A novel penalized inverse-variance weighted estimator for Mendelian randomization with applications to COVID-19 outcomes.

Mendelian randomization utilizes genetic variants as instrumental variables (IVs) to estimate the causal effect of an exposure variable on an outcome of interest even in the presence of unmeasured confounders. However, the popular inverse-variance weighted (IVW) estimator could be biased in the presence of weak IVs, a common challenge in MR studies. In this article, we develop a novel penalized inverse-variance weighted (pIVW) estimator, which adjusts the original IVW estimator to account for the weak IV issue by using a penalization approach to prevent the denominator of the pIVW estimator from being close to zero. Moreover, we adjust the variance estimation of the pIVW estimator to account for the presence of balanced horizontal pleiotropy. We show that the recently proposed debiased IVW (dIVW) estimator is a special case of our proposed pIVW estimator. We further prove that the pIVW estimator has smaller bias and variance than the dIVW estimator under some regularity conditions. We also conduct extensive simulation studies to demonstrate the performance of the proposed pIVW estimator. Furthermore, we apply the pIVW estimator to estimate the causal effects of five obesity-related exposures on three coronavirus disease 2019 (COVID-19) outcomes. Notably, we find that hypertensive disease is associated with an increased risk of hospitalized COVID-19; and peripheral vascular disease and higher body mass index are associated with increased risks of COVID-19 infection, hospitalized COVID-19, and critically ill COVID-19.

Robust association tests for quantitative traits on the X chromosome.

The genome-wide association study is an elementary tool to assess the genetic contribution to complex human traits. However, such association tests are mainly proposed for autosomes, and less attention has been given to methods for identifying loci on the X chromosome due to their distinct biological features. In addition, the existing association tests for quantitative traits on the X chromosome either fail to incorporate the information of males or only detect variance heterogeneity. Therefore, we propose four novel methods, which are denoted as QXcat, QZmax, QMVXcat and QMVZmax. When using these methods, it is assumed that the risk alleles for females and males are the same and that the locus being studied satisfies the generalized genetic model for females. The first two methods are based on comparing the means of the trait value across different genotypes, while the latter two methods test for the difference of both means and variances. All four methods effectively incorporate the information of X chromosome inactivation. Simulation studies demonstrate that the proposed methods control the type I error rates well. Under the simulated scenarios, the proposed methods are generally more powerful than the existing methods. We also apply our proposed methods to data from the Minnesota Center for Twin and Family Research and find 10 single nucleotide polymorphisms that are statistically significantly associated with at least two traits at the significance level of 1 × 10-3.

Gene-Based Methods for Estimating the Degree of the Skewness of X Chromosome Inactivation.

Skewed X chromosome inactivation (XCI-S) has been reported to be associated with some X-linked diseases, and currently several methods have been proposed to estimate the degree of the XCI-S (denoted as γ) for a single locus. However, no method has been available to estimate γ for genes. Therefore, in this paper, we first propose the point estimate and the penalized point estimate of γ for genes, and then derive its confidence intervals based on the Fieller's and penalized Fieller's methods, respectively. Further, we consider the constraint condition of γ∈[0, 2] and propose the Bayesian methods to obtain the point estimates and the credible intervals of γ, where a truncated normal prior and a uniform prior are respectively used (denoted as GBN and GBU). The simulation results show that the Bayesian methods can avoid the extreme point estimates (0 or 2), the empty sets, the noninformative intervals ([0, 2]) and the discontinuous intervals to occur. GBN performs best in both the point estimation and the interval estimation. Finally, we apply the proposed methods to the Minnesota Center for Twin and Family Research data for their practical use. In summary, in practical applications, we recommend using GBN to estimate γ of genes.

BEXCIS: Bayesian methods for estimating the degree of the skewness of X chromosome inactivation.

