On Fisher's Method of Combining p-Values

The problem of combining p-values from independent experiments is discussed. It is shown that Fisher's solution to the problem can be derived from a “weight-free” method that has been suggested for the purpose of ranking vector observations (Biometrics 19: 85–97, 1963). The method implies that the value p = 0.37 is a critical one: p-values below 0.37 suggest that the null hypothesis is more likely to be false, whereas p-values above 0.37 suggest that it is more likely to be true.     

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.     

A Note on Plots of P-Values to Evaluate Many Tests Simultaneously

Schweder and Spjøtvoll (1982) proposed an informal graphical procedure for simultaneous evaluation of possibly related tests, based on a plot of cumulative p-values using the observed significance probabilities. We formalize this notion by application of Holm's (1979) sequentially rejective Bonferroni procedure: this maintains an overall experimentwise significance level, and yields an immediate estimate of the number of true hypotheses.     

Distribution-free Estimation of a Monotonic pth Quantile Function

When analyzing biological data sets, a frequent problem is to estimate the pth quantile of a distribution, when that quantile is assumed to depend on a covariate; in the present paper the dependence of the quantile on the covariate is assumed to be monotonic. Some properties of an isotonic pth quantile regression, considered as an estimator of an increasing pth quantile function, are presented.     

Permanent night workers´ sleep and psychosocial factors in hospital work. A comparison to day and shift work

ABSTRACT

We aimed to study whether permanent night workers sleep and psychosocial factors differ from day workers and shift workers. The participants (n = 9 312, 92% females, average age 45 years, most commonly nurses and departmental secretaries) were day workers (DW, n = 2 672), shift workers (SW, n = 6 486) and permanent night workers (PNW, n = 154). The Finnish Public Sector survey responses from six hospital districts from 2012 were combined to payroll data from 91 days preceding the survey. The data were analyzed using Pearson χ²-test, one-way ANOVA and multinomial logistic regression analysis. The PNWs reported slightly longer average sleep length than the SWs or the DWs (7:27 vs. 7:13 and 7:10 h, p < 0.001). The PNWs reported least often difficulties in maintaining sleep (p < 0.001) compared to the SWs and the DWs. The PNWs reported most often difficulties to fall asleep and fatigue during free-time (p-values <0.001). The DWs and PNWs experienced less often work-life conflict than the SWs (25 and 26 vs. 38%, p < 0.001). The PNWs were more often satisfied with autonomy at work and appreciation and fair treatment by colleagues than the DWs or the SWs (p < 0.001). The SWs and PNWs reported remarkably higher occurrence of verbal (p < 0.001, OR 3.71, 95% CI 3.23–4.27 and OR 7.67, 95% CI 5.35–10.99, respectively) and physical workplace violence (p < 0.001, OR 9.24, 95% CI 7.17–11.90 and OR 28.34, 95% CI 16.64–43.06, respectively) compared to DWs. Conclusively, PNWs reported contradictory differences in sleep quality compared to DWs and SWs. PNWs are more often satisfied with their colleagues and autonomy at work than DWs or SWs but face workplace violence remarkably more often.     

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.     

sdef: an R package to synthesize lists of significant features in related experiments

Background  

In microarray studies researchers are often interested in the comparison of relevant quantities between two or more similar experiments, involving different treatments, tissues, or species. Typically each experiment reports measures of significance (e.g. p-values) or other measures that rank its features (e.g genes). Our objective is to find a list of features that are significant in all experiments, to be further investigated. In this paper we present an R package called sdef, that allows the user to quantify the evidence of communality between the experiments using previously proposed statistical methods based on the ranked lists of p-values. sdef implements two approaches that address this objective: the first is a permutation test of the maximal ratio of observed to expected common features under the hypothesis of independence between the experiments. The second approach, set in a Bayesian framework, is more flexible as it takes into account the uncertainty on the number of genes differentially expressed in each experiment.     

The effects of γ-rays on poly-L-glutamic acid in aqueous solution

Summary Salt-free and 0.2 M NaCl oxygenated aqueous solutions of poly-L-glutamic acid were irradiated with⁶⁰Co--radiation at variouspH's to examine whether or not the changes caused by the exposure to ionizing radiation depend onpH, that is, the conformations of polypeptide.TheG-values (the number of main-chain scissions per 100 eV of energy absorbed) in both salt-free and 0.2 M NaCl solutions of poly-L-glutamic acid were found to change sharply withpH. and to have a maximum value at thepH of a mid-point of helix-coil transition. The change ofG-values withpH was discussed in terms of the conformational change of poly-L-glutamic acid.     

