Power and Predictive Accuracy of Polygenic Risk Scores

Polygenic scores have recently been used to summarise genetic effects among an ensemble of markers that do not individually achieve significance in a large-scale association study. Markers are selected using an initial training sample and used to construct a score in an independent replication sample by forming the weighted sum of associated alleles within each subject. Association between a trait and this composite score implies that a genetic signal is present among the selected markers, and the score can then be used for prediction of individual trait values. This approach has been used to obtain evidence of a genetic effect when no single markers are significant, to establish a common genetic basis for related disorders, and to construct risk prediction models. In some cases, however, the desired association or prediction has not been achieved. Here, the power and predictive accuracy of a polygenic score are derived from a quantitative genetics model as a function of the sizes of the two samples, explained genetic variance, selection thresholds for including a marker in the score, and methods for weighting effect sizes in the score. Expressions are derived for quantitative and discrete traits, the latter allowing for case/control sampling. A novel approach to estimating the variance explained by a marker panel is also proposed. It is shown that published studies with significant association of polygenic scores have been well powered, whereas those with negative results can be explained by low sample size. It is also shown that useful levels of prediction may only be approached when predictors are estimated from very large samples, up to an order of magnitude greater than currently available. Therefore, polygenic scores currently have more utility for association testing than predicting complex traits, but prediction will become more feasible as sample sizes continue to grow.     

Modeling Linkage Disequilibrium Increases Accuracy of Polygenic Risk Scores

Polygenic risk scores have shown great promise in predicting complex disease risk and will become more accurate as training sample sizes increase. The standard approach for calculating risk scores involves linkage disequilibrium (LD)-based marker pruning and applying a p value threshold to association statistics, but this discards information and can reduce predictive accuracy. We introduce LDpred, a method that infers the posterior mean effect size of each marker by using a prior on effect sizes and LD information from an external reference panel. Theory and simulations show that LDpred outperforms the approach of pruning followed by thresholding, particularly at large sample sizes. Accordingly, predicted R² increased from 20.1% to 25.3% in a large schizophrenia dataset and from 9.8% to 12.0% in a large multiple sclerosis dataset. A similar relative improvement in accuracy was observed for three additional large disease datasets and for non-European schizophrenia samples. The advantage of LDpred over existing methods will grow as sample sizes increase.     

Comparison of the Combined versus Conventional Apgar Scores in Predicting Adverse Neonatal Outcomes

Objectives

Assessing the value of the Combined-Apgar score in predicting neonatal mortality and morbidity compared to the Conventional-Apgar.

Methods

This prospective cohort study evaluated 942 neonates (166 very preterm, 233 near term, and 543 term) admitted to a tertiary referral hospital. At 1- and 5-minutes after delivery, the Conventional and Combined Apgar scores were recorded. The neonates were followed, and the following information was recorded: the occurrence of severe hyperbilirubinemia requiring medical intervention, the requirement for mechanical ventilation, the occurrence of intraventricular hemorrhage (IVH), and neonatal mortality.

Results

Before adjusting for the potential confounders, a low Conventional (<7) or Combined (<10) Apgar score at 5-minutes was associated with adverse neonatal outcomes. However, after adjustment for the gestational age, birth weight and the requirement for neonatal resuscitation in the delivery room, a depressed 5-minute Conventional-Apgar score lost its significant associations with all the measured adverse outcomes; after the adjustments, a low 5-minute Combined-Apgar score remained significantly associated with the requirement for mechanical ventilation (OR,18.61; 95%CI,6.75–51.29), IVH (OR,4.8; 95%CI,1.91–12.01), and neonatal mortality (OR,20.22; 95%CI,4.22–96.88). Additionally, using Receiver Operating Characteristics (ROC) curves, the area under the curve was higher for the Combined-Apgar than the Conventional-Apgar for the prediction of neonatal mortality and the measured morbidities among all the admitted neonates and their gestational age subgroups.