BACKGROUND: X chromosome inactivation (XCI) is an epigenetic phenomenon that one of two X chromosomes in females is transcriptionally silenced during early embryonic development. Skewed XCI has been reported to be associated with some X-linked diseases. There have been several methods measuring the degree of the skewness of XCI. However, these methods may still have several limitations. RESULTS: We propose a Bayesian method to obtain the point estimate and the credible interval of the degree of XCI skewing by incorporating its prior information of being between 0 and 2. We consider a normal prior and a uniform prior for it (respectively denoted by BN and BU). We also propose a penalized point estimate based on the penalized Fieller's method and derive the corresponding confidence interval. Simulation results demonstrate that the BN and BU methods can solve the problems of extreme point estimates, noninformative intervals, empty sets and discontinuous intervals. The BN method generally outperforms other methods with the lowest mean squared error in the point estimation, and well controls the coverage probability with the smallest median and the least variation of the interval width in the interval estimation. We apply all the methods to the Graves' disease data and the Minnesota Center for Twin and Family Research data, and find that SNP rs3827440 in the Graves' disease data may undergo skewed XCI towards the allele C. CONCLUSIONS: We recommend the BN method for measuring the degree of the skewness of XCI in practice. The R package BEXCIS is publicly available at https://github.com/Wen-YiYu/BEXCIS .

MRCIP: a robust Mendelian randomization method accounting for correlated and idiosyncratic pleiotropy.

Mendelian randomization (MR) is a powerful instrumental variable (IV) method for estimating the causal effect of an exposure on an outcome of interest even in the presence of unmeasured confounding by using genetic variants as IVs. However, the correlated and idiosyncratic pleiotropy phenomena in the human genome will lead to biased estimation of causal effects if they are not properly accounted for. In this article, we develop a novel MR approach named MRCIP to account for correlated and idiosyncratic pleiotropy simultaneously. We first propose a random-effect model to explicitly model the correlated pleiotropy and then propose a novel weighting scheme to handle the presence of idiosyncratic pleiotropy. The model parameters are estimated by maximizing a weighted likelihood function with our proposed PRW-EM algorithm. Moreover, we can also estimate the degree of the correlated pleiotropy and perform a likelihood ratio test for its presence. Extensive simulation studies show that the proposed MRCIP has improved performance over competing methods. We also illustrate the usefulness of MRCIP on two real datasets. The R package for MRCIP is publicly available at https://github.com/siqixu/MRCIP.

Penalized Fieller's confidence interval for the ratio of bivariate normal means.

Constructing a confidence interval for the ratio of bivariate normal means is a classical problem in statistics. Several methods have been proposed in the literature. The Fieller method is known as an exact method, but can produce an unbounded confidence interval if the denominator of the ratio is not significantly deviated from 0; while the delta and some numeric methods are all bounded, they are only first-order correct. Motivated by a real-world problem, we propose the penalized Fieller method, which employs the same principle as the Fieller method, but adopts a penalized likelihood approach to estimate the denominator. The proposed method has a simple closed form, and can always produce a bounded confidence interval by selecting a suitable penalty parameter. Moreover, the new method is shown to be second-order correct under the bivariate normality assumption, that is, its coverage probability will converge to the nominal level faster than other bounded methods. Simulation results show that our proposed method generally outperforms the existing methods in terms of controlling the coverage probability and the confidence width and is particularly useful when the denominator does not have adequate power to reject being 0. Finally, we apply the proposed approach to the interval estimation of the median response dose in pharmacology studies to show its practical usefulness.

Evaluation of marker selection methods and statistical models for chronological age prediction based on DNA methylation.

In forensic investigation, retrieving biological information from DNA evidence is a promising field of interest. One of the applications is on the estimation of the age of the donor based on DNA methylation. A large number of studies focused on age prediction using the 450 K Human Methylation Beadchip. Various marker selection methods and prediction models have been considered. However, there is a lack of research evaluating different high-dimensional variable selection methods of CpG sites with various models for age prediction. The aim of this study is to evaluate four variable selection methods (forward selection, LASSO, elastic net and SCAD) combined with a classical statistical model and sophisticated machine learning models based on the mean absolute deviation (MAD) and the root-mean-square error (RMSE). We used publicly available 450 K data set containing 991 whole blood samples (age 19-101 years). We found that the multiple linear regression model with 16 markers selected from the forward selection method performed very well in age prediction (MAD = 3.76 years and RMSE = 5.01 years). On the other hand, the highly advanced ultrahigh dimensional variable selection methods and sophisticated machine learning algorithms appeared unnecessary for age prediction based on DNA methylation.

