Missing data methods in Mendelian randomization studies with multiple instruments

Bidirectional causality between micronutrients and mental illness: Mendelian randomization studies

BACKGROUND

Previous observational clinical research has suggested a link between micronutrients and psychiatric conditions. However, the causal relationship between these nutrients and mental health disorders remains uncertain. This study endeavors to fill this knowledge gap by employing a Mendelian randomization (MR) analysis on pooled data from genome-wide association studies (GWAS), aiming to explore the potential causal associations between 20 prevalent micronutrients and 7 common psychiatric disorders.

METHODS

A collection of single nucleotide polymorphisms (SNPs) associated with 20 micronutrients and seven common psychiatric disorders and extracted from a dataset comprising 7,368,835 individuals. MR analysis, including inverse variance weighting (IVW), Mendelian randomization-egger, weighted median, and sensitivity analysis, was used to evaluate the reliability of the study results. A significance threshold of p < 0.05 was used to identify evidence of potential associations.

RESULTS

Our forward MR analysis found some commonalities between certain micronutrients and psychiatric disorders. Notably, Vitamin D level is related to the risk of reducing depression and emotional disorders. Carotene levels were associated with an elevated risk of depression, mood disorders, bipolar disorder (BIPO), and post-traumatic stress disorder (PTSD). Additionally, multivitamins ± minerals and retinol were associated with a decreased risk of BIPO, while folate and selenium levels were associated with decreased risks of dementia and schizophrenia, respectively. The study found a significant association between elevated copper levels and an increased likelihood of Bipolar Disorder (BD), while magnesium levels were observed to be positively correlated with a heightened risk of depression. Our sensitivity study confirmed the results of the IVW MR primary analysis.

CONCLUSION

Our study suggests that carotene, copper, and magnesium are important risk factors for depression, mood disorders, PTSD, phobia, BIPO, and dementia. Elevated levels of these micronutrients are related to an increased likelihood of these disorders.

Missing data approaches in longitudinal studies of aging: A case example using the National Health and Aging Trends Study

PURPOSE

Missing data is a key methodological consideration in longitudinal studies of aging. We described missing data challenges and potential methodological solutions using a case example describing five-year frailty state transitions in a cohort of older adults.

METHODS

We used longitudinal data from the National Health and Aging Trends Study, a nationally-representative cohort of Medicare beneficiaries. We assessed the five components of the Fried frailty phenotype and classified frailty based on their number of components (robust: 0, prefrail: 1-2, frail: 3-5). One-, two-, and five-year frailty state transitions were defined as movements between frailty states or death. Missing frailty components were imputed using hot deck imputation. Inverse probability weights were used to account for potentially informative loss-to-follow-up. We conducted scenario analyses to test a range of assumptions related to missing data.

RESULTS

Missing data were common for frailty components measured using physical assessments (walking speed, grip strength). At five years, 36% of individuals were lost-to-follow-up, differentially with respect to baseline frailty status. Assumptions for missing data mechanisms impacted inference regarding individuals improving or worsening in frailty.

CONCLUSIONS

Missing data and loss-to-follow-up are common in longitudinal studies of aging. Robust epidemiologic methods can improve the rigor and interpretability of aging-related research.

Efficient Nonparametric Causal Inference with Missing Exposure Information

Missing exposure information is a very common feature of many observational studies. Here we study identifiability and efficient estimation of causal effects on vector outcomes, in such cases where treatment is unconfounded but partially missing. We consider a missing at random setting where missingness in treatment can depend not only on complex covariates, but also on post-treatment outcomes. We give a new identifying expression for average treatment effects in this setting, along with the efficient influence function for this parameter in a nonparametric model, which yields a nonparametric efficiency bound. We use this latter result to construct nonparametric estimators that are less sensitive to the curse of dimensionality than usual, e. g. by having faster rates of convergence than the complex nuisance estimators they rely on. Further we show that these estimators can be root-n consistent and asymptotically normal under weak nonparametric conditions, even when constructed using flexible machine learning. Finally we apply these results to the problem of causal inference with a partially missing instrumental variable.

