Gene Level Meta-Analysis of Quantitative Traits by Functional Linear Models

Meta-analysis of genetic data must account for differences among studies including study designs, markers genotyped, and covariates. The effects of genetic variants may differ from population to population, i.e., heterogeneity. Thus, meta-analysis of combining data of multiple studies is difficult. Novel statistical methods for meta-analysis are needed. In this article, functional linear models are developed for meta-analyses that connect genetic data to quantitative traits, adjusting for covariates. The models can be used to analyze rare variants, common variants, or a combination of the two. Both likelihood-ratio test (LRT) and F-distributed statistics are introduced to test association between quantitative traits and multiple variants in one genetic region. Extensive simulations are performed to evaluate empirical type I error rates and power performance of the proposed tests. The proposed LRT and F-distributed statistics control the type I error very well and have higher power than the existing methods of the meta-analysis sequence kernel association test (MetaSKAT). We analyze four blood lipid levels in data from a meta-analysis of eight European studies. The proposed methods detect more significant associations than MetaSKAT and the P-values of the proposed LRT and F-distributed statistics are usually much smaller than those of MetaSKAT. The functional linear models and related test statistics can be useful in whole-genome and whole-exome association studies.     

Distributions of Hardy-Weinberg equilibrium test statistics

It is well established that test statistics and P-values derived from discrete data, such as genetic markers, are also discrete. In most genetic applications, the null distribution for a discrete test statistic is approximated with a continuous distribution, but this approximation may not be reasonable. In some cases using the continuous approximation for the expected null distribution may cause truly null test statistics to appear nonnull. We explore the implications of using continuous distributions to approximate the discrete distributions of Hardy–Weinberg equilibrium test statistics and P-values. We derive exact P-value distributions under the null and alternative hypotheses, enabling a more accurate analysis than is possible with continuous approximations. We apply these methods to biological data and find that using continuous distribution theory with exact tests may underestimate the extent of Hardy–Weinberg disequilibrium in a sample. The implications may be most important for the widespread use of whole-genome case–control association studies and Hardy–Weinberg equilibrium (HWE) testing for data quality control.     

Blinded sample size recalculation in multiple composite population designs with normal data and baseline adjustments

The increasing interest in subpopulation analysis has led to the development of various new trial designs and analysis methods in the fields of personalized medicine and targeted therapies. In this paper, subpopulations are defined in terms of an accumulation of disjoint population subsets and will therefore be called composite populations. The proposed trial design is applicable to any set of composite populations, considering normally distributed endpoints and random baseline covariates. Treatment effects for composite populations are tested by combining p-values, calculated on the subset levels, using the inverse normal combination function to generate test statistics for those composite populations while the closed testing procedure accounts for multiple testing. Critical boundaries for intersection hypothesis tests are derived using multivariate normal distributions, reflecting the joint distribution of composite population test statistics given no treatment effect exists. For sample size calculation and sample size, recalculation multivariate normal distributions are derived which describe the joint distribution of composite population test statistics under an assumed alternative hypothesis. Simulations demonstrate the absence of any practical relevant inflation of the type I error rate. The target power after sample size recalculation is typically met or close to being met.     

Some notes on the distribution and certain modifications of Mahalanobis' generalized distance (D)

Different modifications of Mahalanobis' generalized distance (D²) utilized in anthropological research are given, and it is shown that they all derive from the distribution of D² when the distances between the populations investigated are real. To investigate whether observed distances are real, testing of D² for significance is stressed. It is demonstrated that D² ought to be tested for significance according to its relation to the F-distribution, but that it may be related to the chi-squared distribution as an approximation when the numbers of individuals in the samples are very large. The great disadvantages of utilizing this approximation for smaller numbers of individuals in the samples are demonstrated, as well as the dependence of D² on sample size and the number of measurements used when testing for significance.     

Subset Selection for Exponential Populations: Determination of the Selection Constant

Given are k(≧2) exponential populations differing only in their location parameter. One wishes to choose the best one, that is the population with the largest value of the location parameter. A possible method for solving this problem is to select a subset of the k populations of size at least one which includes the best population with a required confidence P*(k^?1 ≤ P* ≤1). In this paper the required selection constant is determined for different values of k and P*. Also an approximation for the selection constant is derived. A comparison with the exact results is made.     

