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

In SimpleTable: 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

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 φ where phi_k = Pr(W=k) for k=0, ..., K-1. The kth element of Wpriorvector corresponds to the kth element of W.

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.

Value

An object of class SimpleTable.

Author(s)

Kevin M. Quinn

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)

SimpleTable documentation built on May 2, 2019, 10:21 a.m.