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.     

P-values For Discrete Test Statistics

This paper considered the relative merits of the P-value and the mid-P-value. It is shown that inference based on the mid-P-value is in a certain sense on firmer ground. In particular the expected mid-P-value does not change under an irrelevant breakup in the test statistic.     

Small Sample Properties of the Mantel-Haenszel Test Statistic for Density Follow-Up Studies

For the analysis of combinations of 2×2 non-contingency tables as obtained from density follow-up studies (relating a number of events to a number of person-years of follow-up) an analogue of the Mantel-Haenszel test for 2×2 contingency tables is widely used. In this paper the small sample properties of this test, both with and without continuity correction, are evaluated. Also the improvement of the test-statistic by using the first four cumulants via the Edgeworth expansion was studied. Results on continuity correction agree with similar studies on the Mantel-Haenszel statistic for 2×2 contingency tables: Continuity correction gives a p-value which approximates the exact p-value better than the p-value obtained without this correction; both the exact test and its approximations show considerable conservatism in small samples; the uncorrected Mantel-Haenszel test statistic gives a p-value that agrees more with the nominal significance level, but can be anti-conservative. The p-value based on the first four cumulants gives a better approximation of the exact p-value than the continuity corrected test, especially when the distribution has marked skewness.     

MAX-rank: a simple and robust genome-wide scan for case-control association studies

In genome-wide association studies (GWAS), single-marker analysis is usually employed to identify the most significant single nucleotide polymorphisms (SNPs). The trend test has been proposed for analysis of case-control association. Three trend tests, optimal for the recessive, additive and dominant models respectively, are available. When the underlying genetic model is unknown, the maximum of the three trend test results (MAX) has been shown to be robust against genetic model misspecification. Since the asymptotic distribution of MAX depends on the allele frequency of the SNP, using the P-value of MAX for ranking may be different from using the MAX statistic. Calculating the P-value of MAX for 300,000 (300 K) or more SNPs is computationally intensive and the software and program to obtain the P-value of MAX are not widely available. On the other hand, the MAX statistic is very easy to calculate without complex computer programs. Thus, we study whether or not one could use the MAX statistic instead of its P-value to rank SNPs in GWAS. The approaches using the MAX and its P-value to rank SNPs are referred to as MAX-rank and P-rank. By applying MAX-rank and P-rank to simulated and four real datasets from GWAS, we found the ranks of SNPs with true association are very similar using both approaches. Thus, we recommend to use MAX-rank for genome-wide scans. After the top-ranked SNPs are identified, their P-values based on MAX can be calculated and compared with the significance level. The work of Q. Li was partially supported by the Knowledge Innovation Program of the Chinese Academy of Sciences, No. 30465W0 and 30475V0. The research of Z Li was partially sponsored by NIH grant EY014478.     

A note on P-values for two-sided tests

Based on uniformly most powerful unbiased (UMPU) tests for two-sided hypotheses and a short note in Lehmann (1959) on critical levels for randomized tests, Meulepas (1998, 1999) proposed (two-tailed) P -values taking into account the randomization constant(s) of the UMPU-tests. While UMPU-tests need an extra uniform observation if randomization is required, the P -values proposed by Meulepas need no extra uniform observation. At first glance, his idea looks very promising in order to define a suitable and powerful P -value. Unfortunately, such P -values are generally too conservative.     

Fine scale mapping of a genetic locus for conditioned fear

Abstract Fear conditioning is one of a number of models for investigating the genetic basis of individual variation in emotion and learning. Genetic mapping using crosses between strains of laboratory mice has identified a locus on chromosome one that appears to influence not only variation in conditioned fear, but also in other validated tests of fear-related behaviour, (including the open-field and the elevated-plus maze), suggesting that the rodent locus may act in ways consistent with how a locus influencing susceptibility to anxiety in humans is believed to operate. Here we use high-resolution mapping in genetically heterogeneous mice to show that a quantitative trait locus influencing conditioned fear can be separated from loci influencing open-field activity. Mapping in two different heterogeneous stocks, the Boulder and Northport HS, gave similar map locations for open-field activity at two positions on the current mouse physical map, one at 162 Mb on chromosome one (negative log P-value 5.4) the other at 173 Mb (negative log P-value 4.8), while mapping of contextual conditioned fear in the Boulder HS identified a locus at 170 Mb (negative log P-value 5.4). Estimates of the 95% confidence intervals show that the locations do not overlap. The region containing a gene or genes that influence variation in conditioned fear is approximately 1 megabase in size and contains only one gene of known function, a pre-B cell leukaemia factor.     