Evidence that cognitive deficit in children is associated not only with iron deficiency,but also with blood lead concentration: A preliminary study

ObjectiveTo investigate whether blood lead concentrations are elevated in iron-deficient children, and to examine the association between iron deficiency and/or elevated blood lead concentration and cognitive deficits in children.MethodThe present study is a component of the Mothers’ and Children's Environmental Health (MOCEH) study, a multi-center birth cohort project in Korea that began in 2006. The study cohort consisted of 194 children who underwent testing of blood lead and serum C-reactive proteins (CRPs) and ferritin concentrations, and the Korean version of the Wechsler Preschool and Primary Scale of Intelligence, revised edition (WPPSI-R), at 60 months of age. In addition, the mothers’ blood lead concentrations during pregnancy were included in the analyses. Multivariate linear regression analysis was performed to analyze the correlation between high blood lead and low serum ferritin concentrations, after adjustment for covariates, in children, as well as to analyze the association of verbal IQ with serum ferritin and blood lead concentrations.ResultsLead and ferritin concentrations were inversely and significantly associated in children after adjustment for covariates. Moreover, both concentrations were associated with verbal IQ, after adjustment for covariates, and each was associated with cognitive deficits after adjustment for the other. Sobel test statistics showed that blood lead concentration was a significant partial mediator for the relationship between iron deficiency and verbal IQ.ConclusionDue to the results discussed in the present study, cognitive deficit in children seems to be associated not only with iron deficiency, but also with blood lead concentration.     

Adaptive Combination of P-Values for Family-Based Association Testing with Sequence Data

Family-based study design will play a key role in identifying rare causal variants, because rare causal variants can be enriched in families with multiple affected subjects. Furthermore, different from population-based studies, family studies are robust to bias induced by population substructure. It is well known that rare causal variants are difficult to detect from single-locus tests. Therefore, burden tests and non-burden tests have been developed, by combining signals of multiple variants in a chromosomal region or a functional unit. This inevitably incorporates some neutral variants into the test statistics, which can dilute the power of statistical methods. To guard against the noise caused by neutral variants, we here propose an ‘adaptive combination of P-values method’ (abbreviated as ‘ADA’). This method combines per-site P-values of variants that are more likely to be causal. Variants with large P-values (which are more likely to be neutral variants) are discarded from the combined statistic. In addition to performing extensive simulation studies, we applied these tests to the Genetic Analysis Workshop 17 data sets, where real sequence data were generated according to the 1000 Genomes Project. Compared with some existing methods, ADA is more robust to the inclusion of neutral variants. This is a merit especially when dichotomous traits are analyzed. However, there are some limitations for ADA. First, it is more computationally intensive. Second, pedigree structures and founders'' sequence data are required for the permutation procedure. Third, unrelated controls cannot be included. We here show that, for family-based studies, the application of ADA is limited to dichotomous trait analyses with full pedigree information.     

A P-Value for an Exact Two-Sided Test of Hardy-Weinberg Equilibrium

A two-tailed P-value is proposed for testing two-sided departures from Hardy-Weinberg equilibrium at a diallelic locus. The calculation of P uses the exact conditional distribution of the test statistic P, the observed number of heterozygotes in the sample. The proposed P-value is always two-tailed, unlike other P-values proposed in the literature.     

Trials and tribulations of statistical significance in biochemistry and omics

Over recent years many statisticians and researchers have highlighted that statistical inference would benefit from a better use and understanding of hypothesis testing, p-values, and statistical significance. We highlight three recommendations in the context of biochemical sciences. First recommendation: to improve the biological interpretation of biochemical data, do not use p-values (or similar test statistics) as thresholded values to select biomolecules. Second recommendation: to improve comparison among studies and to achieve robust knowledge, perform complete reporting of data. Third recommendation: statistical analyses should be reported completely with exact numbers (not as asterisks or inequalities). Owing to the high number of variables, a better use of statistics is of special importance in omic studies.     

A Two-Tailed P-Value for Fisher's Exact Test

A two-tailed P-value is presented for a significance test in two by two contingency tables. There is no extraneous quasi-observation such as is needed in the exact randomized uniformly most powerful unbiased (UMPU) test of the hypothesis of independence. The proposed P-value can never exceed unity and is always two-tailed, unlike other P-values proposed in the literature     

Modulation of aggregate size- and shape-distributions of the amyloid-β peptide by a designed β-sheet breaker

A peptide with 42 amino acid residues (Aβ42) plays a key role in the pathogenesis of the Alzheimer’s disease. It is highly prone to self aggregation leading to the formation of fibrils which are deposited in amyloid plaques in the brain of diseased individuals. In our study we established a method to analyze the aggregation behavior of the Aβ peptide with a combination of sedimentation velocity centrifugation and enhanced data evaluation software as implemented in the software package UltraScan. Important information which becomes accessible by this methodology is the s-value distribution and concomitantly also the shape-distribution of the Aβ peptide aggregates generated by self-association. With this method we characterized the aggregation modifying effect of a designed β-sheet breaker molecule. This compound is built from three head-to-tail connected aminopyrazole moieties and represents a derivative of the already described Tripyrazole. By addition of this compound to a solution of the Aβ42 peptide the maximum of the s-value distribution was clearly shifted to smaller s-values as compared to solutions where only the vehicle DMSO was added. This shift to smaller s-values was stable for at least 7 days. The information about size- and shape-distributions present in aggregated Aβ42 solutions was confirmed by transmission electron microscopy and by measurement of amyloid formation by thioflavin T fluorescence.     

