Power calculations using exact data simulation: a useful tool for genetic study designs

Using Instrumental Variables to Measure Causation over Time in Cross-Lagged Panel Models

Cross-lagged panel models (CLPMs) are commonly used to estimate causal influences between two variables with repeated assessments. The lagged effects in a CLPM depend on the time interval between assessments, eventually becoming undetectable at longer intervals. To address this limitation, we incorporate instrumental variables (IVs) into the CLPM with two study waves and two variables. Doing so enables estimation of both the lagged (i.e., "distal") effects and the bidirectional cross-sectional (i.e., "proximal") effects at each wave. The distal effects reflect Granger-causal influences across time, which decay with increasing time intervals. The proximal effects capture causal influences that accrue over time and can help infer causality when the distal effects become undetectable at longer intervals. Significant proximal effects, with a negligible distal effect, would imply that the time interval is too long to estimate a lagged effect at that time interval using the standard CLPM. Through simulations and an empirical application, we demonstrate the impact of time intervals on causal inference in the CLPM and present modeling strategies to detect causal influences regardless of the time interval in a study. Furthermore, to motivate empirical applications of the proposed model, we highlight the utility and limitations of using genetic variables as IVs in large-scale panel studies.

Power, measurement error, and pleiotropy robustness in twin-design extensions to Mendelian Randomization

Mendelian Randomization (MR) has become an important tool for causal inference in the health sciences. It takes advantage of the random segregation of alleles to control for background confounding factors. In brief, the method works by using genetic variants as instrumental variables, but it depends on the assumption of exclusion restriction, i.e., that the variants affect the outcome exclusively via the exposure variable. Equivalently, the assumption states that there is no horizontal pleiotropy from the variant to the outcome. This assumption is unlikely to hold in nature, so several extensions to MR have been developed to increase its robustness against horizontal pleiotropy, though not eliminating the problem entirely (Sanderson et al. 2022). The Direction of Causation (DoC) model, which affords information from the cross-twin cross-trait correlations to estimate causal paths, was extended with polygenic scores to explicitly model horizontal pleiotropy and a causal path (MR-DoC, Minică et al 2018). MR-DoC was further extended to accommodate bidirectional causation (MR-DoC2 ; Castro-de-Araujo et al. 2023). In the present paper, we compared the power of the DoC model, MR-DoC, and MR-DoC2. We investigated the effect of phenotypic measurement error and the effect of misspecification of unshared (individual-specific) environmental factors on the parameter estimates.

MR-DoC2: Bidirectional Causal Modeling with Instrumental Variables and Data from Relatives

Establishing causality is an essential step towards developing interventions for psychiatric disorders, substance use and many other conditions. While randomized controlled trials (RCTs) are considered the gold standard for causal inference, they are unethical in many scenarios. Mendelian randomization (MR) can be used in such cases, but importantly both RCTs and MR assume unidirectional causality. In this paper, we developed a new model, MRDoC2, that can be used to identify bidirectional causation in the presence of confounding due to both familial and non-familial sources. Our model extends the MRDoC model (Minică et al. in Behav Genet 48:337-349,  https://doi.org/10.1007/s10519-018-9904-4 , 2018), by simultaneously including risk scores for each trait. Furthermore, the power to detect causal effects in MRDoC2 does not require the phenotypes to have different additive genetic or shared environmental sources of variance, as is the case in the direction of causation twin model (Heath et al. in Behav Genet 23:29-50,  https://doi.org/10.1007/BF01067552 , 1993).

The Analytic Identification of Variance Component Models Common to Behavior Genetics

Many behavior genetics models follow the same general structure. We describe this general structure and analytically derive simple criteria for its identification. In particular, we find that variance components can be uniquely estimated whenever the relatedness matrices that define the components are linearly independent (i.e., not confounded). Thus, we emphasize determining which variance components can be identified given a set of genetic and environmental relationships, rather than the estimation procedures. We validate the identification criteria with several well-known models, and further apply them to several less common models. The first model distinguishes child-rearing environment from extended family environment. The second model adds a gene-by-common-environment interaction term in sets of twins reared apart and together. The third model separates measured-genomic relatedness from the scanner site variation in a hypothetical functional magnetic resonance imaging study. The computationally easy analytic identification criteria allow researchers to quickly address model identification issues and define novel variance components, facilitating the development of new research questions.

