How can you estimate causal effects in observational studies?

2 Matching and propensity score

One method to estimate causal effects in observational studies is to match units that have similar characteristics, except for the treatment level. This way, you can reduce the imbalance between the treated and control groups and create a more comparable sample. One common technique to perform matching is to use the propensity score, which is the probability of receiving the treatment given the observed covariates. You can estimate the propensity score using machine learning methods, such as logistic regression, decision trees, or neural networks. Then, you can match units based on their propensity scores, using different algorithms, such as nearest neighbor, caliper, or optimal matching.

4 Doubly robust methods

A third method to estimate causal effects in observational studies is to use doubly robust methods, which combine inverse probability weighting and regression. The advantage of these methods is that they can provide consistent estimates of the causal effect even if one of the models (the propensity score model or the outcome model) is misspecified, as long as the other model is correct. This makes them more robust to model selection and specification errors. One example of a doubly robust method is the augmented inverse probability weighting estimator, which uses the weighted outcome model to adjust for the residual bias after weighting.

5 Sensitivity analysis

A final step to estimate causal effects in observational studies is to perform sensitivity analysis, which assesses how robust the estimates are to potential violations of the assumptions. One of the key assumptions of causal inference is the ignorability assumption, which states that the treatment assignment is independent of the potential outcomes, conditional on the observed covariates. However, this assumption is often untestable and may be violated by the presence of unmeasured confounders, which are variables that affect both the treatment and the outcome. Sensitivity analysis can help you quantify how much the unmeasured confounders would have to influence the treatment assignment and the outcome to change the estimated causal effect. This can help you gauge the credibility and validity of your estimates.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?