RAPD variation among and within small and large populations of the rare clonal plant Ranunculus reptans (Ranunculaceae)

In the pre-alpine region of Europe numbers and sizes of populations of the clonal lake shore plant Ranunculus reptans have declined because of the regulation of lake water levels. We investigated genetic variation among and within 17 populations of different size (cover 1–10 000 m²) in R. reptans with RAPD (random amplified polymorphic DNA) profiles. We sampled 127 rosettes in 14 populations at Lake Constance and three populations at or near Lake Como. There was significant genetic variation between plants from the two lake regions (5.9%, analysis of molecular variance [AMOVA], P < 0.001), among populations within lake regions (20.4%, P < 0.001), and within populations (73.7%, P < 0.001). Under the assumptions of Wright's island model the variation among populations corresponds to a gene flow of N_em = 0.70. Within the 14 Lake Constance populations we detected significant genetic variation among subpopulations separated by only a few metres (4.0% of the within-population variation; P < 0.05). Molecular variance was 24% smaller in small populations covering <100 m² area than in larger ones (P < 0.03), indicating that samples from large populations were genetically more variable than samples representing comparable areas of smaller populations. We conclude that gene flow among populations is very limited and that genetic drift has caused reduced genetic variability of smaller populations. Conservation of genetic variability in R. reptans requires persistence of large and also of small populations (because of population differentiation), and it could be enhanced by increasing the size of small populations (to counter genetic drift).     

Comparing Power Behaviours for Some Goodness-of-Fit Test Statistics in Sparse Multinomials

This paper is concerned with the power behaviour of four goodness-of-fit test statistics in sparse multinomials with k cells. Most previous work has been concerned only with both Pearson's X² and the likelihood ratio test statistics. We consider in this study, two additional test statistics, namely, the Cressie-Read test statistic – I(2/3) and the modified Freeman-Tukey test (FT) statistic. Because k ≥ 10 in this study, a Monte Carlo procedure based on 1000 simulated samples is used to estimate the powers for the four test statistics. Alternatives on various line segments are employed. Results suggest that none of the test statistics completely dominate the other and that the choice of which test to use depends on the nature of the alternative hypothesis. These results are consistent with those obtained by West and Kempthorne (1972), although, the Pearson's χ² test statistic may be preferred because of its closer approximation to the χ² distribution in terms of the attained α levels.     

Permeability studies on luminous bacteria

Summary The changes in light intensity of suspensions of a luminous bacterium in solutions of different electrolytes and non-electrolytes have been watched using an electronic photometer. The rapidity of the gradual extinction of the light was used as an approximate measure of the rapidity of penetration of the substances tested.The results concerning non-electrolytes and amino-acids are summarized in Table 10. (TheP _r -values of this table represent only quite crude estimations of the permeability.)The permeability towards both cations and anions seems to be very small.On the whole, the permeability properties of the bacterium studied seem fairly similar to those of the cells of higher plants.This investigation has been supported by a grant from The State Scientific Council. The author is indebted to Dr. Veijo Wartiovaara for valuable suggestions and to Mr. Sverker Norrback for careful technical assistance.     

False discovery rate control for multiple testing based on discrete p-values

For multiple testing based on discrete p-values, we propose a false discovery rate (FDR) procedure “BH+” with proven conservativeness. BH+ is at least as powerful as the BH (i.e., Benjamini-Hochberg) procedure when they are applied to superuniform p-values. Further, when applied to mid-p-values, BH+ can be more powerful than it is applied to conventional p-values. An easily verifiable necessary and sufficient condition for this is provided. BH+ is perhaps the first conservative FDR procedure applicable to mid-p-values and to p-values with general distributions. It is applied to multiple testing based on discrete p-values in a methylation study, an HIV study and a clinical safety study, where it makes considerably more discoveries than the BH procedure. In addition, we propose an adaptive version of the BH+ procedure, prove its conservativeness under certain conditions, and provide evidence on its excellent performance via simulation studies.     