Fuzzy p-values in latent variable problems

We consider the problem of testing a statistical hypothesiswhere the scientifically meaningful test statistic is a functionof latent variables. In particular, we consider detection ofgenetic linkage, where the latent variables are patterns ofinheritance at specific genome locations. Introduced by Geyer& Meeden (2005), fuzzy p-values are random variables, describedby their probability distributions, that are interpreted asp-values. For latent variable problems, we introduce the notionof a fuzzy p-value as having the conditional distribution ofthe latent p-value given the observed data, where the latentp-value is the random variable that would be the p-value ifthe latent variables were observed. The fuzzy p-value provides an exact test using two sets of simulationsof the latent variables under the null hypothesis, one unconditionaland the other conditional on the observed data. It providesnot only an expression of the strength of the evidence againstthe null hypothesis but also an expression of the uncertaintyin that expression owing to lack of knowledge of the latentvariables. We illustrate these features with an example of simulateddata mimicking a real example of the detection of genetic linkage.     

Rank Tests for Complete Block Designs

In this article a general univariate K-sample rank test for complete block designs with proportional cell frequencies is derived. It is shown that the test statistic has under H₀ and for arbitrary scores asymptotically a X²-distribution with K — 1 degrees of freedom. Special cases of this test are the Kruskal-Wallis test and the Friedman test. The test is compared with the Benard-van-Elteren test, the Mack-Skillings test and a test proposed by Downton. Finally the application of the test is illustrated by two examples.     

The generalized Fisher's combination and accurate p-value calculation under dependence

Combining dependent tests of significance has broad applications but the related p-value calculation is challenging. For Fisher's combination test, current p-value calculation methods (eg, Brown's approximation) tend to inflate the type I error rate when the desired significance level is substantially less than 0.05. The problem could lead to significant false discoveries in big data analyses. This paper provides two main contributions. First, it presents a general family of Fisher type statistics, referred to as the GFisher, which covers many classic statistics, such as Fisher's combination, Good's statistic, Lancaster's statistic, weighted Z-score combination, and so forth. The GFisher allows a flexible weighting scheme, as well as an omnibus procedure that automatically adapts proper weights and the statistic-defining parameters to a given data. Second, the paper presents several new p-value calculation methods based on two novel ideas: moment-ratio matching and joint-distribution surrogating. Systematic simulations show that the new calculation methods are more accurate under multivariate Gaussian, and more robust under the generalized linear model and the multivariate t-distribution. The applications of the GFisher and the new p-value calculation methods are demonstrated by a gene-based single nucleotide polymorphism (SNP)-set association study. Relevant computation has been implemented to an R package GFisher available on the Comprehensive R Archive Network.     

The Discrete Distribution Used for the Log-rank Test Can Be Inaccurate

When the number of tumors is small, a significance level for the Cox-Mantel (log-rank) test Z is often computed using a discrete approximation to the permutation distribution. For j = 0,…, J let N_j(t) be the number of animals in group j alive and tumor-free at the start of time t. Make a 2 × (1+J) table for each time t of the number of animals R_j(t) with newly palpated tumor out of the total N_j(t) at risk. There are a total of say K tables, one for each distinct time t with observed death or newly palpated tumor. The usual discrete approximation to the permutation distribution of Z is defined by taking tables to be independent with fixed margins N_j(t) and ΣR_j(t) for all t. However, the N_j(t) are random variables for the actual permutation distribution of Z, resulting in dependence among the tables. Calculations for the exact permutation distribution are explained, and examples are given where the exact significance level differs substantially from the usual discrete approximation. The discrepancy arisis primarily because permutations with different Z-scores under the exact distribution can be equal for the discrete approximation, inflating the approximate P-value.     

Regression Trees for Survival Data — an Approach to Select Discontinuous Split Points by Rank Statistics

Regression trees allow to search for meaningful explanatory variables that have a non linear impact on the dependent variable. Often they are used when there are many covariates and one does not want to restrict attention to only few of them. To grow a tree at each stage one has to select a cut point for splitting a group into two subgroups. The basis for this are the maxima of the test statistics related to the possible splits due to every covariate. They or the resulting P-values are compared as measure of importance. If covariates have different numbers of missing values, ties, or even different measurement scales the covariates lead to different numbers of tests. Those with a higher number of tests have a greater chance to achieve a smaller P-value if they are not adjusted. This can lead to erroneous splits even if the P-values are looked at informally. There is some theoretical work by Miller and Siegmund (1982) and Lausen and Schumacher (1992) to give an adjustment rule. But the asymptotic is based on a continuum of split points and may not lead to a fair splitting rule when applied to smaller data sets or to covariates with only few different values. Here we develop an approach that allows determination of P-values for any number of splits. The only approximation that is used is the normal approximation of the test statistics. The starting point for this investigation has been a prospective study on the development of AIDS. This is presented here as the main application.     