Conclusions

The newly proposed Combined-Apgar score can be a good predictor of neonatal mortality and morbidity in the admitted neonates, regardless of their gestational age and resuscitation status. It is also superior to the Conventional-Apgar in predicting adverse neonatal outcomes in very preterm, near term and term neonates.     

Evidence for Polygenic Epistatic Interactions in Man?

Studies of multifactorial inheritance in man have ignored nonadditive gene action or attributed it entirely to dominance. Reanalyses of dermatoglyphic data on monozygotic and dizygotic twins, siblings and parents and offspring suggest that a substantial proportion of variation in total finger pattern intensity is due to epistatic interactions between additive genetic deviations, not dominance. Bootstrapping and power simulations support this interpretation of the data. We believe this is the strongest evidence so far for polygenic epistasis in man.     

Age-Correction of Test Scores Reduces the Validity of Mild Cognitive Impairment in Predicting Progression to Dementia

Objectives

A phase of mild cognitive impairment (MCI) precedes most forms of neurodegenerative dementia. Many definitions of MCI recommend the use of test norms to diagnose cognitive impairment. It is, however, unclear whether the use of norms actually improves the detection of individuals at risk of dementia. Therefore, the effects of age- and education-norms on the validity of test scores in predicting progression to dementia were investigated.

Methods

Baseline cognitive test scores (Syndrome Short Test) of dementia-free participants aged ≥65 were used to predict progression to dementia within three years. Participants were comprehensively examined one, two, and three years after baseline. Test scores were calculated with correction for (1) age and education, (2) education only, (3) age only and (4) without correction. Predictive validity was estimated with Cox proportional hazard regressions. Areas under the curve (AUCs) were calculated for the one-, two-, and three-year intervals.

Results

82 (15.3%) of initially 537 participants, developed dementia. Model coefficients, hazard ratios, and AUCs of all scores were significant (p<0.001). Predictive validity was the lowest with age-corrected scores (−2 log likelihood  = 840.90, model fit χ² (1)  = 144.27, HR  = 1.33, AUCs between 0.73 and 0.87) and the highest with education-corrected scores (−2 log likelihood  = 815.80, model fit χ² (1)  = 171.16, HR  = 1.34, AUCs between 0.85 and 0.88).

Conclusion

The predictive validity of test scores is markedly reduced by age-correction. Therefore, definitions of MCI should not recommend the use of age-norms in order to improve the detection of individuals at risk of dementia.     

Polygenic inheritance of bean mass

Analogies between plants and animals are often a source of confusion in the understanding of sexual reproduction in green plants

The ancient view that plants are non-sexual because they hold a place below animals on the ladder of nature was still held by many scientists in the 1 8th century. Paradoxically, al this time, Linnaeus and others were also postulating the universality of plant sexuality by using analogies with animals to over-extend the slowly emerging experimental evidence about the functions of floral parts. Today's school leavers seem to have similarly diverse views. A lack of school focus on gamete fusion appears to result in a continuing reliance on analogies with animals, and a belief that plants undergo only a qualified version of sexual reproduction. Suggestions for classroom activities to overcome this are offered, and some wider implications are considered.     

A Fast Method that Uses Polygenic Scores to Estimate the Variance Explained by Genome-wide Marker Panels and the Proportion of Variants Affecting a Trait