Unconditional Non-Asymptotic One-Sided Tests for Independent Binomial Proportions When the Interest Lies in Showing Non-Inferiority and/or Superiority

For two independent binomial proportions Barnard (1947) has introduced a method to construct a non-asymptotic unconditional test by maximisation of the probabilities over the ‘classical’ null hypothesis H₀= {(θ₁, θ₂) ∈ [0, 1]²: θ₁ = θ₂}. It is shown that this method is also useful when studying test problems for different null hypotheses such as, for example, shifted null hypotheses of the form H₀ = {(θ₁, θ₂) ∈ [0, 1]²: θ₂ ≤ θ₁ ± Δ } for non-inferiority and 1-sided superiority problems (including the classical null hypothesis with a 1-sided alternative hypothesis). We will derive some results for the more general ‘shifted’ null hypotheses of the form H₀ = {(θ₁, θ₂) ∈ [0, 1]²: θ₂ ≤ g(θ₁ )} where g is a non decreasing curvilinear function of θ₁. Two examples for such null hypotheses in the regulatory setting are given. It is shown that the usual asymptotic approximations by the normal distribution may be quite unreliable. Non-asymptotic unconditional tests (and the corresponding p-values) may, therefore, be an alternative, particularly because the effort to compute non-asymptotic unconditional p-values for such more complex situations does not increase as compared to the classical situation. For ‘classical’ null hypotheses it is known that the number of possible p-values derived by the unconditional method is very large, albeit finite, and the same is true for the null hypotheses studied in this paper. In most of the situations investigated it becomes obvious that Barnard's CSM test (1947) when adapted to the respective null space is again a very powerful test. A theorem is provided which in addition to allowing fast algorithms to compute unconditional non-asymptotical p-values fills a methodological gap in the calculation of exact unconditional p-values as it is implemented, for example, in Stat Xact 3 for Windows (1995).     

A comparative review of estimates of the proportion unchanged genes and the false discovery rate

Background  

In the analysis of microarray data one generally produces a vector of p-values that for each gene give the likelihood of obtaining equally strong evidence of change by pure chance. The distribution of these p-values is a mixture of two components corresponding to the changed genes and the unchanged ones. The focus of this article is how to estimate the proportion unchanged and the false discovery rate (FDR) and how to make inferences based on these concepts. Six published methods for estimating the proportion unchanged genes are reviewed, two alternatives are presented, and all are tested on both simulated and real data. All estimates but one make do without any parametric assumptions concerning the distributions of the p-values. Furthermore, the estimation and use of the FDR and the closely related q-value is illustrated with examples. Five published estimates of the FDR and one new are presented and tested. Implementations in R code are available.     

An improved procedure for gene selection from microarray experiments using false discovery rate criterion

Background  

A large number of genes usually show differential expressions in a microarray experiment with two types of tissues, and the p-values of a proper statistical test are often used to quantify the significance of these differences. The genes with small p-values are then picked as the genes responsible for the differences in the tissue RNA expressions. One key question is what should be the threshold to consider the p-values small. There is always a trade off between this threshold and the rate of false claims. Recent statistical literature shows that the false discovery rate (FDR) criterion is a powerful and reasonable criterion to pick those genes with differential expression. Moreover, the power of detection can be increased by knowing the number of non-differential expression genes. While this number is unknown in practice, there are methods to estimate it from data. The purpose of this paper is to present a new method of estimating this number and use it for the FDR procedure construction.     

Classical biological control in an ephemeral crop habitat with Anticarsia gemmatalis nucleopolyhedrovirus

