interferenceCI (version 1.1)

TV: Conservative exact confidence intervals for treatment effects on a binary outcome in a two-stage randomized experiment with interference

Description

Computes the conservative exact confidence intervals of Tchetgen Tchetgen and VanderWeele (2012) for treatment effects on a binary outcome in a two-stage randomized experiment with interference

Usage

TV(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 $i=1,\ldots,k$ 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

$\alpha_{1}$ 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 $\alpha_{1}$

level

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

Value

est

estimated treatment effect from Hudgens and Halloran (2008)

v

half-width of confidence interval

lower

lower limit of confidence interval

upper

upper limit of confidence interval

Details

Confidence intervals are based on a Hoeffding-type exponential inequality; see section 4.3.2 of Tchetgen Tchetgen and VanderWeele (2012)

References

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

Tchetgen Tchetgen, E. and VanderWeele, T.J. ``On causal inference in the presence of interference.'' Statistical Methods in Medical Research 2012 21:55-75.

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
TV('OE',assign.ex,data.ex,rep(3,10),rep(6,10),0.05)