A robust test for X-chromosome genetic association accounting for X-chromosome inactivation and imprinting.

The X chromosome is known to play an important role in many sex-specific diseases. However, only a few single-nucleotide polymorphisms on the X chromosome have been found to be associated with diseases. Compared to the autosomes, conducting association tests on the X chromosome is more intractable due to the difference in the number of X chromosomes between females and males. On the other hand, X-chromosome inactivation takes place in female mammals, which is a phenomenon in which the expression of one copy of two X chromosomes in females is silenced in order to achieve the same gene expression level as that in males. In addition, imprinting effects may be related to certain diseases. Currently, there are some existing approaches taking X-chromosome inactivation into account when testing for associations on the X chromosome. However, none of them allows for imprinting effects. Therefore, in this paper, we propose a robust test, ZXCII, which accounts for both X-chromosome inactivation and imprinting effects without requiring specifying the genetic models in advance. Simulation studies are conducted in order to investigate the validity and performance of ZXCII under various scenarios of different parameter values. The simulation results show that ZXCII controls the type I error rate well when there is no association. Furthermore, with regards to power, ZXCII is robust in all of the situations considered and generally outperforms most of the existing methods in the presence of imprinting effects, especially under complete imprinting effects.

X-chromosome genetic association test incorporating X-chromosome inactivation and imprinting effects.

Studies have shown that many complex diseases are sex-determined. When conducting genetic association studies on X-chromosome, there are two important epigenetic factors which should be considered simultaneously: X-chromosome inactivation and genomic imprinting. Currently, there have been several association tests accounting for the information on X-chromosome inactivation. However, these tests do not take the imprinting effects into account. In this paper, we propose a novel association test simultaneously incorporating X-chromosome inactivation and imprinting effects based on case-parent trios and control-parent trios for female offspring and case-control data for male offspring, denoted by MLRXCII. Extensive simulation studies are carried out to investigate the type I error rate and the test power of the proposed MLRXCII . Simulation results demonstrate that the proposed test controls the type I error rate well andis more powerful than the existing method when imprinting effects exist. The proposed MLRXCII test is valid and powerful in genetic association studies on X-chromosome for qualitative traits and thus is recommended in practice.

A statistical measure for the skewness of X chromosome inactivation based on case-control design.

BACKGROUND: Skewed X chromosome inactivation (XCI), which is a non-random process, is frequently observed in both healthy and affected females. Furthermore, skewed XCI has been reported to be related to many X-linked diseases. However, no statistical method is available in the literature to measure the degree of the skewness of XCI for case-control design. Therefore, it is necessary to develop methods for such a task. RESULTS: In this article, we first proposed a statistical measure for the degree of XCI skewing by using a case-control design, which is a ratio of two logistic regression coefficients after a simple reparameterization. Based on the point estimate of the ratio, we further developed three types of confidence intervals (the likelihood ratio, Fieller's and delta methods) to evaluate its variation. Simulation results demonstrated that the likelihood ratio method and the Fieller's method have more accurate coverage probability and more balanced tail errors than the delta method. We also applied these proposed methods to analyze the Graves' disease data for their practical use and found that rs3827440 probably undergoes a skewed XCI pattern with 68.7% of cells in heterozygous females having the risk allele T active, while the other 31.3% of cells keeping the normal allele C active. CONCLUSIONS: For practical application, we suggest using the Fieller's method in large samples due to the non-iterative computation procedure and using the LR method otherwise for its robustness despite its slightly heavy computational burden.

A robust and powerful test for case-control genetic association study on X chromosome.

Hundreds of genome-wide association studies were conducted to map the disease genes on autosomes in human beings. It is known that many complex diseases are sex-determined and X chromosome is expected to play an important role. However, only a few single-nucleotide polymorphisms on X chromosome were found to be significantly associated with the diseases under study. On the other hand, to balance the genetic effect between two sexes, X chromosome inactivation occurs in most of X-linked genes by silencing one copy of two X chromosomes in females and dosage compensation is achieved. A few association studies on X chromosome incorporated the information on dosage compensation. However, some of them require the assumption of Hardy-Weinberg equilibrium and some need to specify the underlying genetic model. Therefore, in this article, we propose a novel method for association by taking account of different dosage compensation patterns. The proposed test is a robust approach because it requires neither specifying the underlying genetic models nor the assumption of Hardy-Weinberg equilibrium. Further, the proposed method allows for different deviations from Hardy-Weinberg equilibrium between cases and controls. Simulation results demonstrate that our proposed method generally outperforms the existing methods in terms of controlling the size and the test power. Finally, we apply the proposed test to the meta-analysis of the Graves' disease data for its practical use.

