Estimating structural mean models with multiple instrumental variables using the generalised method of moments

Instrumental variables analysis using genetic markers as instruments is now a widely used technique in epidemiology and biostatistics. As single markers tend to explain only a small proportion of phenotypical variation, there is increasing interest in using multiple genetic markers to obtain more precise estimates of causal parameters. Structural mean models (SMMs) are semi-parametric models that use instrumental variables to identify causal parameters, but there has been little work on using these models with multiple instruments, particularly for multiplicative and logistic SMMs. In this paper, we show how additive, multiplicative and logistic SMMs with multiple discrete instrumental variables can be estimated efficiently using the generalised method of moments (GMM) estimator, how the Hansen J-test can be used to test for model mis-specification, and how standard GMM software routines can be used to fit SMMs. We further show that multiplicative SMMs, like the additive SMM, identify a weighted average of local causal effects if selection is monotonic. We use these methods to reanalyse a study of the relationship between adiposity and hypertension using SMMs with two genetic markers as instruments for adiposity. We find strong effects of adiposity on hypertension, but no evidence of unobserved confounding.

Estimating Structural Mean Models with Multiple Instrumental Variables using the Generalised Method of Moments

Instrumental variables analysis using genetic markers as instruments is now a widely used technique in epidemiology and biostatistics. As single markers tend to explain only a small proportion of phenotypical variation, there is increasing interest in using multiple genetic markers to obtain more precise estimates of causal parameters. Structural mean models (SMMs) are semi-parametric models that use instrumental variables to identify causal parameters, but there has been little work on using these models with multiple instruments, particularly for multiplicative and logistic SMMs. In this paper, we show how additive, multiplicative and logistic SMMs with multiple discrete instrumental variables can be estimated efficiently using the generalised method of moments (GMM) estimator, how the Hansen J-test can be used to test for model mis-specification, and how standard GMM software routines can be used to fit SMMs. We further show that multiplicative SMMs, like the additive SMM, identify a weighted average of local causal effects if selection is monotonic. We use these methods to reanalyse a study of the relationship between adiposity and hypertension using SMMs with two genetic markers as instruments for adiposity. We find strong effects of adiposity on hypertension, but no evidence of unobserved confounding.Structural Mean Models, Multiple Instrumental Variables, Generalised Method of Moments, Mendelian Randomisation, Local Average Treatment Effects

Estimating Structural Mean Models with Multiple Instrumental Variables Using the Generalised Method of Moments

Instrumental variables analysis using genetic markers as instruments is now a widely used technique in epidemiology and biostatistics. As single markers tend to explain only a small proportion of phenotypic variation, there is increasing interest in using multiple genetic markers to obtain more precise estimates of causal parameters. Structural mean models (SMMs) are semiparametric models that use instrumental variables to identify causal parameters. Recently, interest has started to focus on using these models with multiple instruments, particularly for multiplicative and logistic SMMs. In this paper we show how additive, multiplicative and logistic SMMs with multiple orthogonal binary instrumental variables can be estimated efficiently in models with no further (continuous) covariates, using the generalised method of moments (GMM) estimator. We discuss how the Hansen J-test can be used to test for model misspecification, and how standard GMM software routines can be used to fit SMMs. We further show that multiplicative SMMs, like the additive SMM, identify a weighted average of local causal effects if selection is monotonic. We use these methods to reanalyse a study of the relationship between adiposity and hypertension using SMMs with two genetic markers as instruments for adiposity. We find strong effects of adiposity on hypertension

Contributions to 21st century projections of extreme sea-level change around the UK

We provide a synthesis of results of a recent government-funded initiative to make projections of 21st century change in extreme sea levels around the coast of the United Kingdom. We compare four factors that influence future coastal flood risk: (i) time-mean sea-level (MSL) rise; (ii) changes in storm surge activity; (iii) changes in the offshore wave climate; (iv) changes in tidal amplitude arising from the increase in MSL. Our projections are dominated by the effects of MSL rise, which is typically more than five times larger than any of the other contributions. MSL is projected to rise by about 53 to 115 centimetres at the mouth of the Thames and 30 to 90 centimetres at Edinburgh (5th to 95th percentiles at 2100 relative to 1981–2000 average). Surge model projections disagree on the sign of future changes. Typical simulated changes are around +/−7 centimetres. Because of the disagreement, our best estimate is of no change from this contribution, although we cannot rule out changes of either sign. Wave model projections suggest a decrease in significant wave height of the order of 7 centimetres over the 21st century. However, the limited sample size and uncertainty in projections of changes in atmospheric circulation means that we cannot be confident about the sign of future changes in wave climate. MSL rise may induce changes in tidal amplitude of more than 15 centimetres over the 21st century for the Bristol Channel. However, models disagree on the sign of change there. Elsewhere, our projected tidal amplitude changes are mostly less than 7 centimetres. Whilst changes in MSL dominate, we have shown the potential for all processes considered here to make non-negligible contributions over the 21st century

Association of plasma uric acid with ischaemic heart disease and blood pressure: mendelian randomisation analysis of two large cohorts