Handling Missing Data in Instrumental Variable Methods for Causal Inference

It is very common in instrumental variable studies for there to be missing instrument data. For example, in the Wisconsin Longitudinal Study one can use genotype data as a Mendelian randomization-style instrument, but this information is often missing when subjects do not contribute saliva samples, or when the genotyping platform output is ambiguous. Here we review missing-at-random assumptions one can use to identify instrumental variable causal effects, and discuss various approaches for estimation and inference. We consider likelihood-based methods, regression and weighting estimators, and doubly robust estimators. The likelihood-based methods yield the most precise inference, and are optimal under the model assumptions, while the doubly robust estimators can attain the nonparametric efficiency bound while allowing flexible nonparametric estimation of nuisance functions (e.g., instrument propensity scores). The regression and weighting estimators can sometimes be easiest to describe and implement. Our main contribution is an extensive review of this wide array of estimators under varied missing-at-random assumptions, along with discussion of asymptotic properties and inferential tools. We also implement many of the estimators in an analysis of the Wisconsin Longitudinal Study, to study effects of impaired cognitive functioning on depression.

Statistical approaches to harmonize data on cognitive measures in systematic reviews are rarely reported

OBJECTIVES

To identify statistical methods for harmonization, the procedures aimed at achieving the comparability of previously collected data, which could be used in the context of summary data and individual participant data meta-analysis of cognitive measures.

STUDY DESIGN AND SETTING

Environmental scan methods were used to conduct two reviews to identify (1) studies that quantitatively combined data on cognition and (2) general literature on statistical methods for data harmonization. Search results were rapidly screened to identify articles of relevance.

RESULTS

All 33 meta-analyses combining cognition measures either restricted their analyses to a subset of studies using a common measure or combined standardized effect sizes across studies; none reported their harmonization steps before producing summary effects. In the second scan, three general classes of statistical harmonization models were identified (1) standardization methods, (2) latent variable models, and (3) multiple imputation models; few publications compared methods.

CONCLUSION

Although it is an implicit part of conducting a meta-analysis or pooled analysis, the methods used to assess inferential equivalence of complex constructs are rarely reported or discussed. Progress in this area will be supported by guidelines for the conduct and reporting of the data harmonization and integration and by evaluating and developing statistical approaches to harmonization.

High tobacco consumption is causally associated with increased all-cause mortality in a general population sample of 55,568 individuals, but not with short telomeres: a Mendelian randomization study

BACKGROUND

High cumulative tobacco consumption is associated with short telomeres and with increased all-cause mortality. We tested the hypothesis that high tobacco consumption is causally associated with short telomeres and with increased all-cause mortality.

METHODS

We studied 55,568 individuals including 32,823 ever smokers from the Danish general population, of whom 3430 died during 10 years of follow-up. All had telomere length measured, detailed information on smoking history, and CHRNA3 rs1051730 genotype, which is associated with tobacco consumption, determined. In a Mendelian randomization study, we conducted observational, genetic, and mediation analyses.

RESULTS

First, tobacco consumption was 21.1 pack-years in non-carriers, 22.8 in heterozygotes and 24.8 in homozygotes (P-trend<0.001). Second, the observational multivariable adjusted hazard ratio for all-cause mortality was 1.12 [95% confidence interval (CI): 1.09, 1.15] per doubling in tobacco consumption. In Mendelian randomization analysis, the hazard ratio was 1.08 (1.02, 1.14) per minor CHRNA3 allele in ever smokers. Third, in observational analysis telomeres shortened with -13 base pairs (-18, -8) per doubling in tobacco consumption. In Mendelian randomization analysis, the estimate was +3 base pairs (-10, +15) per minor CHRNA3 allele. Finally, individuals with the shortest vs longest telomeres had a multivariable adjusted hazard ratio of 1.30 (1.13, 1.50) for all-cause mortality; however, in mediation analysis short telomeres explained only +0.4% (-3.5%, +4.3%) of the association between high tobacco consumption and increased all-cause mortality.