Evaluation of parentage testing accuracy of child trafficking cases: Combining the exclusion probability and likelihood ratio approaches.

The Chinese government established a national anti-trafficking DNA database in 2009 to help reunite trafficked children with their families. The database collects DNA information from missing children's parents, trafficked and homeless children, then conducts parentage testing using 18 or more loci to find matched pairs. This article evaluates the matching accuracy of parentage testing in child-trafficking cases, under both Hardy-Weinberg equilibrium and population substructure. Both one-parent and two-parent scenarios are considered, and mutations are taken into account. The number of random matches is first evaluated using exclusion probability (PE). It is found that there are a large number of single parent-child pairs that match at 18 loci, but the PE approach cannot tell which are the true positive ones. The likelihood ratio (LR) approach can help distinguish the true positive matches. So the second step is to obtain the true positive rate and false positive rate of matched pairs of single parent and child according to the LR approach. Based on the results of the two-step procedure, it is concluded that more than 18 loci should be used to ensure a correct match of single parent and child.

A powerful parent-of-origin effects test for qualitative traits on X chromosome in general pedigrees.

BACKGROUND: Genomic imprinting is one of the well-known epigenetic factors causing the association between traits and genes, and has generally been examined by detecting parent-of-origin effects of alleles. A lot of methods have been proposed to test for parent-of-origin effects on autosomes based on nuclear families and general pedigrees. Although these parent-of-origin effects tests on autosomes have been available for more than 15 years, there has been no statistical test developed to test for parent-of-origin effects on X chromosome, until the parental-asymmetry test on X chromosome (XPAT) and its extensions were recently proposed. However, these methods on X chromosome are only applicable to nuclear families and thus are not suitable for general pedigrees. RESULTS: In this article, we propose the pedigree parental-asymmetry test on X chromosome (XPPAT) statistic to test for parent-of-origin effects in the presence of association, which can accommodate general pedigrees. When there are missing genotypes in some pedigrees, we further develop the Monte Carlo pedigree parental-asymmetry test on X chromosome (XMCPPAT) to test for parent-of-origin effects, by inferring the missing genotypes given the observed genotypes based on a Monte Carlo estimation. An extensive simulation study has been carried out to investigate the type I error rates and the powers of the proposed tests. Our simulation results show that the proposed methods control the size well under the null hypothesis of no parent-of-origin effects. Moreover, XMCPPAT substantially outperforms the existing tests and has a much higher power than XPPAT which only uses complete nuclear families (with both parents) from pedigrees. We also apply the proposed methods to analyze rheumatoid arthritis data for their practical use. CONCLUSIONS: The proposed XPPAT and XMCPPAT test statistics are valid and powerful in detecting parent-of-origin effects on X chromosome for qualitative traits based on general pedigrees and thus are recommended.

Detection of imprinting effects for qualitative traits on X chromosome based on nuclear families.

Methods for detecting imprinting effects have been developed primarily for autosomal markers. However, no method is available in the literature to test for imprinting effects on X chromosome. Therefore, it is necessary to suggest methods for detecting such imprinting effects. In this article, the parental-asymmetry test on X chromosome (XPAT) is first developed to test for imprinting for qualitative traits in the presence of association, based on family trios each with both parents and their affected daughter. Then, we propose 1-XPAT to deal with parent-daughter pairs, each with one parent and his/her affected daughter. By simultaneously considering family trios and parent-daughter pairs, C-XPAT (the combined test statistic of XPAT and 1-XPAT) is constructed to test for imprinting. Further, we extend the proposed methods to accommodate complete (with both parents) and incomplete (with one parent) nuclear families having multiple daughters of which at least one is affected. Simulation results demonstrate that the proposed methods control the size well, irrespective of the inbreeding coefficient in females being zero or non-zero. By incorporating incomplete nuclear families, C-XPAT is more powerful than XPAT using only complete nuclear families. For practical use, these proposed methods are applied to analyse the rheumatoid arthritis data and Turner's syndrome data.

