Analyzing species distributions among temporary ponds with a permutation test approach to the join-count statistic

The Bluff Springs Sand Ponds (BSSPs) are a set of closely-spaced temporary ponds of varying hydroperiod, depth and surface area. We sampled crustacean communities of 15 ponds throughout hydroperiods in 1996 to examine species distributions among ponds. Although ponds were closely spaced (within ca. 16 ha), most species were present in subsets of the 15 ponds. We then analyzed spatial patterns of 12 crustacean species for complete spatial randomness (CSR) using join-count statistics. However, the join-count was designed for large-samples (n>50), so we further analyzed (by simulation) the join-count and a variation of the join-count (Cliff & Ord, 1981) for small-scale reliability. Simulation results revealed that neither testing distribution was reliable for n<30. We then used a permutation test to analyze species distributions and concluded that some species were distributed non-randomly. Therefore, further investigations of mechanisms causing species distributions (e.g., hydroperiod, physical/chemical conditions, biotic interactions) are clearly prescribed. The permutation test should be useful for studies of species distribution patterns among other temporary waters, and can help focus studies on causal mechanisms of distributions among small numbers of temporary aquatic habitats.     

Relationship between the fine structure and statistic fluctuations in measurement result distributions

The "near zone effect" described first in the macroscopic fluctuations researches was studied by numerical modeling. Possible mechanisms of its formation were proposed, and the lengths of portions of experimental data that retain the fine structure of histograms necessary for studying the "near zone effect" and provide the minimum level of statistical noise.     

On the Asymptotic Relative Efficiency of the Mantel-Haenszel Test

The Mantel-Haenszel test is optimal when the odds ratio is constant. This paper investigates the effects of departures from the assumption of a constant odds ratio on the behavior of the Mantel-Haenzel test. A simple approximation is proposed for the non-null distribution of the test statistic. Based on this approximation, the asymptotic relative efficiency of the Mantel-Haenszel test, compared to the overall χ² test for no partial association, is calculated. For the case of 2 strata, it is shown that the Mantel-Haenszel test is efficient as long as the logarithms of the odds ratios are of the same sign and their absolute values exceed 1.     

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.     

Small-sample inference for the comparison of means of log-normal distributions

We propose a likelihood-based test for comparing the means of two or more log-normal distributions, with possibly unequal variances. A modification to the likelihood ratio test is needed when sample sizes are small. The performance of the proposed procedures is compared with the F-ratio test using Monte Carlo simulations.     

A test statistic to detect errors in sib-pair relationships.

Several authors have proposed algorithms to detect Mendelian errors in human genetic linkage data. Most currently available methods use likelihood-based methods on multiplex family data to identify typing or pedigree errors. These algorithms cannot be applied in many sib-pair collections, because of lack of parental-genotype information. Nonetheless, misspecifying the relationships between individuals has serious consequences for sib-pair linkage studies: false relationships bias the statistics designed to identify linkage with disease phenotypes. To test the hypothesis that two individuals are sibs, we propose a test statistic based on the summation, over a large number of genetic markers, of the number of alleles shared identical by state by a pair of individuals, for each marker. The test statistic has an approximately normal distribution under the null hypothesis, and extreme negative values correspond to nonsib pairs. Power and significance studies show that the test statistic calculated by use of 50 unlinked markers has 96% power to detect half-sibs and has 100% power to detect unrelated individuals as not full-sib pairs, with a 5% false-positive rate. Furthermore, extreme positive values of the test statistic identify sibs as MZ twins.     

Testing hypotheses in case-control studies--equivalence of Mantel-Haenszel statistics and logit score tests.

The two approaches in common use for the analysis of case-control studies are cross-classification by confounding variables, and modeling the logarithm of the odds ratio as a function of exposure and confounding variables. We show here that score statistics derived from the likelihood function in the latter approach are identical to the Mantel-Haenszel test statistics appropriate for the former approach. This identity holds in the most general situation considered, testing for marginal homogeneity in mK tables. This equivalence is demonstrated by a permutational argument which leads to a general likelihood expression in which the exposure variable may be a vector of discrete and/or continuous variables and in which more than two comparison groups may be considered. This likelihood can be used in analyzing studies in which there are multiple controls for each case or in which several disease categories are being compared. The possibility of including continuous variables makes this likelihood useful in situations that cannot be treated using the Mantel-Haenszel cross-classification approach.