Anticarsia gemmatalis nucleopolyhedrovirus(AgNPV) was released as a single spray in soybean at two sites in Louisiana, near Crowley and Baton Rouge, after which viral prevalence and population density were monitored for 3--4 years. Each site had a plot with no treatment (control) and two virus-treated plots, one planted with soybean yearly for 3-4 years, and the other planted with soybean for 3-4 years except for rotation to a different crop in year 2. In year 1, the single spray ofAgNPV resulted in viral prevalence rates ranging from 25--100% A. gemmatalis mortality over the entire growing season. By the end of this season, viral accumulation in soil averaged 4.1 ×10⁴ occlusion bodies (OB)/g at Crowley and 7.4× 10³ OB/g at Baton Rouge, which had a sandier soil than Crowley. At Crowley, prevalence of AgNPVreached 49% insect mortality in the unrotated plot in year 2, and 31% in the rotated plot and 38% in the unrotated plot in year 3, in spite of moderate to low population densities of A. gemmatalis. At Baton Rouge, AgNPV prevalence decreased to peak prevalence rates of 25% insect mortality in year 2,4% in year 3, and 11% in year 4, even though A. gemmatalis population densities were moderate in years 2 and 3. Viral concentration in soil decreased to 2.7 × 10² OB/g (rotated plot) and1.4 × 10⁴ OB/g (unrotated plot) by the end of year 3 at Crowley and to 10 OB/g (rotated plot) and31 OB/g (unrotated plot) by the end of year 4 at Baton Rouge. In forward stepwise multiple regressions, the concentration of OB in soil was significantly (p = 0.0001) and positively correlated with AgNPV prevalence, but correlations of the latter parameter with host population density and rainfall were not significant (p > 0.05). Prevalence rates of the fungal entomopathogen Nomuraea rileyi were significantly (p < 0.01) and negatively correlated with AgNPV prevalence at Crowley but not in the combined data set. Prevalence of N. rileyi was negatively correlated (p = 0.0001) with precipitation and positively correlated (p = 0.0001) with A.gemmatalis population density. The research demonstrated that AgNPV can be introduced and established for long-term suppression of A.gemmatalis in an ephemeral crop habitat, but certain site-related conditions, perhaps relating to soil, are necessary for its continued success. This revised version was published online in July 2006 with corrections to the Cover Date.     

GABA accumulation and oxidative damage responses to salt,osmotic and H2O2 treatments in two lentil (Lens culinaris Medik) accessions

Abiotic stresses such as cold, drought, heat, salinity, nutrient deficiency, and toxicity adversely affect lentil yields worldwide. Therefore, the purpose of this study was to investigate the response of two lentil cultivars (Lens culinaris Medik) (Jordan 1 and Jordan 2) to NaCl, mannitol, sorbitol, and H₂O₂ via the characterization of seed germination, accumulation of reactive oxygen species, and γ-aminobutyric acid (GABA) level. There was a significant increase in GABA and malondialdehyde (MDA) levels in the two lentil cultivars under all treatments. Jordan 1 showed the highest germination percentages with p-values: 0.009, 0.013, 0.026, and 0.015, while Jordan 2 seedlings showed the highest GABA levels with p-values: 0.023, 0.007, 0.023, and 0.019 and MDA accumulation with p-values: 0.009, 0.012, 0.007, and 0.009 under salt, osmotic, and oxidative stresses, respectively, compared with Jordan 1 seedlings under the same treatments. Our results indicate that GABA shunt is a key signaling and metabolic pathway that allows adaptation of lentil seedlings to salt, osmotic, and oxidative stresses. In addition, Jordan 1 cultivar showed significant tolerance to abiotic stress treatments and it is the most recommended lentil cultivar to be used in soil with high salt and osmotic contents.     

A weighted FDR procedure under discrete and heterogeneous null distributions

Multiple testing (MT) with false discovery rate (FDR) control has been widely conducted in the “discrete paradigm” where p-values have discrete and heterogeneous null distributions. However, in this scenario existing FDR procedures often lose some power and may yield unreliable inference, and for this scenario there does not seem to be an FDR procedure that partitions hypotheses into groups, employs data-adaptive weights and is nonasymptotically conservative. We propose a weighted p-value-based FDR procedure, “weighted FDR (wFDR) procedure” for short, for MT in the discrete paradigm that efficiently adapts to both heterogeneity and discreteness of p-value distributions. We theoretically justify the nonasymptotic conservativeness of the wFDR procedure under independence, and show via simulation studies that, for MT based on p-values of binomial test or Fisher's exact test, it is more powerful than six other procedures. The wFDR procedure is applied to two examples based on discrete data, a drug safety study, and a differential methylation study, where it makes more discoveries than two existing methods.     

rPCMP: robust <Emphasis Type="Italic">p</Emphasis>-value combination by multiple partitions with applications to ATAC-seq data

Background

Evaluating the significance for a group of genes or proteins in a pathway or biological process for a disease could help researchers understand the mechanism of the disease. For example, identifying related pathways or gene functions for chromatin states of tumor-specific T cells will help determine whether T cells could reprogram or not, and further help design the cancer treatment strategy. Some existing p-value combination methods can be used in this scenario. However, these methods suffer from different disadvantages, and thus it is still challenging to design more powerful and robust statistical method.