Two Powerful Tests for Parent-of-Origin Effects at Quantitative Trait Loci on the X Chromosome.

Parent-of-origin effects, which describe an occurrence where the expression of a gene depends on its parental origin, are an important phenomenon in epigenetics. Statistical methods for detecting parent-of-origin effects on autosomes have been investigated for 20 years, but the development of statistical methods for detecting parent-of-origin effects on the X chromosome is relatively new. In the literature, a class of Q-XPAT-type tests are the only tests for the parent-of-origin effects for quantitative traits on the X chromosome. In this paper, we propose two simple and powerful classes of tests to detect parent-of-origin effects for quantitative trait values on the X chromosome. The proposed tests can accommodate complete and incomplete nuclear families with any number of daughters. The simulation study shows that our proposed tests produce empirical type I error rates that are close to their respective nominal levels, as well as powers that are larger than those of the Q-XPAT-type tests. The proposed tests are applied to a real data set on Turner's syndrome, and the proposed tests give a more significant finding than the Q-C-XPAT test.

Generalized disequilibrium test for association in qualitative traits incorporating imprinting effects based on extended pedigrees.

BACKGROUND: For dichotomous traits, the generalized disequilibrium test with the moment estimate of the variance (GDT-ME) is a powerful family-based association method. Genomic imprinting is an important epigenetic phenomenon and currently, there has been increasing interest of incorporating imprinting to improve the test power of association analysis. However, GDT-ME does not take imprinting effects into account, and it has not been investigated whether it can be used for association analysis when the effects indeed exist. RESULTS: In this article, based on a novel decomposition of the genotype score according to the paternal or maternal source of the allele, we propose the generalized disequilibrium test with imprinting (GDTI) for complete pedigrees without any missing genotypes. Then, we extend GDTI and GDT-ME to accommodate incomplete pedigrees with some pedigrees having missing genotypes, by using a Monte Carlo (MC) sampling and estimation scheme to infer missing genotypes given available genotypes in each pedigree, denoted by MCGDTI and MCGDT-ME, respectively. The proposed GDTI and MCGDTI methods evaluate the differences of the paternal as well as maternal allele scores for all discordant relative pairs in a pedigree, including beyond first-degree relative pairs. Advantages of the proposed GDTI and MCGDTI test statistics over existing methods are demonstrated by simulation studies under various simulation settings and by application to the rheumatoid arthritis dataset. Simulation results show that the proposed tests control the size well under the null hypothesis of no association, and outperform the existing methods under various imprinting effect models. The existing GDT-ME and the proposed MCGDT-ME can be used to test for association even when imprinting effects exist. For the application to the rheumatoid arthritis data, compared to the existing methods, MCGDTI identifies more loci statistically significantly associated with the disease. CONCLUSIONS: Under complete and incomplete imprinting effect models, our proposed GDTI and MCGDTI methods, by considering the information on imprinting effects and all discordant relative pairs within each pedigree, outperform all the existing test statistics and MCGDTI can recapture much of the missing information. Therefore, MCGDTI is recommended in practice.

Detection of Imprinting Effects for Quantitative Traits on X Chromosome Using Nuclear Families with Multiple Daughters.

Genomic imprinting is an epigenetic phenomenon in which the expression of an allele copy depends on its parental origin. This mechanism has been found to play an important role in many complex diseases. Statistical tests for imprinting effects have been developed for more than 15 years, but they are only suitable for autosomes. It was not until recently that the parental-asymmetry test on the X chromosome (XPAT) was proposed to test for imprinting effects. However, this test can only be used for qualitative traits. Therefore, in this article, we propose a class of PAT-type tests to test for imprinting for quantitative traits on the X chromosome in the presence of association, namely, Q-XPAT(c), Q-1-XPAT(c) and Q-C-XPAT(c), where c is a constant. These methods can accommodate complete and incomplete nuclear families with an arbitrary number of daughters. Extensive simulation studies demonstrate that the proposed tests control the size well under the null hypothesis of no imprinting effects and are powerful under various family structures. Moreover, by setting the inbreeding coefficient in females to be nonzero and using the assortative mating pattern in simulations, the proposed tests are shown to be valid under Hardy-Weinberg disequilibrium.

