A latent outcome variable approach for Mendelian randomization using the stochastic expectation maximization algorithm.

Mendelian randomization (MR) is a widely used tool to uncover causal relationships between exposures and outcomes. However, existing MR methods can suffer from inflated type I error rates and biased causal effects in the presence of invalid instruments. Our proposed method enhances MR analysis by augmenting latent phenotypes of the outcome, explicitly disentangling horizontal and vertical pleiotropy effects. This allows for explicit assessment of the exclusion restriction assumption and iteratively refines causal estimates through the expectation-maximization algorithm. This approach offers a unique and potentially more precise framework compared to existing MR methods. We rigorously evaluate our method against established MR approaches across diverse simulation scenarios, including balanced and directional pleiotropy, as well as violations of the Instrument Strength Independent of Direct Effect (InSIDE) assumption. Our findings consistently demonstrate superior performance of our method in terms of controlling type I error rates, bias, and robustness to genetic confounding, regardless of whether individual-level or summary data is used. Additionally, our method facilitates testing for directional horizontal pleiotropy and outperforms MR-Egger in this regard, while also effectively testing for violations of the InSIDE assumption. We apply our method to real data, demonstrating its effectiveness compared to traditional MR methods. This analysis reveals the causal effects of body mass index (BMI) on metabolic syndrome (MetS) and a composite MetS score calculated by the weighted sum of its component factors. While the causal relationship is consistent across most methods, our proposed method shows fewer violations of the exclusion restriction assumption, especially for MetS scores where horizontal pleiotropy persists and other methods suffer from inflation.