Nonparametric Bounds for the Causal Effect in a Binary Instrumental-Variable Model

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 recreation 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.

Bayesian Modelling for Binary Outcomes in the Regression Discontinuity Design

“…These indicated that for our data it was possible to find unique solutions to the MSMM and LSMM moment conditions. The Balke–Pearl bounds (Balke and Pearl, ; Palmer et al ., ) were also in line with our results.…”

Lee (2009) Treatment-Effect Bounds for Nonrandom Sample Selection

“…In addition to calculating point estimates for the bounds, the command accommodates the calculation of confidence intervals for the treatment effect and tightened bounds on the basis of covariates. leebounds complements the contributions of Beresteanu and Manski (2000) and Palmer et al (2011), who have made other bounds estimators available to Stata users that, unlike Lee's estimator, deal with selection into treatment and imperfect compliance with a randomly assigned treatment.…”

“…These alternative bounds impose more structure on the assumed selection mechanism and allow for outcome variables with unbounded support while often yielding more narrow bounds. Thereby, leebounds complements the contributions of Beresteanu and Manski (2000) and Palmer et al (2011), who have already made other bounds estimators available to Stata users. Beresteanu and Manski (2000) provide Stata code for the bounds estimators introduced by Manski (1990) and add further refinements (Manski 1994(Manski , 1995(Manski , 1997Manski and Pepper 2000) to the original approach.…”

Epidemiology, genetic epidemiology and Mendelian randomisation: more need than ever to attend to detail

“…The interpretation of the bounds is that the data are compatible with values of a causal effect anywhere between the lower and upper bound. We do not go into technical details here as these are provided elsewhere (Manski 1990; Balke and Pearl 1994;Palmer et al 2011a).…”

“…Returning to the example above ("Testing for a causal effect by testing for a G-Y association"), we consider bounding the causal effect of dichotomised homocysteine level (low/high) on presence or absence of cardiovascular disease (CVD) using the MTHFR genotype (now with all three levels) as an IV (Palmer et al 2011a). Since the data come from a case-control study, the analysis is performed by converting back to the required population frequencies under plausible assumptions about the prevalence of CVD (Didelez and Sheehan 2007b).…”