CONCLUSIONS

High tobacco consumption is causally associated with increased all-cause mortality. High cumulative tobacco consumption is associated with short telomeres observationally, but there is no clear genetic association.

Use of allele scores as instrumental variables for Mendelian randomization

Background An allele score is a single variable summarizing multiple genetic variants associated with a risk factor. It is calculated as the total number of risk factor-increasing alleles for an individual (unweighted score), or the sum of weights for each allele corresponding to estimated genetic effect sizes (weighted score). An allele score can be used in a Mendelian randomization analysis to estimate the causal effect of the risk factor on an outcome.

Methods Data were simulated to investigate the use of allele scores in Mendelian randomization where conventional instrumental variable techniques using multiple genetic variants demonstrate ‘weak instrument’ bias. The robustness of estimates using the allele score to misspecification (for example non-linearity, effect modification) and to violations of the instrumental variable assumptions was assessed.

Results Causal estimates using a correctly specified allele score were unbiased with appropriate coverage levels. The estimates were generally robust to misspecification of the allele score, but not to instrumental variable violations, even if the majority of variants in the allele score were valid instruments. Using a weighted rather than an unweighted allele score increased power, but the increase was small when genetic variants had similar effect sizes. Naive use of the data under analysis to choose which variants to include in an allele score, or for deriving weights, resulted in substantial biases.

Conclusions Allele scores enable valid causal estimates with large numbers of genetic variants. The stringency of criteria for genetic variants in Mendelian randomization should be maintained for all variants in an allele score.

Sample size and power calculations in Mendelian randomization with a single instrumental variable and a binary outcome

Background: Sample size calculations are an important tool for planning epidemiological studies. Large sample sizes are often required in Mendelian randomization investigations.

Methods and results: Resources are provided for investigators to perform sample size and power calculations for Mendelian randomization with a binary outcome. We initially provide formulae for the continuous outcome case, and then analogous formulae for the binary outcome case. The formulae are valid for a single instrumental variable, which may be a single genetic variant or an allele score comprising multiple variants. Graphs are provided to give the required sample size for 80% power for given values of the causal effect of the risk factor on the outcome and of the squared correlation between the risk factor and instrumental variable. R code and an online calculator tool are made available for calculating the sample size needed for a chosen power level given these parameters, as well as the power given the chosen sample size and these parameters.

Conclusions: The sample size required for a given power of Mendelian randomization investigation depends greatly on the proportion of variance in the risk factor explained by the instrumental variable. The inclusion of multiple variants into an allele score to explain more of the variance in the risk factor will improve power, however care must be taken not to introduce bias by the inclusion of invalid variants.

Mendelian randomization analysis with multiple genetic variants using summarized data

Genome-wide association studies, which typically report regression coefficients summarizing the associations of many genetic variants with various traits, are potentially a powerful source of data for Mendelian randomization investigations. We demonstrate how such coefficients from multiple variants can be combined in a Mendelian randomization analysis to estimate the causal effect of a risk factor on an outcome. The bias and efficiency of estimates based on summarized data are compared to those based on individual-level data in simulation studies. We investigate the impact of gene–gene interactions, linkage disequilibrium, and ‘weak instruments’ on these estimates. Both an inverse-variance weighted average of variant-specific associations and a likelihood-based approach for summarized data give similar estimates and precision to the two-stage least squares method for individual-level data, even when there are gene–gene interactions. However, these summarized data methods overstate precision when variants are in linkage disequilibrium. If the P-value in a linear regression of the risk factor for each variant is less than , then weak instrument bias will be small. We use these methods to estimate the causal association of low-density lipoprotein cholesterol (LDL-C) on coronary artery disease using published data on five genetic variants. A 30% reduction in LDL-C is estimated to reduce coronary artery disease risk by 67% (95% CI: 54% to 76%). We conclude that Mendelian randomization investigations using summarized data from uncorrelated variants are similarly efficient to those using individual-level data, although the necessary assumptions cannot be so fully assessed.