Testing the ratio of two poisson rates

In this paper we compare the properties of four different general approaches for testing the ratio of two Poisson rates. Asymptotically normal tests, tests based on approximate p -values, exact conditional tests, and a likelihood ratio test are considered. The properties and power performance of these tests are studied by a Monte Carlo simulation experiment. Sample size calculation formulae are given for each of the test procedures and their validities are studied. Some recommendations favoring the likelihood ratio and certain asymptotic tests are based on these simulation results. Finally, all of the test procedures are illustrated with two real life medical examples.     

Simple Methods for Testing the Molecular Evolutionary Clock Hypothesis

Simple statistical methods for testing the molecular evolutionary clock hypothesis are developed which can be applied to both nucleotide and amino acid sequences. These methods are based on the chi-square test and are applicable even when the pattern of substitution rates is unknown and/or the substitution rate varies among different sites. Furthermore, some of the methods can be applied even when the outgroup is unknown. Using computer simulations, these methods were compared with the likelihood ratio test and the relative rate test. The results indicate that the powers of the present methods are similar to those of the likelihood ratio test and the relative rate test, in spite of the fact that the latter two tests assume that the pattern of substitution rates follows a certain model and that the substitution rate is the same among different sites, while such assumptions are not necessary to apply the present methods. Therefore, the present methods might be useful.     

Likelihood ratio tests for detecting positive selection and application to primate lysozyme evolution

An excess of nonsynonymous substitutions over synonymous ones is an important indicator of positive selection at the molecular level. A lineage that underwent Darwinian selection may have a nonsynonymous/synonymous rate ratio (dN/dS) that is different from those of other lineages or greater than one. In this paper, several codon-based likelihood models that allow for variable dN/dS ratios among lineages were developed. They were then used to construct likelihood ratio tests to examine whether the dN/dS ratio is variable among evolutionary lineages, whether the ratio for a few lineages of interest is different from the background ratio for other lineages in the phylogeny, and whether the dN/dS ratio for the lineages of interest is greater than one. The tests were applied to the lysozyme genes of 24 primate species. The dN/dS ratios were found to differ significantly among lineages, indicating that the evolution of primate lysozymes is episodic, which is incompatible with the neutral theory. Maximum- likelihood estimates of parameters suggested that about nine nonsynonymous and zero synonymous nucleotide substitutions occurred in the lineage leading to hominoids, and the dN/dS ratio for that lineage is significantly greater than one. The corresponding estimates for the lineage ancestral to colobine monkeys were nine and one, and the dN/dS ratio for the lineage is not significantly greater than one, although it is significantly higher than the background ratio. The likelihood analysis thus confirmed most, but not all, conclusions Messier and Stewart reached using reconstructed ancestral sequences to estimate synonymous and nonsynonymous rates for different lineages.      

The effect of conditional dependence on the evaluation of diagnostic tests

The accuracy of a new diagnostic test is often determined by comparison with a reference test which also has unknown error rates. Maximum likelihood estimation of the error rates of both tests is possible if they are simultaneously applied to two populations with different disease prevalences. The estimation procedure assumes that the two tests are independent, conditional on a subject's true diagnostic status. If the tests are conditionally dependent, error rates for both tests can be substantially underestimated. Estimators for the prevalence rates in the two populations can be positively or negatively biased, depending on the relative magnitude of the two conditional covariances and the value of the prevalence parameter.     

Nonparametric estimation and testing in a cure model.

Nonparametric generalized maximum likelihood product limit point estimators and confidence intervals are given for a cure model with random censorship. One-, two-, and K-sample likelihood ratio tests for inference on the cure rates are developed. In the two-sample case its power is compared to the power of several alternatives, including the log-rank and Gray and Tsiatis (1989, Biometrics 45, 899-904) tests. Implications for the use of the likelihood ratio test in a clinical trial designed to compare cure rates are discussed.     

