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Instrumental variable approaches for estimating causal effects in settings with multivariate outcomes

Wednesday 11 February 2015, 1.00PM to 2:00pm

Speaker(s): Richard Grieve, London School of Hygiene and Tropical Medicine


In randomised controlled trials (RCTs) that have non-compliance with the treatment assigned, policy makers require unbiased estimates of the causal effect of the treatment received. Instrumental variable (IV) approaches can provide estimates that can be interpreted as complier average causal effects (CACE). A concern for existing IV methods such as two-stage least squares (2SLS), is that they have not been extended to settings with multivariate outcomes.

We consider a three-stage least squares (3SLS) regression approach, whereby estimates from the first stage regression of treatment received conditional on assignment, feed into a seemingly unrelated regression (SUR) system of equations that recognise the correlation between the outcomes. However, 3SLS requires good asymptotic properties which may not be satisfied, when for example, the sample sizes are small and the outcome (e.g. cost) is non-normally distributed. We therefore also develop a Bayesian approach, which models jointly the effects of random assignment on treatment received, and the bivariate outcome. We compare these approaches to a 2SLS model applied to each outcome independently.  

We consider the relative performance of these methods in a simulation study, where costs are assumed to follow Normal or Gamma distributions, to have positive and negative correlation with health outcomes, the instrument is strong (30% non-compliance) or weak (70% non-compliance), and the sample size, moderate (n=1,000) or small (n=100). We find that the proposed IV methods generally perform well. For example in scenarios with Normally distributed cost data and a strong instrument, each method reports unbiased estimates. However, in these settings the 2SLS approach reports levels of Confidence Interval (CI) coverage that are above (positive correlation) and below (negative correlation) nominal levels. By contrast both the 3SLS and Bayesian methods report CI coverage close to nominal levels.

We illustrate these approaches in a reanalysis of published study, where about one third of patients randomised to surgery actually received medical management.


Location: ARRC Auditorium (A/RC014)

Admission: All welcome.