Mendelian randomization uses genetic variants to make causal inferences about the effect of a risk factor on an outcome. With fine‐mapped genetic data, there may be hundreds of genetic variants in a single gene region any of which could be used to assess this causal relationship. However, using too many genetic variants in the analysis can lead to spurious estimates and inflated Type 1 error rates. But if only a few genetic variants are used, then the majority of the data is ignored and estimates are highly sensitive to the particular choice of variants. We propose an approach based on summarized data only (genetic association and correlation estimates) that uses principal components analysis to form instruments. This approach has desirable theoretical properties: it takes the totality of data into account and does not suffer from numerical instabilities. It also has good properties in simulation studies: it is not particularly sensitive to varying the genetic variants included in the analysis or the genetic correlation matrix, and it does not have greatly inflated Type 1 error rates. Overall, the method gives estimates that are less precise than those from variable selection approaches (such as using a conditional analysis or pruning approach to select variants), but are more robust to seemingly arbitrary choices in the variable selection step. Methods are illustrated by an example using genetic associations with testosterone for 320 genetic variants to assess the effect of sex hormone related pathways on coronary artery disease risk, in which variable selection approaches give inconsistent inferences.
This paper presents a simple Bayesian approach to sample size determination in clinical trials. It is required that the trial should be large enough to ensure that the data collected will provide convincing evidence either that an experimental treatment is better than a control or that it fails to improve upon control by some clinically relevant difference. The method resembles standard frequentist formulations of the problem, and indeed in certain circumstances involving 'non-informative' prior information it leads to identical answers. In particular, unlike many Bayesian approaches to sample size determination, use is made of an alternative hypothesis that an experimental treatment is better than a control treatment by some specified magnitude. The approach is introduced in the context of testing whether a single stream of binary observations are consistent with a given success rate p(0). Next the case of comparing two independent streams of normally distributed responses is considered, first under the assumption that their common variance is known and then for unknown variance. Finally, the more general situation in which a large sample is to be collected and analysed according to the asymptotic properties of the score statistic is explored.
Objective To examine the causal relevance of lifelong differences in low-density lipoprotein cholesterol (LDL-C) for ischemic stroke (IS) relative to that for coronary heart disease (CHD) using a Mendelian randomization approach. Methods We undertook a 2-sample Mendelian randomization, based on summary data, to estimate the causal relevance of LDL-C for risk of IS and CHD. Information from 62 independent genetic variants with genome-wide significant effects on LDL-C levels was used to estimate the causal effects of LDL-C for IS and IS subtypes (based on 12,389 IS cases from METASTROKE) and for CHD (based on 60,801 cases from CARDIoGRAMplusC4D). We then assessed the effects of LDL-C on IS and CHD for heterogeneity. Results A 1 mmol/L higher genetically determined LDL-C was associated with a 50% higher risk of CHD (odds ratio [OR] 1.49, 95% confidence interval [CI] 1.32−1.68, p = 1.1 × 10 −8 ). By contrast, the causal effect of LDL-C was much weaker for IS (OR 1.12, 95% CI 0.96−1.30, p = 0.14; p for heterogeneity = 2.6 × 10 −3 ) and, in particular, for cardioembolic stroke (OR 1.06, 95% CI 0.84−1.33, p = 0.64; p for heterogeneity = 8.6 × 10 −3 ) when compared with that for CHD. Conclusions In contrast with the consistent effects of LDL-C-lowering therapies on IS and CHD, genetic variants that confer lifelong LDL-C differences show a weaker effect on IS than on CHD. The relevance of etiologically distinct IS subtypes may contribute to the differences observed.
Aims PCSK9 genetic variants that have large effects on low-density lipoprotein cholesterol (LDL-C) and coronary heart disease (CHD) have prompted the development of therapeutic PCSK9-inhibition. However, there is limited evidence that PCSK9 variants are associated with ischaemic stroke (IS).Methods and resultsAssociations of the loss-of-function PCSK9 genetic variant (rs11591147; R46L), and five additional PCSK9 variants, with IS and IS subtypes (cardioembolic, large vessel, and small vessel) were estimated in a meta-analysis involving 10 307 IS cases and 19 326 controls of European ancestry. They were then compared with the associations of these variants with LDL-C levels (in up to 172 970 individuals) and CHD (in up to 60 801 CHD cases and 123 504 controls). The rs11591147 T allele was associated with 0.5 mmol/L lower LDL-C level (P = 9 × 10−143) and 23% lower CHD risk [odds ratio (OR): 0.77, 95% confidence interval (CI): 0.69–0.87, P = 7 × 10−6]. However, it was not associated with risk of IS (OR: 1.04, 95% CI: 0.84–1.28, P = 0.74) or IS subtypes. Information from additional PCSK9 variants also indicated consistently weaker effects on IS than on CHD.Conclusion PCSK9 genetic variants that confer life-long lower PCSK9 and LDL-C levels appear to have significantly weaker, if any, associations with risk of IS than with risk of CHD. By contrast, similar proportional reductions in risks of IS and CHD have been observed in randomized trials of therapeutic PCSK9-inhibition. These findings have implications for our understanding of when Mendelian randomization can be relied upon to predict the effects of therapeutic interventions.
Although more complex in design, ASDs have the potential to be more efficient and more powerful than conventional designs.
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