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Identifying the odds ratio estimated by a two-stage instrumental variable analysis with a logistic regression model
1Department of Public Health and Primary Care, Strangeways Research Laboratory, Wort's Causeway, Cambridge, CB1 8RN, U.K.
Statistics in Medicine
|June 5, 2013
Summary
Instrumental variable methods provide a consistent estimate of causal effects, even with confounding. The ratio or two-stage instrumental variable estimate calculates a relevant odds ratio for population risk factor distributions, particularly useful in Mendelian randomization studies.
Area of Science:
- Epidemiology
- Biostatistics
- Genetic Epidemiology
Background:
- Adjusting for uncorrelated covariates in logistic regression alters odds ratios.
- Odds ratios are influenced by the risk factor's distribution, not just unit increases.
- Instrumental variables (IV) offer a method to estimate causal effects despite confounding.
Purpose of the Study:
- To demonstrate that ratio or two-stage IV estimates consistently estimate a specific type of odds ratio.
- To clarify the interpretation of IV-estimated odds ratios in logistic regression models.
- To highlight the relevance of IV estimates for epidemiologists and policymakers, especially in Mendelian randomization.
Main Methods:
- Utilized logistic regression with an instrumental variable approach.
- Derived the formula for the IV-estimated odds ratio, defining it in relation to population risk factor distributions.
- Analyzed the behavior of the IV estimate when the instrument explains a small proportion of variance in the risk factor.
Main Results:
- The ratio or two-stage IV estimate is consistent for an odds ratio reflecting population-level changes in a risk factor.
- This IV-estimated odds ratio is conditional on the instrument but marginal across other covariates and averaged over the risk factor distribution.
- When the instrument's explanatory power is low, the IV estimate approximates the odds ratio from an unadjusted randomized controlled trial (RCT).
Conclusions:
- The ratio or two-stage IV method is not biased but estimates a different, arguably more relevant, odds ratio than adjusted regression models.
- This IV-derived odds ratio is particularly valuable for understanding population-level effects and in genetic epidemiology contexts like Mendelian randomization.
- The findings clarify the interpretation and utility of IV methods in causal inference for observational and genetic studies.
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