Bayesian methods for meta-analysis of causal relationships estimated using genetic instrumental variables

Genetic markers can be used as instrumental variables, in an analogous way to randomization in a clinical trial, to estimate the causal relationship between a phenotype and an outcome variable. Our purpose is to extend the existing methods for such Mendelian randomization studies to the context of multiple genetic markers measured in multiple studies, based on the analysis of individual participant data. First, for a single genetic marker in one study, we show that the usual ratio of coefficients approach can be reformulated as a regression with heterogeneous error in the explanatory variable. This can be implemented using a Bayesian approach, which is next extended to include multiple genetic markers. We then propose a hierarchical model for undertaking a meta-analysis of multiple studies, in which it is not necessary that the same genetic markers are measured in each study. This provides an overall estimate of the causal relationship between the phenotype and the outcome, and an assessment of its heterogeneity across studies. As an example, we estimate the causal relationship of blood concentrations of C-reactive protein on fibrinogen levels using data from 11 studies. These methods provide a flexible framework for efficient estimation of causal relationships derived from multiple studies. Issues discussed include weak instrument bias, analysis of binary outcome data such as disease risk, missing genetic data, and the use of haplotypes.

Effect of nitrogen fertilization on the growth of Sporobolomyces roseus on wheat leaves

Green flag leaves of spring wheat grown with low or high nitrogen supply in the form of Ca(NO3)2 were inoculated with Sporobolomyces roseus. Growth of the yeast in a controlled environment was followed for several days by culturing techniques. No consistent differences were found between the development of S. roseus on leaves from low or high nitrogen treated plants, suggesting that leaf exudates from low nitrogen treated plants still contain enough nitrogen compounds to support growth of S. roseus. Nitrogen fertilization obviously seems not to be an appropriate means to manipulate the phyllosphere mycoflora.