Notes on Three Decades of Methodology Workshops

Since 1987, a group of behavior geneticists have been teaching an annual methodology workshop on how to use state-of-the-art methods to analyze genetically informative data. In the early years, the focus was on analyzing twin and family data, using information of their known genetic relatedness to infer the role of genetic and environmental factors on phenotypic variation. With the rapid evolution of genotyping and sequencing technology and availability of measured genetic data, new methods to detect genetic variants associated with human traits were developed and became the focus of workshop teaching in alternate years. Over the years, many of the methodological advances in the field of statistical genetics have been direct outgrowths of the workshop, as evidence by the software and methodological publications authored by workshop faculty. We provide data and demographics of workshop attendees and evaluate the impact of the methodology workshops on scientific output in the field by evaluating the number of papers applying specific statistical genetic methodologies authored by individuals who have attended workshops.

Incorporating Polygenic Risk Scores in the ACE Twin Model to Estimate A-C Covariance

The assumption in the twin model that genotypic and environmental variables are uncorrelated is primarily made to ensure parameter identification, not because researchers necessarily think that these variables are uncorrelated. Although the biasing effects of such correlations are well understood, a method to estimate these parameters in the twin model would be useful. Here we explore the possibility of relaxing this assumption by adding polygenic scores to the (univariate) twin model. We demonstrate that this extension renders the additive genetic (A)—common environmental (C) covariance (σ_AC) identified. We study the statistical power to reject σ_AC = 0 in the ACE model and present the results of simulations.

The Power to Detect Cultural Transmission in the Nuclear Twin Family Design With and Without Polygenic Risk Scores and in the Transmitted-Nontransmitted (Alleles) Design

We compare the power of two different approaches to detect passive genotype-environment (GE) covariance originating from cultural and genetic transmission operating simultaneously. In the traditional nuclear twin family (NTF) design, cultural transmission is estimated from the phenotypic covariance matrices of the mono- and dizygotic twins and their parents. Here, phenotyping is required in all family members. A more recent method is the transmitted-nontransmitted (T-NT) allele design, which exploits measured genetic variants in parents and offspring to test for effects of nontransmitted alleles from parents. This design requires two-generation genome-wide data and a powerful genome-wide association study (GWAS) for the phenotype in addition to phenotyping in offspring. We compared the power of both designs. Using exact data simulation, we demonstrate three points: how the power of the T-NT design depends on the predictive power of polygenic risk scores (PRSs); that when the NTF design can be applied, its power to detect cultural transmission and GE covariance is high relative to T-NT; and that, given effect sizes from contemporary GWAS, adding PRSs to the NTF design does not yield an appreciable increase in the power to detect cultural transmission. However, it may be difficult to collect phenotypes of parents and the possible importance of gene × age interaction, and secular generational effects can cause complications for many important phenotypes. The T-NT design avoids these complications.

Extending Causality Tests with Genetic Instruments: An Integration of Mendelian Randomization with the Classical Twin Design

Although experimental studies are regarded as the method of choice for determining causal influences, these are not always practical or ethical to answer vital questions in health and social research (e.g., one cannot assign individuals to a "childhood trauma condition" in studying the causal effects of childhood trauma on depression). Key to solving such questions are observational studies. Mendelian Randomization (MR) is an influential method to establish causality in observational studies. MR uses genetic variants to test causal relationships between exposures/risk factors and outcomes such as physical or mental health. Yet, individual genetic variants have small effects, and so, when used as instrumental variables, render MR liable to weak instrument bias. Polygenic scores have the advantage of larger effects, but may be characterized by horizontal pleiotropy, which violates a central assumption of MR. We developed the MR-DoC twin model by integrating MR with the Direction of Causation twin model. This model allows us to test pleiotropy directly. We considered the issue of parameter identification, and given identification, we conducted extensive power calculations. MR-DoC allows one to test causal hypotheses and to obtain unbiased estimates of the causal effect given pleiotropic instruments, while controlling for genetic and environmental influences common to the outcome and exposure. Furthermore, the approach allows one to employ strong instrumental variables in the form of polygenic scores, guarding against weak instrument bias, and increasing the power to detect causal effects of exposures on potential outcomes. Beside allowing to test pleiotropy directly, incorporating in MR data collected from relatives provide additional within-family data that resolve additional assumptions like random mating, the absence of the gene-environment interaction/covariance, no dyadic effects. Our approach will enhance and extend MR's range of applications, and increase the value of the large cohorts collected at twin/family registries as they correctly detect causation and estimate effect sizes even in the presence of pleiotropy.