Preponderance of slightly deleterious polymorphism in mitochondrial DNA: nonsynonymous/synonymous rate ratio is much higher within species than between species

We estimated synonymous (dN) and nonsynonymous (dS) substitution rates for protein-coding genes of the mitochondrial genome from two individuals each of the species human, chimpanzee, and gorilla. The genes were analyzed both separately and in a combined data set. Pairwise sequence comparisons suggest that the dN/dS rate ratios are about 5-10 times higher in within-species comparisons than in between-species comparisons. This result is confirmed by a more rigorous likelihood ratio test, which rejected the null hypothesis that the dN/dS rate ratios are identical within and between species. The likelihood models account for the genetic code structure, transition/transversion rate ratio, and codon usage bias and are expected to produce more reliable results than the commonly used contingency test. Separate analyses of different genes show that the dN/dS rate ratios are higher within species than between species for all 13 mitochondrial genes, with the difference being statistically significant for all except three small or slowly evolving genes. Furthermore, in conserved genes, nonsynonymous rates within species tend to be higher than the between-species rates by a greater proportion than in fast-changing genes. Our findings confirm and extend earlier results obtained from smaller data sets and suggest the operation of slightly deleterious mutations throughout the mitochondrial genome in the hominoids. Implications of the results for evolutionary studies and, in particular, for studies of the origin of modern humans, are discussed.     

Sample size calculations for noninferiority trials with Poisson distributed count data

Clinical trials with Poisson distributed count data as the primary outcome are common in various medical areas such as relapse counts in multiple sclerosis trials or the number of attacks in trials for the treatment of migraine. In this article, we present approximate sample size formulae for testing noninferiority using asymptotic tests which are based on restricted or unrestricted maximum likelihood estimators of the Poisson rates. The Poisson outcomes are allowed to be observed for unequal follow‐up schemes, and both the situations that the noninferiority margin is expressed in terms of the difference and the ratio are considered. The exact type I error rates and powers of these tests are evaluated and the accuracy of the approximate sample size formulae is examined. The test statistic using the restricted maximum likelihood estimators (for the difference test problem) and the test statistic that is based on the logarithmic transformation and employs the maximum likelihood estimators (for the ratio test problem) show favorable type I error control and can be recommended for practical application. The approximate sample size formulae show high accuracy even for small sample sizes and provide power values identical or close to the aspired ones. The methods are illustrated by a clinical trial example from anesthesia.     

Tests for an Epidemic Change in a Sequence of Exponentially Distributed Random Variables

Consider a sequence of independent exponential random variables that is susceptible to a change in the means. We would like to test whether the means have been subjected to an epidemic change after an unknown point, for an unknown duration in the sequence. The likelihood ratio statistic and a likelihood ratio type statistic are derived. The distribution theories and related properties of the test statistics are discussed. Percentage points and powers of the tests are tabulated for selected values of the parameters. The powers of these two tests are then compared to the two statistics proposed by Aly and Bouzar. The tests are applied to find epidemic changes in the set of Stanford heart transplant data and air traffic arrival data.     

Omnibus tests for comparison of competing risks with adjustment for covariate effects

This article develops omnibus tests for comparing cause-specific hazard rates and cumulative incidence functions at specified covariate levels. Confidence bands for the difference and the ratio of two conditional cumulative incidence functions are also constructed. The omnibus test is formulated in terms of a test process given by a weighted difference of estimates of cumulative cause-specific hazard rates under Cox proportional hazards models. A simulation procedure is devised for sampling from the null distribution of the test process, leading to graphical and numerical technques for detecting significant differences in the risks. The approach is applied to a cohort study of type-specific HIV infection rates.     

Likelihood ratio tests for a mixture of two von Mises distributions

It is proposed that the orientation of elongate objects, such as bones, may be used to identify the flow direction of ancient river deposits. If true, elongate objects could be of great value when ancient bedforms such as ripples and dunes are not visible. Two sandstone quarries were investigated wherein the paleoflow direction was determined from both bedforms and elongate dinosaur bones. A mixture of two von Mises distributions captures the observation that elongate bones transported under unidirectional flow conditions will align both parallel and perpendicular to the flow direction. Likelihood ratio tests for a mixture of two von Mises distributions are given. The power of these tests is investigated by simulation since the direction of dinosaur bones agrees with the primary bedforms if the hypothesis test comparing the dominant mean direction of the bones to the paleoflow direction fails to reject. The likelihood ratio test on the dominant mean direction has reasonable power. If the two mean directions in the mixture distribution are pi apart, a more powerful likelihood ratio test can be used. The likelihood ratio test on the hypothesis that the two mean directions are exactly pi apart is useful in determining if the assumptions of the more powerful test are satisfied.     