Objectives: To assess the associations between both uric acid levels and hyperuricaemia, with ischaemic heart disease and blood pressure, and to explore the potentially confounding role of body mass index. Design: Mendelian randomisation analysis, using variation at specific genes (SLC2A9 (rs7442295) as an instrument for uric acid; and FTO (rs9939609), MC4R (rs17782313), and TMEM18 (rs6548238) for body mass index). Setting: Two large, prospective cohort studies in Denmark. Participants: We measured levels of uric acid and related covariables in 58 072 participants from the Copenhagen General Population Study and 10 602 from the Copenhagen City Heart Study, comprising 4890 and 2282 cases of ischaemic heart disease, respectively. Main outcome: Blood pressure and prospectively assessed ischaemic heart disease. Results: Estimates confirmed known observational associations between plasma uric acid and hyperuricaemia with risk of ischaemic heart disease and diastolic and systolic blood pressure. However, when using genotypic instruments for uric acid and hyperuricaemia, we saw no evidence for causal associations between uric acid, ischaemic heart disease, and blood pressure. We used genetic instruments to investigate body mass index as a potentially confounding factor in observational associations, and saw a causal effect on uric acid levels. Every four unit increase of body mass index saw a rise in uric acid of 0.03 mmol/L (95% confidence interval 0.02 to 0.04), and an increase in risk of hyperuricaemia of 7.5% (3.9% to 11.1%). Conclusion: By contrast with observational findings, there is no strong evidence for causal associations between uric acid and ischaemic heart disease or blood pressure. However, evidence supports a causal effect between body mass index and uric acid level and hyperuricaemia. This finding strongly suggests body mass index as a confounder in observational associations, and suggests a role for elevated body mass index or obesity in the development of uric acid related conditions

Evaluating the relationship between circulating lipoprotein lipids and apolipoproteins with risk of coronary heart disease: A multivariable Mendelian randomisation analysis.

BACKGROUND: Circulating lipoprotein lipids cause coronary heart disease (CHD). However, the precise way in which one or more lipoprotein lipid-related entities account for this relationship remains unclear. Using genetic instruments for lipoprotein lipid traits implemented through multivariable Mendelian randomisation (MR), we sought to compare their causal roles in the aetiology of CHD. METHODS AND FINDINGS: We conducted a genome-wide association study (GWAS) of circulating non-fasted lipoprotein lipid traits in the UK Biobank (UKBB) for low-density lipoprotein (LDL) cholesterol, triglycerides, and apolipoprotein B to identify lipid-associated single nucleotide polymorphisms (SNPs). Using data from CARDIoGRAMplusC4D for CHD (consisting of 60,801 cases and 123,504 controls), we performed univariable and multivariable MR analyses. Similar GWAS and MR analyses were conducted for high-density lipoprotein (HDL) cholesterol and apolipoprotein A-I. The GWAS of lipids and apolipoproteins in the UKBB included between 393,193 and 441,016 individuals in whom the mean age was 56.9 y (range 39-73 y) and of whom 54.2% were women. The mean (standard deviation) lipid concentrations were LDL cholesterol 3.57 (0.87) mmol/L and HDL cholesterol 1.45 (0.38) mmol/L, and the median triglycerides was 1.50 (IQR = 1.11) mmol/L. The mean (standard deviation) values for apolipoproteins B and A-I were 1.03 (0.24) g/L and 1.54 (0.27) g/L, respectively. The GWAS identified multiple independent SNPs associated at P < 5 × 10-8 for LDL cholesterol (220), apolipoprotein B (n = 255), triglycerides (440), HDL cholesterol (534), and apolipoprotein A-I (440). Between 56%-93% of SNPs identified for each lipid trait had not been previously reported in large-scale GWASs. Almost half (46%) of these SNPs were associated at P < 5 × 10-8 with more than one lipid-related trait. Assessed individually using MR, LDL cholesterol (odds ratio [OR] 1.66 per 1-standard-deviation-higher trait; 95% CI: 1.49-1.86; P < 0.001), triglycerides (OR 1.34; 95% CI: 1.25-1.44; P < 0.001) and apolipoprotein B (OR 1.73; 95% CI: 1.56-1.91; P < 0.001) had effect estimates consistent with a higher risk of CHD. In multivariable MR, only apolipoprotein B (OR 1.92; 95% CI: 1.31-2.81; P < 0.001) retained a robust effect, with the estimate for LDL cholesterol (OR 0.85; 95% CI: 0.57-1.27; P = 0.44) reversing and that of triglycerides (OR 1.12; 95% CI: 1.02-1.23; P = 0.01) becoming weaker. Individual MR analyses showed a 1-standard-deviation-higher HDL cholesterol (OR 0.80; 95% CI: 0.75-0.86; P < 0.001) and apolipoprotein A-I (OR 0.83; 95% CI: 0.77-0.89; P < 0.001) to lower the risk of CHD, but these effect estimates attenuated substantially to the null on accounting for apolipoprotein B. A limitation is that, owing to the nature of lipoprotein metabolism, measures related to the composition of lipoprotein particles are highly correlated, creating a challenge in making exclusive interpretations on causation of individual components. CONCLUSIONS: These findings suggest that apolipoprotein B is the predominant trait that accounts for the aetiological relationship of lipoprotein lipids with risk of CHD

Cryo-EM single-particle structure refinement and map calculation using Servalcat.

In 2020, cryo-EM single-particle analysis achieved true atomic resolution thanks to technological developments in hardware and software. The number of high-resolution reconstructions continues to grow, increasing the importance of the accurate determination of atomic coordinates. Here, a new Python package and program called Servalcat is presented that is designed to facilitate atomic model refinement. Servalcat implements a refinement pipeline using the program REFMAC5 from the CCP4 package. After the refinement, Servalcat calculates a weighted Fo - Fc difference map, which is derived from Bayesian statistics. This map helps manual and automatic model building in real space, as is common practice in crystallography. The Fo - Fc map helps in the visualization of weak features including hydrogen densities. Although hydrogen densities are weak, they are stronger than in the electron-density maps produced by X-ray crystallography, and some H atoms are even visible at ∼1.8 Å resolution. Servalcat also facilitates atomic model refinement under symmetry constraints. If point-group symmetry has been applied to the map during reconstruction, the asymmetric unit model is refined with the appropriate symmetry constraints