Estimation of Fixed and Random Effects in the Functional Nonlinear Errors-in-Variable Model

Consider an experiment where a nonlinear continuous functional relationship exists between y and X. Assume that this relationship has been measured at n replicated points of X from each of t treatments or populations. Assume further that the X are fixed unknown vectors and that the location parameter v is either a fixed unknown vector or a vector of random variables. In the first case various linear hypotheses are to be tested about v, such as tests for main effects and interaction; in the second case, the mean and variance of the random variable v are to be estimated. A two-step procedure based on asymptotic theory is presented to test hypotheses or develop estimates for the fixed effects or random effects functional errors-in-variable model. An example of a one-way random effects model is given.     

Modelling p-value distributions to improve theme-driven survival analysis of cancer transcriptome datasets

Background  

Theme-driven cancer survival studies address whether the expression signature of genes related to a biological process can predict patient survival time. Although this should ideally be achieved by testing two separate null hypotheses, current methods treat both hypotheses as one. The first test should assess whether a geneset, independent of its composition, is associated with prognosis (frequently done with a survival test). The second test then verifies whether the theme of the geneset is relevant (usually done with an empirical test that compares the geneset of interest with random genesets). Current methods do not test this second null hypothesis because it has been assumed that the distribution of p-values for random genesets (when tested against the first null hypothesis) is uniform. Here we demonstrate that such an assumption is generally incorrect and consequently, such methods may erroneously associate the biology of a particular geneset with cancer prognosis.     

陕北烟田多异瓢虫空间分布型与抽样技术研究

根据1995年烟田多异瓢虫Hippodamiavariegats（Goeze）调查,计算了6种分布型指数,以及频次拟合优度检验,结果表明：该虫幼虫、蛹在陕北烟田里聚集分布,其聚集强度随种群密度增加而降低,聚集原因是环境差异;卵块分布同时具有聚集和随机的趋势,成虫为随机分布。同时建立了各虫态的理论抽样量公式,估测种群密度公式。     

Estimating the distribution of a renewal process from times at which events from an independent process are detected

The analysis of length-biased data has been mostly limited to the interarrival interval of a renewal process covering a specific time point. Motivated by a surveillance problem, we consider a more general situation where this time point is random and related to a specific event, for example, status change or onset of a disease. We also consider the problem when additional information is available on whether the event intervals (interarrival intervals covering the random event) end within or after a random time period (which we call a window period) following the random event. Under the assumptions that the occurrence rate of the random event is low and the renewal process is independent of the random event, we provide formulae for the estimation of the distribution of interarrival times based on the observed event intervals. Procedures for testing the required assumptions are also furnished. We apply our results to human immunodeficiency virus (HIV) test data from public test sites in Seattle, Washington, where the random event is HIV infection and the window period is from the onset of HIV infection to the time at which a less sensitive HIV test becomes positive. Results show that the estimator of the intertest interval length distribution from event intervals ending within the window period is less biased than the estimator from all event intervals; the latter estimator is affected by right truncation. Finally, we discuss possible applications to estimating HIV incidence and analyzing length-biased samples with right or left truncated data.     

On the False Discovery Rate and Expected Type I Errors

The paper is concerned with expected type I errors of some stepwise multiple test procedures based on independent p‐values controlling the so‐called false discovery rate (FDR). We derive an asymptotic result for the supremum of the expected type I error rate(EER) when the number of hypotheses tends to infinity. Among others, it will be shown that when the original Benjamini‐Hochberg step‐up procedure controls the FDR at level α, its EER may approach a value being slightly larger than α/4 when the number of hypotheses increases. Moreover, we derive some least favourable parameter configuration results, some bounds for the FDR and the EER as well as easily computable formulae for the familywise error rate (FWER) of two FDR‐controlling procedures. Finally, we discuss some undesirable properties of the FDR concept, especially the problem of cheating.     