A maximum likelihood method for analyzing pseudogene evolution: implications for silent site evolution in humans and rodents.

We present a new likelihood method for detecting constrained evolution at synonymous sites and other forms of nonneutral evolution in putative pseudogenes. The model is applicable whenever the DNA sequence is available from a protein-coding functional gene, a pseudogene derived from the protein-coding gene, and an orthologous functional copy of the gene. Two nested likelihood ratio tests are developed to test the hypotheses that (1) the putative pseudogene has equal rates of silent and replacement substitutions; and (2) the rate of synonymous substitution in the functional gene equals the rate of substitution in the pseudogene. The method is applied to a data set containing 74 human processed-pseudogene loci, 25 mouse processed-pseudogene loci, and 22 rat processed-pseudogene loci. Using the informatics resources of the Human Genome Project, we localized 67 of the human-pseudogene pairs in the genome and estimated the GC content of a large surrounding genomic region for each. We find that, for pseudogenes deposited in GC regions similar to those of their paralogs, the assumption of equal rates of silent and replacement site evolution in the pseudogene is upheld; in these cases, the rate of silent site evolution in the functional genes is approximately 70% the rate of evolution in the pseudogene. On the other hand, for pseudogenes located in genomic regions of much lower GC than their functional gene, we see a sharp increase in the rate of silent site substitutions, leading to a large rate of rejection for the pseudogene equality likelihood ratio test.     

Effective population size and tests of neutrality at cytoplasmic genes in Arabidopsis.

Cytoplasmic genomes typically lack recombination, implying that genetic hitch-hiking could be a predominant force structuring nucleotide polymorphism in the chloroplast and mitochondria. We test this hypothesis by analysing nucleotide polymorphism data at 28 loci across the chloroplast and mitochondria of the outcrossing plant Arabidopsis lyrata, and compare patterns with multiple nuclear loci, and the highly selfing Arabidopsis thaliana. The maximum likelihood estimate of the ratio of effective population size at cytoplasmic relative to nuclear genes in A. lyrata does not depart from the neutral expectation of 0.5. Similarly, the ratio of effective size in A. thaliana is close to unity, the neutral expectation for a highly selfing species. The results are thus consistent with neutral organelle polymorphism in these species or with comparable effects of hitch-hiking in both cytoplasmic and nuclear genes, in contrast to the results of recent studies on gynodioecious taxa. The four-gamete test and composite likelihood estimation provide evidence for very low levels of recombination in the organelles of A. lyrata, although permutation tests do not suggest that adjacent polymorphic sites are more closely linked than more distant sites across the two genomes, suggesting that mutation hotspots or very low rates of gene conversion could explain the data.     

A Comparison of the Three Conditional Exact Tests in Two‐way Contingency Tables Using the Unconditional Exact Power

The conditional exact tests of homogeneity of two binomial proportions are often used in small samples, because the exact tests guarantee to keep the size under the nominal level. The Fisher's exact test, the exact chi‐squared test and the exact likelihood ratio test are popular and can be implemented in software StatXact. In this paper we investigate which test is the best in small samples in terms of the unconditional exact power. In equal sample cases it is proved that the three tests produce the same unconditional exact power. A symmetry of the unconditional exact power is also found. In unequal sample cases the unconditional exact powers of the three tests are computed and compared. In most cases the Fisher's exact test turns out to be best, but we characterize some cases in which the exact likelihood ratio test has the highest unconditional exact power. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A likelihood-based approach to estimating and testing for isolation by distance