Two brothers' alleged paternity for a child: who is the father?

In paternity cases where individuals are close relatives, it may be necessary to evaluate mother's DNA profile (trio test) and to increase the number of polymorphic STR loci that are analyzed. In our case, two alleged fathers who are brothers and the child (duo case) were analyzed based on 20 STR loci; however, no exclusions could be achieved. Then trio test (with mother) was performed using the Identifiler Plus kit (Applied Biosystems) and no exclusions could be achieved again. Analysis performed with the ESS Plex Plus kit (Qiagen), the paternity of one of the two alleged fathers was rejected only on 2 STR loci. We made the calculations of power of exclusion values to interpret our results more properly. The probability of exclusion (PE) is calculated as 0.9776546 in 15 loci of Identifiler Plus kit without mother. The PE is calculated as 0.9942803, if 5 additional loci from ESS Plex Plus kit are typed. The PE becomes 0.9961048 for the Identifiler Plus kit in trio analysis. If both Identifiler Plus and ESS Plex Plus kits are used for testing, the PE is calculated as 0.999431654, which indicates that the combined kits are highly discriminating.

A powerful association test for qualitative traits incorporating imprinting effects using general pedigree data.

For qualitative traits and diallelic marker loci, the pedigree disequilibrium test (PDT) based on general pedigrees and its extension (Monte Carlo PDT (MCPDT)) for dealing with missing genotypes are simple and powerful tests for association. There is an increasing interest of incorporating imprinting into association analysis. However, PDT and MCPDT do not take account of the information on imprinting effects in the analysis, which may reduce their test powers when the effects are present. On the other hand, the transmission disequilibrium test with imprinting (TDTI*) combines imprinting into the mapping of association variants. However, TDTI* only accommodates two-generation nuclear families and thus is not suitable for extended pedigrees. In this article, we first extend PDT to incorporate imprinting and propose PDTI for complete pedigrees (no missing genotypes). To fully utilize pedigrees with missing genotypes, we further develop the Monte Carlo PDTI (MCPDTI) statistic based on Monte Carlo sampling and estimation. Both PDTI and MCPDTI are derived in a two-stage framework. Simulation study shows that PDTI and MCPDTI control the size well under the null hypothesis of no association and are more powerful than PDT and TDTI* (based on a sample of nuclear families randomly selecting from pedigrees) when imprinting effects exist.

Detection of parent-of-origin effects for quantitative traits using general pedigree data.

Genomic imprinting is a genetic phenomenon in which certain alleles are differentially expressed in a parent-of-origin-specific manner, and plays an important role in the study of complex traits. For a diallelic marker locus in human, the parentalasymmetry tests Q-PAT(c) with any constant c were developed to detect parent-of-origin effects for quantitative traits. However, these methods can only be applied to deal with nuclear families and thus are not suitable for extended pedigrees. In this study, by making no assumption about the distribution of the quantitative trait, we first propose the pedigree parentalasymmetry tests Q-PPAT(c) with any constant c for quantitative traits to test for parent-of-origin effects based on nuclear families with complete information from general pedigree data, in the presence of association between marker alleles under study and quantitative traits. When there are any genotypes missing in pedigrees, we utilize Monte Carlo (MC) sampling and estimation and develop the Q-MCPPAT(c) statistics to test for parent-of-origin effects. Various simulation studies are conducted to assess the performance of the proposed methods, for different sample sizes, genotype missing rates, degrees of imprinting effects and population models. Simulation results show that the proposed methods control the size well under the null hypothesis of no parent-of-origin effects and Q-PPAT(c) are robust to population stratification. In addition, the power comparison demonstrates that Q-PPAT(c) and Q-MCPPAT(c) for pedigree data are much more powerful than Q-PAT(c) only using two-generation nuclear families selected from extended pedigrees.