Confidence Intervals and Tests of Hypotheses on Variance Components in an Unbalanced Two-fold Nested Design

Confidence intervals and tests of hypotheses on variance components are required in studies that employ a random effects design. The unbalanced random two-fold nested design is considered in this paper and confidence intervals are proposed for the variance components σ2/A and σ2/B. Computer simulation is used to show that even in very unbalanced designs, these intervals generally maintain the stated confidence coefficient. The hypothesis test for σ2/A based on the lower bound of the recommended confidence interval is shown to be better than previously proposed approximate tests.     

A completion simulator for the two-sided truncated normal distribution

This paper presents simulation formulae of two-sided truncated normal random variables using a completion distribution and its two corresponding conditionals generated via a Gibbs sampler. This procedure extends formulae given by Robert and Casella for the one-sided case.     

STORM: software for testing hypotheses of relatedness and mating patterns

Storm is a software package that allows users to test a variety of hypotheses regarding patterns of relatedness and patterns of mate choice and/or mate compatibility within a population. These functions are based on four main calculations that can be conducted either independently or in the hypothesis-testing framework: internal relatedness; homozygosity by loci; pairwise relatedness; and a new metric called allele inheritance, which calculates the proportion of loci at which an offspring inherits a paternal allele different from that inherited from its mother. STORM allows users to test four hypotheses based on these calculations and Monte Carlo simulations: (i) are individuals within observed associations or groupings more/less related than expected; (ii) do observed offspring have more/less genetic variability (based on internal relatedness or homozygosity by loci) than expected from the gene pool; (iii) are observed mating pairs more/less related than expected if mating is random with respect to relatedness; and (iv) do observed offspring inherit paternal alleles different from those inherited from the mother more/less often than expected based on Mendelian inheritance.     

Tests of Occupancy Rates for Clustered Populations: Case Where the Cluster Sizes are Known

A modified chi-squared statistic Z is proposed for testing hypotheses about category occupancy rates for individuals distributed by clusters, when the cluster sizes are observed. This statistic is the Pearson chi-square statistic based on the individuals' counts divided by 1 + M* where M* is the mean number of other individuals per cluster per individual. The kind of alternative hypothesis for which the Z-based test compares favourably in power with the Pearson chi-square test based on the cluster frequencies is given. However, we prove that this latter test is more powerful than the former one as long as the equidistribution of the random choice vectors is assumed.     

Primary attraction and random landing in host‐selection by wood‐feeding insects: a matter of scale?

1 Most plant‐feeding insects show some degree of specialization and use a variety of cues to locate their host. Two main mechanisms of host location, primary attraction and random landing, have been investigated for such insects. 2 Research has led to contradictory conclusions about those hypotheses, especially for wood‐feeding insects; however, recent studies suggest that both mechanisms may take place in a single taxon but at different scales. 3 We developed a field experiment to test the hypothesis that primary attraction occurs at larger scale and random landing at finer scale in wood‐feeding insects. Landing rates, measured using sticky traps, were compared first between patches and then between individual trees according to their distance to a baited central tree. 4 Polynomial functions describing landing rate to distance relationships were compared with a function produced by a null model describing what should occur under the random landing hypothesis. Scolytidae and Cerambycidae (Coleoptera) responded to volatiles at the patch scale, supporting the primary attraction hypothesis, but the landing patterns of some groups at finer scale matched closely the predictions of our null model, giving support to the random landing hypothesis. 5 Our results show that the primary attraction and random landing hypotheses are not mutually exclusive and that prelanding use of host‐produced volatile is scale‐dependant. Scale considerations should thus be included in the study of prelanding host‐selection of wood‐feeding insects.     