The effects of human tear electrolytes on the viability and hydrogel colonization of Pseudomonas aeruginosa and Staphylococcus aureus

This study was designed to evaluate the effects of the inorganic electrolytes present in human tear film on the viability and colonization of bacteria to hydrogels. Pseudomonas aeruginosa and Staphylococcus aureus were used in these experiments. A D-value test was performed to investigate any bacteriostatic effect by measuring the reduction of viable test microorganisms over time when exposed to the inorganic electrolyte solution. No D-value was calculable for S. aureus in electrolyte solution whereas a D-value of 8.1 h was obtained for P. aeruginosa in electrolyte solution. The D-value data indicate that staphylococci have a greater survivability potential in a hypertonic environment than do pseudomonads. Bacterial adhesion to high water, ionic hydrogels was studied using the Modified Robbins Device (MRD). The data for P. aeruginosa recovered from the lenses showed an 82% decrease in bacterial counts in electrolyte solution as compared to bacteria incubated in control solution. In contrast there were slight increases in S. aureus counts recovered from the lenses. Journal of Industrial Microbiology & Biotechnology (2000) 25, 17–19. Received 12 August 1999/ Accepted in revised form 05 January 2000     

The Relationship Between Two Statistical Tests for the Comparison of Two Exponential Distributions

To compare two exponential distributions with or without censoring, two different statistics are often used; one is the F test proposed by COX (1953) and the other is based on the efficient score procedure. In this paper, the relationship between these tests is investigated and it is shown that the efficient score test is a large-sample approximation of the F test.     

Identification of a combination of SNPs associated with Graves’ disease using swarm intelligence

Graves’ disease, the production of thyroid-stimulating hormone receptor-stimulating antibodies leading to hyperthyroidism, is one of the most common forms of human autoimmune disease. It is widely agreed that complex diseases are not controlled simply by an individual gene or DNA variation but by their combination. Single nucleotide polymorphisms (SNPs), which are the most common form of DNA variation, have great potential as a medical diagnostic tool. In this paper, the P-value is used as a SNP pre-selection criterion, and a wrapper algorithm with binary particle swarm optimization is used to find the rule for discriminating between affected and control subjects. We analyzed the association between combinations of SNPs and Graves’ disease by investigating 108 SNPs in 384 cases and 652 controls. We evaluated our method by differentiating between cases and controls in a five-fold cross validation test, and it achieved a 72.9% prediction accuracy with a combination of 17 SNPs. The experimental results showed that SNPs, even those with a high P-value, have a greater effect on Graves’ disease when acting in a combination.     

Genetic association analysis of KCNQ3 and juvenile myoclonic epilepsy in a South Indian population

Juvenile myoclonic epilepsy (JME) is a common subtype of idiopathic generalized epilepsy that shows a complex pattern of inheritance. We have tested the association between JME phenotype and an intragenic marker in KCNQ3 by using the transmission disequilibrium test in 119 probands and their parents. Mutations in KCNQ3 are known to cause benign familial neonatal convulsions and are involved in the physiologically important M current in neurons. Our results provide suggestive evidence of allelic association between JME and KCNQ3 (P-value=0.008) and raise an interesting possibility of a genetic contribution to JME, viz., of a gene that causes a monogenic form of human epilepsy.     

The influence of radioactive phosphate level on the absorption of phosphate by plants and on the determination of labile soil phosphate

Summary Previous work has suggested that the presence of P³² in fertilizers inhibits the uptake of the applied phosphate from the soil by plants, and also that if the applied phosphate is not incorporated uniformly in the soil there will be preferential uptake from regions of low specific activity. This made it desirable to determine the effect of P³²-level on phosphate uptake and the determination ofL-values in pot experiments in which the labelled phosphate source is added as discrete particles of the phosphate form of an anion-exchange resin.Increasing the level of P³² from 0.05 to 1.25 mo per gram of phosphorus in the added phosphate did not have a significant effect on the fresh weight, dry weight or total phosphorus uptake of the ryegrass crop. The measuredL-value showed a significant increase, about 15 per cent for a five-fold increase in P³² level, on each of the four soil types used, as would be expected if P³² depressed the uptake of labelled fertilizer phosphate.Although a significant effect of P³² was observed this does not invalidate a comparison of soils with respect toL-value.     

