Causal bounds and instruments

Instrumental variables have proven useful, in particular within the social sciences and economics, for making inference about the causal effect of a random variable, B, on another random variable, C, in the presence of unobserved confounders. In the case where relationships are linear, causal effects can be identified exactly from studying the regression of C on A and the regression of B on A, where A is the instrument. In the more general case, bounds have been developed in the literature for the causal effect of B on C, given observational data on the joint distribution of C, B, and A. Using an approach based on the analysis of convex polytopes, we develop bounds for the same causal effect when given data on (C, A) and (B, A) only. The bounds developed are thus in direct analogy to the standard use of instruments in econometrics, but we make no assumption of linearity. Use of the bounds is illustrated for experiments with partial compliance. The bounds are, for example, relevant in genetic epidemiology, where the 'Mendelian instrument' S represents a genotype, and where joint data on all of C, B, and A may rarely be available but studies involving pairs of these may be abundant. Other examples of bounding causal effects are considered to show that the method applies to DAGs in general, subject to certain conditions

Causal bounds and instruments

Instrumental variables have proven useful, in particular within the social sciences and economics, for making inference about the causal effect of a random variable, B, on another random variable, C, in the presence of unobserved confounders. In the case where relationships are linear, causal effects can be identified exactly from studying the regression of C on A and the regression of B on A, where A is the instrument. In the more general case, bounds have been developed in the literature for the causal effect of B on C, given observational data on the joint distribution of C, B, and A. Using an approach based on the analysis of convex polytopes, we develop bounds for the same causal effect when given data on (C, A) and (B, A) only. The bounds developed are thus in direct analogy to the standard use of instruments in econometrics, but we make no assumption of linearity. Use of the bounds is illustrated for experiments with partial compliance. The bounds are, for example, relevant in genetic epidemiology, where the 'Mendelian instrument' S represents a genotype, and where joint data on all of C, B, and A may rarely be available but studies involving pairs of these may be abundant. Other examples of bounding causal effects are considered to show that the method applies to DAGs in general, subject to certain conditions.Citation: Ramsahai, R. R. (2007) Causal bounds and instruments. In: Proceedings of the 23rd Conference on Uncertainty in Artificial Intelligence, July 19-22 2007, Vancouver, BC, Canada. AUAI Press. pp. 310-317

Extending iterative matching methods: an approach to improving covariate balance that allows prioritisation

Comparative effectiveness studies can identify the causal effect of treatment if treatment is unconfounded with outcome conditional on a set of measured covariates. Matching aims to ensure that the covariate distributions are similar between treatment and control groups in the matched samples, and this should be done iteratively by checking and improving balance. However, an outstanding concern facing matching methods is how to prioritise competing improvements in balance across different covariates. We address this concern by developing a ‘loss function’ that an iterative matching method can minimise. Our ‘loss function’ is a transparent summary of covariate imbalance in a matched sample and follows general recommendations in prioritising balance amongst covariates. We illustrate this approach by extending Genetic Matching (GM), an automated approach to balance checking. We use the method to reanalyse a high profile comparative effectiveness study of right heart catheterisation. We find that our loss function improves covariate balance compared to a standard GM approach, and to matching on the published propensity score

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

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