# The role of the geometric mean in case-control studies

arXiv: https://arxiv.org/abs/2207.09016 · HTML: https://mlsanity.com/paper/2207.09016/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 45 references that are in the map.
- First posted on arXiv 19 Jul 2022.

## Builds on (most cited first, 4 of 4)

- [Semiparametric doubly robust targeted double machine learning: a review](https://mlsanity.com/paper/2203.06469/) (2022)
- [Semiparametric counterfactual density estimation](https://mlsanity.com/paper/2102.12034/) (2021)
- [Sharp instruments for classifying compliers and generalizing causal effects](https://mlsanity.com/paper/1801.03635/) (2018)
- [Causal Inference under Outcome-Based Sampling with Monotonicity Assumptions](https://mlsanity.com/paper/2004.08318/) (2020)

## Built on by (most cited first, 1 of 1)

- [A Double Machine Learning Approach for the Evaluation of COVID-19 Vaccine Effectiveness under the Test-Negative Design: Analysis of Qu'ebec Administrative Data](https://mlsanity.com/paper/2310.04578/) (2023)

## Abstract (arXiv)

Historically used in settings where the outcome is rare or data collection is expensive, outcome-dependent sampling is relevant to many modern settings where data is readily available for a biased sample of the target population, such as public administrative data. Under outcome-dependent sampling, common effect measures such as the average risk difference and the average risk ratio are not identified, but the conditional odds ratio is. Aggregation of the conditional odds ratio is challenging since summary measures are generally not identified. Furthermore, the marginal odds ratio can be larger (or smaller) than all conditional odds ratios. This so-called non-collapsibility of the odds ratio is avoidable if we use an alternative aggregation to the standard arithmetic mean. We provide a new definition of collapsibility that makes this choice of aggregation method explicit, and we demonstrate that the odds ratio is collapsible under geometric aggregation. We describe how to partially identify, estimate, and do inference on the geometric odds ratio under outcome-dependent sampling. Our proposed estimator is based on the efficient influence function and therefore has doubly robust-style properties.