Comparison of Twin and Extended Pedigree Designs for Obtaining Heritability Estimates

This study explores power assumptions relating to extended pedigree designs (EPD) and classical twin designs (CTD). We conducted statistical analyses to compare the power of the two designs for examining neuroimaging phenotypes, varying heritability and varying whether shared environmental variance is fixed or free. Results indicated that CTDs have more power to estimate heritability, with the exception of one condition: in EPDs, the power increases relative to CTDs when shared environmental variance contributes to sibling similarity only. We additionally show that assuming a priori that shared environmental effects play no role in a phenotype-as is commonly done in pedigree designs-can lead to substantially biased heritability estimates. General results indicate that both CTDs and EPDs obtain quite precise heritability estimates. Finally, we discuss methodological considerations relating to assumptions about age effects and shared environment.

GE covariance through phenotype to environment transmission: an assessment in longitudinal twin data and application to childhood anxiety

We considered identification of phenotype (at occasion t) to environment (at occasion t + 1) transmission in longitudinal model comprising genetic, common and unique environmental simplex models (autoregressions). This type of transmission, which gives rise to genotype-environment covariance, is considered to be important in developmental psychology. Having established identifying constraints, we addressed the issue of statistical power to detect such transmission given a limited set of parameter values. The power is very poor in the ACE simplex, but is good in the AE model. We investigated misspecification, and found that fitting the standard ACE simplex to covariance matrices generated by an AE simplex with phenotype to E transmission produces the particular result of a rank 1 C (common environment) covariance matrix with positive transmission, and a rank 1 D (dominance) matrix given negative transmission. We applied the models to mother ratings of anxiety in female twins (aged 3, 7, 10, and 12 years), and obtained support for the positive effect of one twin's phenotype on the other twin's environment.

The use of imputed sibling genotypes in sibship-based association analysis: on modeling alternatives, power and model misspecification

When phenotypic, but no genotypic data are available for relatives of participants in genetic association studies, previous research has shown that family-based imputed genotypes can boost the statistical power when included in such studies. Here, using simulations, we compared the performance of two statistical approaches suitable to model imputed genotype data: the mixture approach, which involves the full distribution of the imputed genotypes and the dosage approach, where the mean of the conditional distribution features as the imputed genotype. Simulations were run by varying sibship size, size of the phenotypic correlations among siblings, imputation accuracy and minor allele frequency of the causal SNP. Furthermore, as imputing sibling data and extending the model to include sibships of size two or greater requires modeling the familial covariance matrix, we inquired whether model misspecification affects power. Finally, the results obtained via simulations were empirically verified in two datasets with continuous phenotype data (height) and with a dichotomous phenotype (smoking initiation). Across the settings considered, the mixture and the dosage approach are equally powerful and both produce unbiased parameter estimates. In addition, the likelihood-ratio test in the linear mixed model appears to be robust to the considered misspecification in the background covariance structure, given low to moderate phenotypic correlations among siblings. Empirical results show that the inclusion in association analysis of imputed sibling genotypes does not always result in larger test statistic. The actual test statistic may drop in value due to small effect sizes. That is, if the power benefit is small, that the change in distribution of the test statistic under the alternative is relatively small, the probability is greater of obtaining a smaller test statistic. As the genetic effects are typically hypothesized to be small, in practice, the decision on whether family-based imputation could be used as a means to increase power should be informed by prior power calculations and by the consideration of the background correlation.

Prediction of a time-to-event trait using genome wide SNP data

Background

A popular objective of many high-throughput genome projects is to discover various genomic markers associated with traits and develop statistical models to predict traits of future patients based on marker values.

Results

In this paper, we present a prediction method for time-to-event traits using genome-wide single-nucleotide polymorphisms (SNPs). We also propose a MaxTest associating between a time-to-event trait and a SNP accounting for its possible genetic models. The proposed MaxTest can help screen out nonprognostic SNPs and identify genetic models of prognostic SNPs. The performance of the proposed method is evaluated through simulations.

Conclusions

In conjunction with the MaxTest, the proposed method provides more parsimonious prediction models but includes more prognostic SNPs than some naive prediction methods. The proposed method is demonstrated with real GWAS data.

