SimpleTable (version 0.1-2)

analyze2x2xK: Analyze 2 x 2 x K Table in the Presence of Unmeasured Confounding

Description

analyze2x2xK performs a causal Bayesian analysis of a 2 x 2 x K table in which it is assumed that unmeasured confounding is present. The binary treatment variable is denoted $X = 0$ (control), $1$ (treatment); the binary outcome variable is denoted $Y = 0$ (failure), $1$ (success); and the categorical measured confounder is denoted $W=0, ..., K-1$. The notation and terminology are from Quinn (2008).

Usage

analyze2x2xK(SimpleTableList, Wpriorvector)

Arguments

SimpleTableList

A list of $K$ SimpleTable objects formed by using analyze2x2 to analyze the $K$ conditional $(X,Y)$ tables given each level of the measured confounder $W$.

Wpriorvector

$K$-vector giving the parameters of the Dirichlet prior for $\phi$ where $phi_k = Pr(W=k)$ for $k=0, ..., K-1$. The $k$th element of Wpriorvector corresponds to the $k$th element of $W$.

Value

An object of class SimpleTable.

Details

analyze2x2xK performs the Bayesian analysis of a 2 x 2 x K table described in Quinn (2008). summary and plot methods can be used to examine the output.

References

Quinn, Kevin M. 2008. ``What Can Be Learned from a Simple Table: Bayesian Inference and Sensitivity Analysis for Causal Effects from 2 x 2 and 2 x 2 x K Tables in the Presence of Unmeasured Confounding.'' Working Paper.

See Also

ConfoundingPlot, analyze2x2, ElicitPsi, summary.SimpleTable, plot.SimpleTable

Examples

## Not run: 
# ## Example from Quinn (2008)
# ## (original data from Oliver and Wolfinger. 1999. 
# ##   ``Jury Aversion and Voter Registration.'' 
# ##     American Political Science Review. 93: 147-152.)
# ##
# ##
# ##             W=0
# ##          Y=0   Y=1
# ##  X=0      1     21
# ##  X=1     10     93
# ##
# ##
# ##             W=1
# ##          Y=0   Y=1
# ##  X=0      5     32
# ##  X=1     27     92
# ##
# ##
# ##             W=2
# ##          Y=0   Y=1
# ##  X=0      4     44
# ##  X=1     52    186
# ##
# ##
# ##             W=3
# ##          Y=0   Y=1
# ##  X=0      7     20
# ##  X=1     19     47
# ##
# ##
# ##             W=4
# ##          Y=0   Y=1
# ##  X=0      2     26
# ##  X=1      6     55
# ##
# 
# 
# ## a prior belief in an essentially negative monotonic treatment effect 
# ## with the largest effects among those for whom W <= 2
# 
# S.mono.0 <- analyze2x2(C00=1, C01=21, C10=10, C11=93, 
#                        a00=.25, a01=.25, a10=.25, a11=.25,
#                        b00=0.02, c00=10, b01=25, c01=3, 
#                        b10=3, c10=25, b11=10, c11=0.02)
# 
# S.mono.1 <- analyze2x2(C00=5, C01=32, C10=27, C11=92, 
#                        a00=.25, a01=.25, a10=.25, a11=.25,
#                        b00=0.02, c00=10, b01=25, c01=3, 
#                        b10=3, c10=25, b11=10, c11=0.02)
# 
# S.mono.2 <- analyze2x2(C00=4, C01=44, C10=52, C11=186, 
#                        a00=.25, a01=.25, a10=.25, a11=.25,
#                        b00=0.02, c00=10, b01=25, c01=3, 
#                        b10=3, c10=25, b11=10, c11=0.02)
# 
# S.mono.3 <- analyze2x2(C00=7, C01=20, C10=19, C11=47, 
#                        a00=.25, a01=.25, a10=.25, a11=.25,
#                        b00=0.02, c00=10, b01=15, c01=1, 
#                        b10=1, c10=15, b11=10, c11=0.02)
# 
# S.mono.4 <- analyze2x2(C00=2, C01=26, C10=6, C11=55, 
#                        a00=.25, a01=.25, a10=.25, a11=.25,
#                        b00=0.02, c00=10, b01=15, c01=1, 
#                        b10=1, c10=15, b11=10, c11=0.02)
# 
# S.mono.all <- analyze2x2xK(list(S.mono.0, S.mono.1, S.mono.2, 
# 	                        S.mono.3, S.mono.4), 
#                            c(0.2, 0.2, 0.2, 0.2, 0.2))
# 
# summary(S.mono.all)
# plot(S.mono.all)
# 
# ## End(Not run)