Several methods have been proposed to estimate the variance in disease liability explained by large sets of genetic markers. However, current methods do not scale up well to large sample sizes. Linear mixed models require solving high-dimensional matrix equations, and methods that use polygenic scores are very computationally intensive. Here we propose a fast analytic method that uses polygenic scores, based on the formula for the non-centrality parameter of the association test of the score. We estimate model parameters from the results of multiple polygenic score tests based on markers with p values in different intervals. We estimate parameters by maximum likelihood and use profile likelihood to compute confidence intervals. We compare various options for constructing polygenic scores, based on nested or disjoint intervals of p values, weighted or unweighted effect sizes, and different numbers of intervals, in estimating the variance explained by a set of markers, the proportion of markers with effects, and the genetic covariance between a pair of traits. Our method provides nearly unbiased estimates and confidence intervals with good coverage, although estimation of the variance is less reliable when jointly estimated with the covariance. We find that disjoint p value intervals perform better than nested intervals, but the weighting did not affect our results. A particular advantage of our method is that it can be applied to summary statistics from single markers, and so can be quickly applied to large consortium datasets. Our method, named AVENGEME (Additive Variance Explained and Number of Genetic Effects Method of Estimation), is implemented in R software.     

Estimating Polygenic Models for Multivariate Data on Large Pedigrees

We have developed algorithms for the likelihood estimation of additive genetic models for quantitative traits on large pedigrees. The approach uses the expectation L-maximization (EM) algorithm, but avoids intensive computation. In this paper, we focus on extensions of previous work to the case of multivariate data. We exemplify the approach by analyses of bivariate data on a four-generation, 949-member pedigree of the snail Lymnaea elodes, and on a three-generation pedigree of the guppy Poecilia reticulata containing about 400 individuals.     

Polygenic disease: methods for mapping complex disease traits

Improved genotyping technology has made it feasible to use a genetic approach to map genes involved in the etiology of common human diseases. We discuss here recent developments in several different statistical approaches to linkage analysis of these traits, including affected-sib-pair methods, the affected-pedigree-member method, regressive models and linkage-disequilibrium-based approaches. We discuss advantages and disadvantages of the various approaches, as well as factors influencing study design and the ability to detect loci. Statistical methodology in this area is advancing rapidly and will help enable the mapping and cloning of loci involved in susceptibility to common multifactorial diseases.     

Polygenic score for neuroticism is related to sleep difficulties

Neuroticism, a broad trait measure of the tendency to experience negative emotions and vulnerability to stress, is consistently related to poor sleep quality. Less is known about potential pleiotropy in the genetic risk for high neuroticism and poor sleep. Therefore, the present study examined whether polygenic score (PGS) for neuroticism is related to sleep quality in two large samples of adults. In addition, depressive symptoms, anxiety and phenotypical neuroticism were tested as mediators in both samples. Participants were 8316 individuals aged from 50 to 101 years (mean age = 68.29, SD = 9.83) from the Health and Retirement Study, and 4973 individuals aged from 63 to 67 years (mean age = 64.30, SD = 0.68) from the Wisconsin Longitudinal Study. Participants from both samples were genotyped and answered questions on sleep quality. A higher PGS for neuroticism was related to lower sleep quality concurrently and over time in both samples. Anxiety, depressive symptoms and neuroticism mediated these relationships in the two samples. Although effect sizes were small, the present study provides replicable evidence that individuals with a higher genetic predisposition to experience negative emotions and distress are at risk of sleep difficulties.     

Predicting Adolescent Anxiety Ratings From Infant Behavioral Style in Response to Expectancy Violation

Nearly 15 years after infants participated in an operant conditioning task, contact was once again established with the former participants to determine relations between infant behavior in response to expectancy violation during mobile conjugate reinforcement and reported anxiety ratings during adolescence. Shifting infants from a high-stimulation reinforcement contingency to a low-stimulation contingency violated expectancy during the learning task, which elicited negative reactivity, crying, in a number of infants. Original participants and 1 parent were later asked to complete a behavioral assessment questionnaire. Results were consistent with studies that have established relations between early negative reactivity and later internalizing behavior. Infant negative reactivity and poor environmental regulation together significantly contributed to the prediction of higher ratings on a later anxiety scale. Also, infant fear and crying were related and higher fear predicted higher anxiety. Findings also suggested fear is a distinct negative emotional reaction and even early in development can be differentiated from other negative reactivity styles.