confidence interval

lower.ch

lower limit to Chebyshev confidence interval

upper.ch

upper limit to Chebyshev confidence interval

Author(s)

Joseph Rigdon jrigdon@bios.unc.edu

References

Hudgens, M.G. and Halloran, M.E. “Toward causal inference with interference.” Journal of the American Statistical Association 2008 103:832-842.

Liu, L. and Hudgens, M.G. “Large sample randomization inference of causal effects in the presence of interference.” Journal of the American Statistical Association 2014 109:288-301.

Examples

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#Table 3 from Hudgens and Halloran (2008) 
hh = array(c(16,18,12541-16,12541-18,26,54,11513-26,11513-54,17,119,10772-17,
     25134-119,22,122,8883-22,20727-122,15,92,5627-15,13130-92),c(2,2,5))
e1 = HH('OE',c(1,1,0,0,0),hh,round(0.3*c(25082,23026,35906,29610,18757),0),
     round(0.5*c(25082,23026,35906,29610,18757),0),0.05)
round(1000*e1$est,3)
round(1000000*e1$v,3)