SimpleTable (version 0.1-2)

analyze2x2: Analyze 2 x 2 Table in the Presence of Unmeasured Confounding

Description

analyze2x2 performs a causal Bayesian analysis of a 2 x 2 table in which it is assumed that unmeasured confounding is present. The binary treatment variable is denoted $X = 0$ (control), $1$ (treatment); and the binary outcome variable is denoted $Y = 0$ (failure), $1$ (success). The notation and terminology are from Quinn (2008).

Usage

analyze2x2(C00, C01, C10, C11, a00, a01, a10, a11,  b00, b01, b10, b11, c00, c01, c10, c11, nsamp = 50000)

Arguments

C00

The number of observations in $(X=0, Y=0)$ cell of the table. In other words, the number of observations that received control and failed.

C01

The number of observations in $(X=0, Y=1)$ cell of the table. In other words, the number of observations that received control and succeeded.

C10

The number of observations in $(X=1, Y=0)$ cell of the table. In other words, the number of observations that received treatment and failed.

C11

The number of observations in $(X=1, Y=1)$ cell of the table. In other words, the number of observations that received treatment and succeeded.

a00

One of four parameters (with a01, a10, and a11 governing the Dirichlet prior for $theta$ (the joint probabilities of $X$ and $Y$). This prior has the effect of adding a00 - 1 observations to the $(X=0, Y=0)$ cell of the table.

a01

One of four parameters (with a00, a10, and a11 governing the Dirichlet prior for $theta$ (the joint probabilities of $X$ and $Y$). This prior has the effect of adding a01 - 1 observations to the $(X=0, Y=1)$ cell of the table.

a10

One of four parameters (with a00, a01, and a11 governing the Dirichlet prior for $theta$ (the joint probabilities of $X$ and $Y$). This prior has the effect of adding a10 - 1 observations to the $(X=1, Y=0)$ cell of the table.

a11

One of four parameters (with a00, a01, and a10 governing the Dirichlet prior for $theta$ (the joint probabilities of $X$ and $Y$). This prior has the effect of adding a11 - 1 observations to the $(X=1, Y=1)$ cell of the table.

b00

One of two parameters (with c00) governing the beta prior for the distribution of potential outcome types within the $(X=0, Y=0)$ cell of the table. This prior adds the same information as would be gained from observing b00 - 1 Helped units in the $(X=0, Y=0)$ cell of the table.

b01

One of two parameters (with c01) governing the beta prior for the distribution of potential outcome types within the $(X=0, Y=1)$ cell of the table. This prior adds the same information as would be gained from observing b01 - 1 Always Succeed units in the $(X=0, Y=1)$ cell of the table.

b10

One of two parameters (with c10) governing the beta prior for the distribution of potential outcome types within the $(X=1, Y=0)$ cell of the table. This prior adds the same information as would be gained from observing b10 - 1 Hurt units in the $(X=1, Y=0)$ cell of the table.

b11

One of two parameters (with c11) governing the beta prior for the distribution of potential outcome types within the $(X=1, Y=1)$ cell of the table. This prior adds the same information as would be gained from observing b11 - 1 Always Succeed units in the $(X=1, Y=1)$ cell of the table.

c00

One of two parameters (with b00) governing the beta prior for the distribution of potential outcome types within the $(X=0, Y=0)$ cell of the table. This prior adds the same information as would be gained from observing b00 - 1 Never Succeed units in the $(X=0, Y=0)$ cell of the table.

c01

One of two parameters (with b01) governing the beta prior for the distribution of potential outcome types within the $(X=0, Y=1)$ cell of the table. This prior adds the same information as would be gained from observing c01 - 1 Hurt units in the $(X=0, Y=1)$ cell of the table.

c10

One of two parameters (with b10) governing the beta prior for the distribution of potential outcome types within the $(X=1, Y=0)$ cell of the table. This prior adds the same information as would be gained from observing c10 - 1 Never Succeed units in the $(X=1, Y=0)$ cell of the table.

c11

One of two parameters (with b11) governing the beta prior for the distribution of potential outcome types within the $(X=1, Y=1)$ cell of the table. This prior adds the same information as would be gained from observing b11 - 1 Helped units in the $(X=1, Y=1)$ cell of the table.

nsamp

Size of the Monte Carlo sample used to summarize the posterior.

Value

An object of class SimpleTable.

Details

analyze2x2 performs the Bayesian analysis of a 2 x 2 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, analyze2x2xK, 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.)
# ##
# ##        Y=0       Y=1
# ## X=0    19        143
# ## X=1    114       473
# ##
# 
# ## uniform prior on the potential outcome distributions
# S.unif <- analyze2x2(C00=19, C01=143, C10=114, C11=473, 
#                      a00=.25, a01=.25, a10=.25, a11=.25,
#                      b00=1, c00=1, b01=1, c01=1, 
#                      b10=1, c10=1, b11=1, c11=1)
# 
# summary(S.unif)
# plot(S.unif)
# 
# 
# ## a prior belief in an essentially negative monotonic treatment effect 
# S.mono <- analyze2x2(C00=19, C01=143, C10=114, C11=473, 
#                      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)
# 
# summary(S.mono)
# plot(S.mono)
# ## End(Not run)