Genetic association in multivariate phenotypic data: power in five models

This article concerns the power of various data analytic strategies to detect the effect of a single genetic variant (GV) in multivariate data. We simulated exactly fitting monozygotic and dizygotic phenotypic data according to single and two common factor models, and simplex models. We calculated the power to detect the GV in twin 1 data in an ANOVA of phenotypic sum scores, in a MANOVA, and in exploratory factor analysis (EFA), in which the common factors are regressed on the genetic variant. We also report power in the full twin model, and power of the single phenotype ANOVA. The results indicate that (1) if the GV affects all phenotypes, the sum score ANOVA and the EFA are most powerful, while the MANOVA is less powerful. Increasing phenotypic correlations further decreases the power of the MANOVA; and (2) if the GV affects only a subset of the phenotypes, the EFA or the MANOVA are most powerful, while sum score ANOVA is less powerful. In this case, an increase in phenotypic correlations may enhance the power of MANOVA and EFA. If the effect of the GV is modeled directly on the phenotypes in the EFA, the power of the EFA is approximately equal to the power of the MANOVA.

Phenotypic complexity, measurement bias, and poor phenotypic resolution contribute to the missing heritability problem in genetic association studies

BACKGROUND

The variance explained by genetic variants as identified in (genome-wide) genetic association studies is typically small compared to family-based heritability estimates. Explanations of this 'missing heritability' have been mainly genetic, such as genetic heterogeneity and complex (epi-)genetic mechanisms.

METHODOLOGY

We used comprehensive simulation studies to show that three phenotypic measurement issues also provide viable explanations of the missing heritability: phenotypic complexity, measurement bias, and phenotypic resolution. We identify the circumstances in which the use of phenotypic sum-scores and the presence of measurement bias lower the power to detect genetic variants. In addition, we show how the differential resolution of psychometric instruments (i.e., whether the instrument includes items that resolve individual differences in the normal range or in the clinical range of a phenotype) affects the power to detect genetic variants.

CONCLUSION

We conclude that careful phenotypic data modelling can improve the genetic signal, and thus the statistical power to identify genetic variants by 20-99%.

Very low frequencies of Toll-like receptor 2 supposed-2029T and 2258A (RS5743708) mutant alleles in southern Brazilian critically ill patients: would it be a lack of worldwide-accepted clinical applications of Toll-like receptor 2 variants?

Toll-like receptor 2 (TLR2) is a recognition receptor for the widest repertoire of pathogen-associated molecular patterns. Two polymorphisms of TLR2 could be linked to reduced nuclear factor kappa-light-chain-enhancer of activated B cells (NF-kB) activation and to increased risk of infection (supposed-2029C>T and 2258G>A). We investigated the supposed-2029C>T and 2258G>A TLR2 polymorphisms in 422 critically ill patients of European origin from southern Brazil (295 with sepsis and 127 without sepsis) and reviewed 33 studies on these polymorphisms, conducting a quality assessment with a score system. Among our patients we found only one heterozygote (1/422) for the supposed-2029C>T and none for the 2258G>A (0/422) single nucleotide polymorphism (SNP). We were unable to find a clinical application of supposed-2029T and 2258A allele analyses in our southern Brazilian population. Our review detected that current TLR2 SNP assays had very controversial and contradictory results derived from reports with a variety of investigation quality criteria. We suggest that, if analyzed alone, the supposed-2029C>T and 2258G>A TLR2 SNP are not good candidates for genetic markers in studies that search for direct or indirect clinical applications between genotype and phenotype. Future efforts to improve the knowledge and to provide other simultaneous genetic markers might reveal a more effective TLR2 effect on the susceptibility to infectious diseases.

A general test for gene-environment interaction in sib pair-based association analysis of quantitative traits

Several association studies support the hypothesis that genetic variants can modify the influence of environmental factors on behavioral outcomes, i.e., G × E interaction. The case-control design used in these studies is powerful, but population stratification with respect to allele frequencies can give rise to false positive or false negative associations. Stratification with respect to the environmental factors can lead to false positives or false negatives with respect to environmental main effects and G × E interaction effects as well. Here we present a model based on Fulker et al. (1999) and Purcell (2002) for the study of G × E interaction in family-based association designs, in which the effects of stratification can be controlled. Simulations illustrate the power to detect genetic and environmental main effects, and G × E interaction effects for the sib pair design. The power to detect interaction was studied in eight different situations, both with and without the presence of population stratification, and for categorical and continuous environmental factors. Results show that the power to detect genetic and environmental main effects, and G × E interaction effects, depends on the allele frequencies and the distribution of the environmental moderator. Admixture effects of realistic effect size lead only to very small stratification effects in the G × E component, so impractically large numbers of sib pairs are required to detect such stratification.