Symmetric group sequential test designs

In Phase III clinical trials, ethical considerations often demand interim analyses in order that the better treatment be made available to all patients as soon as possible. Group sequential test designs that do not treat the hypotheses symmetrically may not fully address this concern since early termination of the study may be easier under one of the hypotheses. We present a one-parameter family of symmetric one-sided group sequential designs that are nearly fully efficient in terms of the average sample number. The symmetric tests are then extended to a two-sided hypothesis test. These symmetric two-sided group sequential tests are found to have improved overall efficiency when compared to the tests proposed by Pocock (1977, Biometrika 64, 191-199) and O'Brien and Fleming (1979, Biometrics 35, 549-556). Tables of critical values for both one-sided and two-sided symmetric designs are provided, thus allowing easy determination of sample sizes and stopping boundaries for a group sequential test. Approximate tests based on these designs are proposed for use when the number and timing of analyses are random.     

On using Lehmann alternatives with nonresponders.

The problem of testing for treatment effect when some subjects in the treatment group may be unaffected by the treatment is considered. A form of the Lehmann alternative suggested by Conover and Salsburg is used that assumes that each control score has the same distribution as the minimum of the known number of responses in the treatment group. It is shown that the locally most powerful test leads to a test statistic that, under the hypothesis of no treatment effect, is the sum of independent pareto random variables whereas under the alternative hypothesis it is the sum of independent random variables from a mixture of two pareto distributions. The limiting distribution of the test statistic under both hypotheses is in the domain of attraction of a stable distribution whose indices are derived. The power of the test is given, and its properties are discussed. A set of data from clinical research involving development of a new drug is used to show application of the procedure and demonstrate its usefulness.     

A note on testing separability in spatial-temporal marked point processes

Summary .   In environmental risk analysis, it is common to assume the stochastic independence (or separability) between the marks associated with the random events of a spatial-temporal point process. Schoenberg (2004, Biometrics 60, 471–481) proposed several test statistics for this hypothesis and used simulated data to evaluate their performance. He found that a Cramér-von Mises-type test is powerful to detect gradual departures from separability although it is not uniformly powerful over a large class of alternative models. We present a semiparametric approach to model alternative hypotheses to separability and derive a score test statistic. We show that there is a relationship between this score test and some of the test statistics proposed by Schoenberg. Specifically, all are different versions of weighted Cramér-von Mises-type statistics. This gives some insight into the reasons for the similarities and differences between the test statistics' performance. We also point out some difficulties in controlling the type I error probability in Schoenberg's residual test.     

Statistical distributions of test statistics used for quantitative trait association mapping in structured populations

Background

Spurious associations between single nucleotide polymorphisms and phenotypes are a major issue in genome-wide association studies and have led to underestimation of type 1 error rate and overestimation of the number of quantitative trait loci found. Many authors have investigated the influence of population structure on the robustness of methods by simulation. This paper is aimed at developing further the algebraic formalization of power and type 1 error rate for some of the classical statistical methods used: simple regression, two approximate methods of mixed models involving the effect of a single nucleotide polymorphism (SNP) and a random polygenic effect (GRAMMAR and FASTA) and the transmission/disequilibrium test for quantitative traits and nuclear families. Analytical formulae were derived using matrix algebra for the first and second moments of the statistical tests, assuming a true mixed model with a polygenic effect and SNP effects.

Results

The expectation and variance of the test statistics and their marginal expectations and variances according to the distribution of genotypes and estimators of variance components are given as a function of the relationship matrix and of the heritability of the polygenic effect. These formulae were used to compute type 1 error rate and power for any kind of relationship matrix between phenotyped and genotyped individuals for any level of heritability. For the regression method, type 1 error rate increased with the variability of relationships and with heritability, but decreased with the GRAMMAR method and was not affected with the FASTA and quantitative transmission/disequilibrium test methods.

Conclusions

The formulae can be easily used to provide the correct threshold of type 1 error rate and to calculate the power when designing experiments or data collection protocols. The results concerning the efficacy of each method agree with simulation results in the literature but were generalized in this work. The power of the GRAMMAR method was equal to the power of the FASTA method at the same type 1 error rate. The power of the quantitative transmission/disequilibrium test was low. In conclusion, the FASTA method, which is very close to the full mixed model, is recommended in association mapping studies.     