Results

The existing method of Group combined p-value (GCP) first partitions p-values to several groups using a set of several truncation points, but the method is often sensitive to these truncation points. Another method of adaptive rank truncated product method(ARTP) makes use of multiple truncation integers to adaptively combine the smallest p-values, but the method loses statistical power since it ignores the larger p-values. To tackle these problems, we propose a robust p-value combination method (rPCMP) by considering multiple partitions of p-values with different sets of truncation points. The proposed rPCMP statistic have a three-layer hierarchical structure. The inner-layer considers a statistic which combines p-values in a specified interval defined by two thresholds points, the intermediate-layer uses a GCP statistic which optimizes the statistic from the inner layer for a partition set of threshold points, and the outer-layer integrates the GCP statistic from multiple partitions of p-values. The empirical distribution of statistic under null distribution could be estimated by permutation procedure.

Conclusions

Our proposed rPCMP method has been shown to be more robust and have higher statistical power. Simulation study shows that our method can effectively control the type I error rates and have higher statistical power than the existing methods. We finally apply our rPCMP method to an ATAC-seq dataset for discovering the related gene functions with chromatin states in mouse tumors T cell.

     

Stability and Folding of Endoglucanase I (CEL7B) from Humicoia Insolens

Cellulases are of economic significance, particularly in the detergent and textile industries, where they are subjected to a wide range of operating conditions affecting their stability. To increase our insight into the properties of this class of enzymes, we have carried out a study of the stability and folding behavior of the 413-residue endoglucanase I (Ce17B) from Humicola insolens. Data from chemical denaturation in guanidinium chloride agree satisfactorily with calorimetric measurements, revealing an optimum stability of ca. 20 kcal mol^?1 around p^H 7 and a peak half-width of 3 -4 p^H units. Stability and activity show very similar p^H-profiles, but this is probably fortuitous. Judging from equilibrium m-values (the dependence of the log of the equilibrium unfolding constant on the denaturant concentration), the denatured state becomes significantly more compact outside p^H 6–9.

Folding and unfolding proceed very slowly with relaxation half times up to 6h. Single- and double-jump kinetic data at p^H 7 suggest a folding scheme involving two intermediates with native-like secondary structure but varying degrees of tertiary structure.     

Considerations on Representative Water Quality Data

The aim of this paper is to give a brief summary concerning important methodological aspects in establishing the reliability of empirical water quality data. These considerations are relevant for applied work e.g. monitoring programmes, as well as theoretical research, e.g. to validate models. The paper concerns data from Swedish lakes on Hg in pike, perch, water and sediments, and a broad set of limnological data (pH, Secchi depth, temperature, alkalinity, total-P, conductivity, Fe, Ca, hardness, chlorophyll-a and colour). These standard parameters generally vary in a lake, both temporally and areally. The focus of this paper is on such variations and how to express lake-typical values. There are large differences in analytical reliability for different parametres; e.g. Hg (in fish and sediments but not in water) and lake pH can generally be determined with a comparatively great accuracy; the average relative standard deviation (V) is only about 2-3% for pH. Colour, Fe-, total-P-concentration and alkalinity, on the other hand, generally give high V-values. In natural lakes, the variability is often at least twice as large as the “methodological” variability for parameters such as colour, P, Fe and alkalinity (V-values ranging between 20 and 40% on average in our lakes). This implies that for most parameters one must analyse many samples to obtain representative, lake-typical values with a given statistical reliability. A general furmula expressing how many samples are required to establish lake-typical mean values is discussed as well as statistical aspects concerning the range of empirical data in models based on such data.     

International Society of Chronobiology: Membership Information

Most variables of interest in laboratory medicine show predictable changes with several frequencies in the span of time investigated. The waveform of such nonsinusoidal rhythms can be well described by the use of multiple components rhythmometry, a method that allows fitting a linear model with several cosine functions. The method, originally described for analysis of longitudinal time series, is here extended to allow analysis of hybrid data (time series sampled from a group of subjects, each represented by an individual series). Given k individual series, we can fit the same linear model with m different frequencies (harmonics or not from one fundamental period) to each series. This fit will provide estimations for 2m + 1 parameters, namely, the amplitude and acrophase of each component, as well as the rhythm-adjusted mean. Assuming that the set of parameters obtained for each individual is a random sample from a multivariate normal population, the corresponding population parameter estimates can be based on the means of estimates obtained from individuals in the sample. Their confidence intervals depend on the variability among individual parameter estimates. The vari-ance-covariance matrix can then be estimated on the basis of the sample covariances. Confidence intervals for the rhythm-adjusted mean, as well as for the amplitude-acrophase pair, of each component can then be computed using the estimated covariance matrix. The p-values for testing the zero-amplitude assumption for each component, as well as for the global model, can finally be derived using those confidence intervals and the t and F distributions. The method, validated by a simulation study and illustrated by an example of modeling the circadian variation of heart rate, represents a new step in the development of statistical procedures in chronobiology.