Nonparametric bounds for the causal effect in a binary instrumental-variable model
Tom M. Palmer
MRC Centre for Causal Analyses in Translational Epidemiology
School of Social and Community Medicine
University of Bristol, UK
[email protected]
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Roland R. Ramsahai
Statistical Laboratory
University of Cambridge, UK
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Vanessa Didelez
School of Mathematics
University of Bristol, UK
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Nuala A. Sheehan
Departments of Health Sciences and Genetics
University of Leicester, UK
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Abstract. Instrumental variables can be used to make inferences about causal
effects in the presence of unmeasured confounding. For a model in which the
instrument, intermediate/treatment, and outcome variables are all binary, Balke
and Pearl (1997, Journal of the American Statistical Association
92: 1172–1176)
derived nonparametric bounds for the intervention probabilities and the average
causal effect. We have implemented these bounds in two commands: bpbounds and
bpboundsi. We have also implemented several extensions to
these bounds. One
of these extensions applies when the instrument and outcome are measured in one
sample and the instrument and intermediate are measured in another sample. We
have also implemented the bounds for an instrument with three categories, as is
common in Mendelian randomization analyses in epidemiology and for the case
where a monotonic effect of the instrument on the intermediate can be assumed.
In each case, we calculate the instrumental-variable inequality constraints as a
check for gross violations of the instrumental-variable conditions. The use of the
commands is illustrated with a re-creation of the original Balke and Pearl analysis
and with a Mendelian randomization analysis. We also give a simulated example to
demonstrate that the instrumental-variable inequality constraints can both detect
and fail to detect violations of the instrumental-variable conditions.
View all articles by these authors:
Tom M. Palmer, Roland R. Ramsahai, Vanessa Didelez, Nuala A. Sheehan
View all articles with these keywords:
bpbounds, bpboundsi, average causal effect, causal inference, instrumental variables, nonparametric bounds
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