Solar disinfection of water (a case study from Kenya)

Solar disinfection of water (a case study from Kenya

Solar disinfection of water (a case study from Kenya)

Solar disinfection of water (a case study from Kenya

Additional file 1 of Causal role of high body mass index in multiple chronic diseases: a systematic review and meta-analysis of Mendelian randomization studies

Additional file 1: Tables S1-S2. Table S1 – Study quality assessment. Table S2 – Mendelian randomization studies included in the meta-analyses of genetically predicted body mass index in relation to diabetes mellitus, diseases of the circulatory, respiratory, digestive, musculoskeletal, and nervous systems, and neoplasms

Additional file 1: of Serum magnesium levels and risk of coronary artery disease: Mendelian randomisation study

Table S1. Association of genetically predicted 0.1-mmol/L increase in serum magnesium with coronary artery disease in inverse-variance weighted and sensitivity analyses. Table S2. Genes located in or near the loci for serum magnesium and their biological roles. (DOCX 56 kb

A Guide for Selection of Genetic Instruments in Mendelian randomisation (MR) studies of Type-2 diabetes and HbA1c: towards an integrated approach

This study examines the instrument selection strategies currently employed throughout the type-2 diabetes and HbA1c MR literature. We then argue for a more integrated and thorough approach, providing a framework to do this in the context of HbA1c and diabetes. We conducted a literature search for Mendelian randomisation studies that have instrumented diabetes and/or HbA1c. We also used data from the UK Biobank (N=349,326) to calculate instrument strength metrics that are key in MR studies (the F-statistic for average strength and R2 for total strength) with two different methods (‘Individual-level data regression’ and Cragg-Donald formula). We used a 157-SNP instrument for diabetes and a 51-SNP instrument (as well as partitioned into glycaemic and erythrocytic) for HbA1c. Our literature search yielded 48 studies for diabetes and 22 for HbA1c. Our UKB empirical examples showed that irrespective of, the method used to calculate metrics of strength and whether the instrument was the main one or was partitioned by function, the HbA1c genetic instrument is strong in terms of both average and total strength. For diabetes, a 157-SNP instrument was shown to have good average and total strength, but these were both substantially smaller than those of the HbA1c instrument. We provide a careful set of five recommendations to researchers who wish to genetically instrument type-2 diabetes and/or HbA1c. MR studies of glycaemia should take a more integrated approach when selecting genetic instruments and we give specific guidance on how to do this. </p

Results of the doubly-ranked method and residual method for model D (coarsened exposures) with three different causal relationship between the exposure and the outcome (denoted by D1, D2, D3).

Boxplot results represent the LACE estimates within the 10 strata. Red points represent the target causal effects within strata. Box indicates lower quartile, median, and upper quartile; error bars represent the minimal and maximal data point falling in the 1.5 interquartile range distance from the lower/upper quartile; estimates outside this range are plotted separately.</p

Results of the doubly-ranked method and residual method for model A (linearity and homogeneity) with three different causal relationship between the exposure and the outcome (denoted by A1, A2, A3).

Boxplot results represent the LACE estimates within the 10 strata. Red points represent the target causal effects within strata. Box indicates lower quartile, median, and upper quartile; error bars represent the minimal and maximal data point falling in the 1.5 interquartile range distance from the lower/upper quartile; estimates outside this range are plotted separately.</p

Comparison of the stratification and PolyMR methods: Proportion of datasets in which the null hypothesis of homogeneity of stratum-specific estimates (for stratification methods) or linearity (for PolyMR) was rejected at a 5% significance level in various scenarios with a null causal effect (scenarios A1, B1, C1, D1, and A1+U3; proportion represents empirical Type I error rate) and with a quadratic causal effect (scenarios A2, B2, C2, D2, and A2+U3; proportion represents empirical power).

Note that scenarios A1+U3 and A2+U3 are equivalent to scenarios A1 and A2, except that the confounder effect on the outcome is non-linear (see Text B in S1 Text for details).</p

Diagram illustrating the rank preserving assumption for a dichotomous instrumental variable <i>Z</i> ∈ {0, 1} with counterfactual exposure distributions <i>X</i>(0) (the black group) and <i>X</i>(1) (the blue group).

The dashed arrow represents the one-to-one mapping from the counterfactual exposure value with Z = 0 to the counterfactual covariate value with Z = 1.</p

Supplementary materials.

Non-linear Mendelian randomization is an extension to standard Mendelian randomization to explore the shape of the causal relationship between an exposure and outcome using an instrumental variable. A stratification approach to non-linear Mendelian randomization divides the population into strata and calculates separate instrumental variable estimates in each stratum. However, the standard implementation of stratification, referred to as the residual method, relies on strong parametric assumptions of linearity and homogeneity between the instrument and the exposure to form the strata. If these stratification assumptions are violated, the instrumental variable assumptions may be violated in the strata even if they are satisfied in the population, resulting in misleading estimates. We propose a new stratification method, referred to as the doubly-ranked method, that does not require strict parametric assumptions to create strata with different average levels of the exposure such that the instrumental variable assumptions are satisfied within the strata. Our simulation study indicates that the doubly-ranked method can obtain unbiased stratum-specific estimates and appropriate coverage rates even when the effect of the instrument on the exposure is non-linear or heterogeneous. Moreover, it can also provide unbiased estimates when the exposure is coarsened (that is, rounded, binned into categories, or truncated), a scenario that is common in applied practice and leads to substantial bias in the residual method. We applied the proposed doubly-ranked method to investigate the effect of alcohol intake on systolic blood pressure, and found evidence of a positive effect of alcohol intake, particularly at higher levels of alcohol consumption.</div