TY - JOUR

T1 - Nonparametric bounds for the causal effect in a binary instrumental variable model

AU - Palmer, Thomas Michael

AU - Ramsahai, Roland

AU - Didelez, Vanessa

AU - Sheehan, Nuala A.

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

KW - bpbounds

KW - bpboundsi

KW - average causal effect

KW - causal inference

KW - instrumental variables

KW - nonparametric bounds

M3 - Journal article

VL - 11

SP - 345

EP - 367

JO - Stata Journal

JF - Stata Journal

SN - 1536-867X

IS - 3

ER -