A large number of studies have highlighted the importance of gut microbiome composition in shaping fat deposition in mammals. Several studies have also highlighted how host genome controls the abundance of certain species that make up the gut microbiota. We propose a systematic approach to infer how the host genome can control the gut microbiome, which in turn contributes to the host phenotype determination. We implemented a mediation test that can be applied to measured and latent dependent variables to describe fat deposition in swine (Sus scrofa). In this study, we identify several host genomic features having a microbiome-mediated effects on fat deposition. This demonstrates how the host genome can affect the phenotypic trait by inducing a change in gut microbiome composition that leads to a change in the phenotype. Host genomic variants identified through our analysis are different than the ones detected in a traditional genome-wide association study. In addition, the use of latent dependent variables allows for the discovery of additional host genomic features that do not show a significant effect on the measured variables. Microbiome-mediated host genomic effects can help understand the genetic determination of fat deposition. Since their contribution to the overall genetic variance is usually not included in association studies, they can contribute to filling the missing heritability gap and provide further insights into the host genome - gut microbiome interplay. Further studies should focus on the portability of these effects to other populations as well as their preservation when pro-/pre-/anti-biotics are used (i.e. remediation).

Mendelian randomization (MR) analysis uses genotypes as instruments to estimate the causal effect of an exposure in the presence of unobserved confounders. The existing MR methods focus on the data generated from prospective cohort studies. We develop a procedure for studying binary outcomes under a case-control design. The proposed procedure is built upon two working models commonly used for MR analyses and adopts a quasi-empirical likelihood framework to address the ascertainment bias from case-control sampling. We derive various approaches for estimating the causal effect and hypothesis testing under the empirical likelihood framework. We conduct extensive simulation studies to evaluate the proposed methods. We find that the proposed empirical likelihood estimate is less biased than the existing estimates. Among all the approaches considered, the Lagrange multiplier (LM) test has the highest power, and the confidence intervals derived from the LM test have the most accurate coverage. We illustrate the use of our method in MR analysis of prostate cancer case-control data with vitamin D level as exposure and three single nucleotide polymorphisms as instruments.