Comparison of two unsupervised learning algorithms

The binary decision element described by the decision rule depending upon weight vector w is a model of neuron examined in this paper. The environment of the element is described by some unknown, stationary distribution p(x). The input signals x[n] of the element appear in each step n independently in accordance with the distribution p(x). During an unsupervised learning process the weight vector w[n] is changed on the base of the input vector x[n]. In the paper there are regarded two self-learning algorithms which are stochastic approximation type. For both algorithms the same rule of past experiences neglecting or the rule of weight decrease has been introduced. The first algorithm differs from the other one by a rule of weight increase. It has been proved that only one of these algorithms always leads to the same decision rule in a given environment p(x).This work was done during stay of Dr. L. Bobrowski at the University of Salerno in the frame of Polish-Italian Agreement on Scientific Cooperation     

Das Vorkommen von Phytol und Geranylgeraniol in den Bacteriochlorophyllen roter und grüner Schwefelbakterien

The bacteriochlorophylls a of 38 strains belonging to 15 different species of the purple sulfur bacteria (Chromatiaceae) were studied with respect to the nature of the esterifying alcohol. The classical bacteriochlorophyll a_P containing phytol is the main bacteriochlorophyll in all strains. The new bacteriochlorophyll a_Gg occurs as a minor component in addition to bacteriochlorophyll a_P only in five species.The esterifying alcohol of the bacteriochlorophyll a of the reaction centers of all seven type strains of the Chlorobiaceae was shown to be phytol.The compounds withR _f -values between the bacteriophaeophytins a_P and a_Gg found by thin-layer-chromatography were shown to be artifacts of the preparation technique.All strains of the bacteriochlorophyll b-containing purple bacteria have phytol as the major esterifying alcohol; in addition, small amounts of bacteriochlorophyll b are esterified with another alcohol which is most probably all-trans-geranylgeraniol.

---

Abkürzungen DSM Deutsche Sammlung von Mikroorganismen - Bchl. Bacteriochlorophyll Herrn Prof. Dr. Dr. e. h. Hans Brockmann zum 70. Geburtstag gewidmet.     

Thermal Inactivation of Salmonella Serotypes in Red Meat as Affected by Fat Content

Survival curves of a cocktail of eight serotypes of Salmonella in ground beef and pork meat of different levels of fat (4% to 28%), at temperatures that ranged from 58°C to 65°C, were examined. Asymptotic D-values (D-values for large times) and initial D-values (D-values for small times, near zero) were estimated by identifying regions where the survival curves were linear, and performing linear regressions on data within the identified regions. The initial lag D-values increase with increasing fat levels for both beef and pork. The relationship of the asymptotic D-values with fat levels and temperature is complex, and definitive conclusions could not be made. It appears that, for ground beef, asymptotic D-values increase with increasing fat levels, but this was not the case for ground pork. The shapes of the survival curves were concave, convex, and sigmoidal, and depended upon the temperature, where for the lower temperatures studied (58°C and 60°C) the curves exhibited tailing. The Gompertz function was found to provide a good fit to the data over the range of temperatures and fat levels studied. These results, particularly for beef, suggest the importance of determining the shape of the survival curves (concave, convex or sigmoidal) when estimating times needed to obtain an adequate margin of safety for thermal processes of red meat.     

Eveningness as a risk for behavioral problems in late adolescence

Circadian preference toward eveningness has been associated with increased risk for mental health problems both in early adolescence and in adulthood. However, in late adolescence, when circadian rhythm naturally shifts to later, its significance for mental health is not clear. Accordingly, we studied how circadian rhythm estimated both by self-reported chronotype and by actigraph-defined midpoint of sleep was associated with self-reported psychiatric problems based on Youth Self Report (YSR). The study builds on a community cohort born in 1998, Helsinki, Finland. At age 17 years (mean age = 16.9, SD = 0.1 years), 183 adolescents (65.6% of the invited) participated in the study. We used the shortened version of the Horne-Östberg morningness–eveningness Questionnaire to define the chronotype, and actigraphs to define the naturally occur circadian rhythm over a 4 to 17 days’ period (mean nights N = 8.3, SD = 1.8). The Achenbach software was used to obtain T-score values for YSR psychiatric problem scales. The analyses were adjusted for important covariates including gender, socioeconomic status, body mass index, pubertal maturation, mother’s licorice consumption during pregnancy, and actigraph-defined sleep duration and quality. Eveningness was associated with higher scores in rule-breaking behavior and conduct problems (as assessed either by midpoint of sleep or by self-reported chronotype, p-values <0.05), attention deficit/hyperactivity problems (by self-reported chronotype, p-values <0.05), with affective problems (by midpoint of sleep and by self-reported chronotype, p-values <0.05) and somatic complaints (by self-reported chronotype, p-values <0.05), as compared to circadian tendency toward morningness. Our results suggest that the association between eveningness and externalizing problem behavior, present in children and younger adolescents, is also present in late adolescence when circadian rhythms shift toward evening.