A Regional analysis of Maize Biological Diversity in Southeastern Guanajuato, MéXico

Four environments with contrasting potential for agricultural productivity and infrastructure development were identified in Guanajuato State, México, to test hypotheses about the relaciónship of maize biological diversity to the region’s potential for agricultural productivity and infrastructure development. Samples of all types of maize grown by a random sample of farmers were collected from each environment. Landraces were the dominant maize class in all four environments; the use of improved varieties was negligible. Several diversity indices were calculated, and no statistically significant differences were apparent between the environments with the most contrasting agroecological and infrastructural conditions. Statistical differences in diversity are apparent when the development of infrastructure interacts with agroecological factors in an environment. Qualitative data suggest that the richness of maize populations may be associated with maize yield potential in a geographical area, whereas the evenness of maize populations may be associated with the presence of infrastructure. These findings suggest further hypotheses about regional patterns of maize diversity.     

Spike correlations in a songbird agree with a simple markov population model

The relationships between neural activity at the single-cell and the population levels are of central importance for understanding neural codes. In many sensory systems, collective behaviors in large cell groups can be described by pairwise spike correlations. Here, we test whether in a highly specialized premotor system of songbirds, pairwise spike correlations themselves can be seen as a simple corollary of an underlying random process. We test hypotheses on connectivity and network dynamics in the motor pathway of zebra finches using a high-level population model that is independent of detailed single-neuron properties. We assume that neural population activity evolves along a finite set of states during singing, and that during sleep population activity randomly switches back and forth between song states and a single resting state. Individual spike trains are generated by associating with each of the population states a particular firing mode, such as bursting or tonic firing. With an overall modification of one or two simple control parameters, the Markov model is able to reproduce observed firing statistics and spike correlations in different neuron types and behavioral states. Our results suggest that song- and sleep-related firing patterns are identical on short time scales and result from random sampling of a unique underlying theme. The efficiency of our population model may apply also to other neural systems in which population hypotheses can be tested on recordings from small neuron groups.     

Random Networks of Catalytie Biochemical Reactions

Formulae for the probabilities of components and cycles and of their numerical distribution are obtained for large random networks by computer experiments and combinatorical considerations. Probability considerations are made and formulae for the occurrence and distribution of cycles and of components of certain number, size and structure are received for random networks.     

Exact and Asymptotic Power Determination For Dose‐Response Studies With Ordinal Response

In this article, we describe a conditional score test for detecting a monotone dose‐response relationship with ordinal response data. We consider three different versions of this test: asymptotic, conditional exact, and mid‐P conditional score test. Exact and asymptotic power formulae based on these tests will be studied. Asymptotic sample size formulae based on the asymptotic conditional score test will be derived. The proposed formulae are applied to a vaccination study and a developmental toxicity study for illustrative purposes. Actual significance level and exact power properties of these tests are compared in a small empirical study. The mid‐P conditional score test is observed to be the most powerful test with actual significance level close to the pre‐specified nominal level.     

EVALUATING KINSHIP OF NEWLY SETTLED JUVENILES WITHIN SOCIAL GROUPS OF THE CORAL REEF FISH ANTHIAS SQUAMIPINNIS

It is conventionally assumed that eggs and/or larvae of most coral reef fishes are thoroughly mixed during a pelagic phase, so that juvenile recruits at any particular reef site represent a random sample of the reproductive products entering the local gene pool. However, a recent review of biological factors that might limit mixing raised the testable hypothesis that groups of genetically related individuals may sometimes persist through the pelagic phase and settle as sibling cohorts (Shapiro, 1983). Here we provide a critical genetic test of this hypothesis by examining allozyme variation in juvenile aggregations of the serranid reef fish, Anthias squamipinnis. Results demonstrate that juvenile cohorts within large social groups in Anthias are not composed exclusively or predominantly of siblings, but rather represent a random sample of progeny from many matings. Also included are considerations of allelic and genotypic criteria by which hypotheses about sibling assemblages might generally be evaluated.