Transmission disequilibrium and sequence variants at the leptin receptor gene in extremely obese German children and adolescents

Genetic determinants of the degree of obesity and body fat distribution have been demonstrated by family studies. The heritability has been estimated to be in the range 0.2–0.7. Mutation leading to obesity in humans has been described for only two genes, one of them the leptin gene. The leptin gene codes for a cytokine secreted by fat cells that binds to the leptin receptor (Lep-R), which exerts some of its biological functions by expression in the brain. Hence, the Lep-R gene appears to be a promising candidate for the determination of obesity in humans. We isolated genomic DNA clones from the Lep-R gene region and identified a new polymorphic microsatellite marker (OBR-CA) within 80 kb of the translation start of Lep-R. We genotyped this and a second, intragenic microsatellite marker (D1S2852) in 130 nuclear families consisting of extremely obese children and adolescents and both parents. Using the most frequent parental allele of both markers, our analysis revealed a significant transmission disequilibrium for the 266-bp allele of D1S2852 (corrected P-value=0.042). No significant result was obtained with the most frequent allele of OBR-CA (corrected P-value=1.0). However, two rare alleles showed transmission disequilibrium and were subsequently used for constructing a haplotype with the 266-bp allele. This haplotype had a transmission rate of 80% (nominal P-value=0.02). In order to identify the underlying mutation, we sequenced all coding exons of Lep-R and the partially overlapping gene encoding the obese receptor gene-related protein (ob-rgrp) in individuals carrying this haplotype. We found one new mutation (Ser675Thr) in the Lep-R gene in one proband and several other mutations known to be not associated with obesity in other study groups. As this new mutation cannot explain our positive linkage result, the transmission disequilibrium of the 266-bp allele and the high transmission rate of the identified haplotype point towards a mutation in close proximity to marker D1S2852. Received: 9 March 1998 / Accepted: 17 July 1998     

A genetic association test through combining two independent tests

Gene- and pathway-based variant association tests are important tools in finding genetic variants that are associated with phenotypes of interest. Although some methods have been proposed in the literature, powerful and robust statistical tests are still desirable in this area. In this study, we propose a statistical test based on decomposing the genotype data into orthogonal parts from which powerful and robust independent p-value combination approaches can be utilized. Through a comprehensive simulation study, we compare the proposed test with some existing popular ones. Our simulation results show that the new test has great performance in terms of controlling type I error rate and statistical power. Real data applications are also conducted to illustrate the performance and usefulness of the proposed test.     

Expression of insulin-like growth factor-II,matrix metalloproteinases,and their tissue inhibitors as predictive markers in the peripheral blood of HCC patients

Background/aim: Elevated relative expression of insulin-like growth factor-II (IGF-II) was observed in hepatocellular carcinoma (HCC) liver tissues with a role in neovascularization and associated with poor prognosis. IGF-II is influenced by the proteolytic cleavage of IGF-binding protein 3 and by matrix metalloproteinases (MMP), which are further regulated by their tissue inhibitors tissue inhibitor of metalloprotienase-1 (TIMP-1). Our aim is to study new molecular markers for HCC.

Patients/methods: RNA was extracted from the peripheral blood for evaluating the relative expression of IGF-II, MMP-9, and TIMP-1 in correlation with clinical staging of 39 HCC patients and 15 healthy controls using TaqMan real-time PCR.

Results: The relative expression of IGF-II and MMP-9 mRNA were significantly elevated in HCC patients compared with healthy controls; P-value <0.0001 for both. There was a significant correlation between MMP-9 and different HCC stages. On the other hand, TIMP-1 was significantly down-regulated in HCC patients; P?=?0.0003 with the elevation of the IGF-II/TIMP-1 ratio. Significant correlation between TIMP-1 and HCC Stage III and Stage IV was found; P-value?=?0.0138.

Conclusion: These results highlight the importance of profiling the expression of IGF-II, MMP-9, and TIMP-1 in the peripheral blood as prognostic molecular biomarkers in HCC.     

Smoking-related DNA adducts in anal epithelium

Several studies have identified tobacco smoking as a risk factor for anal cancer in both women and men. Samples of anal epithelium from haemorrhoidectomy specimens from current smokers (n=20) and age-matched life-long non-smokers (n=16) were analysed for DNA adducts by the nuclease P₁ digestion enhancement procedure of ³²P-postlabelling analysis. The study included 14 men and 22 women. Both qualitative and quantitative differences in the adduct profiles were observed between the smokers and non-smokers. The mean adduct level was significantly higher in the smokers than in the non-smokers (1.88±0.71 (S.D.) versus 1.36±0.60 adducts per 10⁸ nucleotides, P=0.02, two-tailed unpaired t-test with Welch’s correction); furthermore, the adduct pattern seen in two-dimensional chromatograms revealed the smoking-related diagonal radioactive zone in 17/20 smokers, but not in any of the non-smokers (P<0.00001, Fisher’s exact test). These results indicate that components of tobacco smoke inflict genotoxic damage in the anal epithelium of smokers and provide a plausible mechanism for a causal association between smoking and anal cancer.