How to find causal truth when you cannot run a controlled experiment

How to find causal truth when you cannot run a controlled experiment
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In short: In epidemiology, researchers often face a dilemma: they cannot randomly assign treatments to people. This leaves them with biased, observed data. But a clever statistical technique called Inverse Probability Weighting allows scientists to mathematically reconstruct what might have happened in a perfectly controlled world.

When studying health outcomes, researchers often deal with 'confounders'—common prior causes that influence both whether someone is exposed to a factor and whether they develop a disease. To find a true causal effect, one must account for these variables. While methods like restriction, matching, or regression adjustment exist, Inverse Probability Weighting (IPW) offers a unique approach by using weights to balance the study groups.

This method works by constructing a logistic regression model to calculate how likely a person is to undergo a particular exposure. By using this predicted probability as a weight in subsequent analyses, researchers can 'inflate' the importance of under-represented subjects. This is particularly useful when dealing with missing data or selection bias, such as loss-to-follow-up in a study. It allows for the estimation of quantities for a target population that differs from the one actually sampled, which is often necessary due to cost, time, or ethical constraints.

IPW is deeply rooted in the potential outcomes framework. The goal is to estimate 'counterfactuals'—the outcome that would have been observed if all subjects had been assigned a different treatment. By weighting observations by the inverse of their probability of receiving the observed treatment, the estimator can simulate a randomized trial. This technique is essential for constructing marginal structural models and can even be used to estimate the effect of exposure on the entire population, provided certain assumptions regarding 'doomed' and 'immune' individuals are met.

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