Simple regression of genetic similarities between pairs of populations on their corresponding geographic distances is frequently used to detect the presence of isolation by distance (IBD). However, these pairwise values are obviously not independent and there is no parametric procedure for estimating and testing for the IBD intercepts and slopes based on standard regression theory. Nonparametric tests, such as the Mantel test, and resampling techniques, such as bootstrapping, have been exploited with limited success. Here, I describe a likelihood-based analysis to allow for simultaneously detecting patterns of correlated residuals and estimating and testing for the presence of IBD. It is shown, through the analysis of two molecular datasets in pine species, that different covariance structures of the residuals exist. More over, the likelihood ratio tests under these covariance structures are less sensitive to the presence of IBD than the Mantel test and the simple regression analysis but more sensitive than the bootstrap and jackknife samples over independent populations or population pairs. Because the likelihood analysis directly models and accounts for nonindependence of residuals, it should legitimately detect the presence of IBD, thereby allowing for accurate inferences about evolutionary and demographic processes influencing the extent and patterns of IBD.     

Body size effects and rates of cytochrome b evolution in tube-nosed seabirds

Variation in rates of molecular evolution now appears to be widespread. The demonstration that body size is correlated with rates of molecular evolution suggests that physiological and ecological factors may be involved in molecular rate variation, but large-scale comparative studies are still lacking. Here, we use complete cytochrome b sequences from 85 species of tube-nosed seabirds (order Procellariiformes) and 5 outgroup species of penguins (order Sphenisciformes) to test for an association between body mass and rates of molecular evolution within the former avian order. Cladistic analysis of the 90 sequences estimates a phylogeny largely consistent with the traditional taxonomy of the Procellariiformes. The Diomedeidae, Procellariidae, and Pelecanoididae are monophyletic, while the Hydrobatidae are basal and paraphyletic. However, the two subfamilies within the Hydrobatidae (Hydrobatinae and Oceanitinae) are monophyletic. A likelihood ratio test detects significant deviation from clocklike evolution in our data. Using a sign test for an association between body mass and branch length in the seabird phylogeny, we find that larger taxa tend to have shorter terminal branch lengths than smaller taxa. This observation suggests that rates of mitochondrial DNA evolution are slower for larger taxa. Rate calibrations based on the fossil record reveal concordant body size effects. We interpret these results as evidence for a metabolic rate effect, as the species in this order exhibit large differences in metabolic rates, which are known to be highly correlated with body mass in this group. Our results support previous findings of body size effects and show that this effect can be significant even within a single avian order. This suggests that even lineage-specific molecular clocks may not be tenable if calibrations involve taxa with different metabolic rates.      

A Likelihood Ratio Test for the Nonparametric Behrens‐Fisher Problem

The nonparametric Behrens‐Fisher hypothesis is the most appropriate null hypothesis for the two‐sample comparison when one does not wish to make restrictive assumptions about possible distributions. In this paper, a numerical approach is described by which the likelihood ratio test can be calculated for the nonparametric Behrens‐Fisher problem. The approach taken here effectively reduces the number of parameters in the score equations to one by using a recursive formula for the remaining parameters. The resulting single dimensional problem can be solved numerically. The power of the likelihood ratio test is compared by simulation to that of a generalized Wilcoxon test of Brunner and Munzel. The tests have similar power for all alternatives considered when a simulated null distribution is used to generate cutoff values for the tests. The methods are illustrated on data on shoulder pain from a clinical trial.     

The use of score tests for inference on variance components

Whenever inference for variance components is required, the choice between one-sided and two-sided tests is crucial. This choice is usually driven by whether or not negative variance components are permitted. For two-sided tests, classical inferential procedures can be followed, based on likelihood ratios, score statistics, or Wald statistics. For one-sided tests, however, one-sided test statistics need to be developed, and their null distribution derived. While this has received considerable attention in the context of the likelihood ratio test, there appears to be much confusion about the related problem for the score test. The aim of this paper is to illustrate that classical (two-sided) score test statistics, frequently advocated in practice, cannot be used in this context, but that well-chosen one-sided counterparts could be used instead. The relation with likelihood ratio tests will be established, and all results are illustrated in an analysis of continuous longitudinal data using linear mixed models.     

Testing hypotheses about interclass correlations from familial data

Testing problems concerning interclass correlations from familial data are considered in the case where the number of siblings varies among families. Under the assumption of multivariate normality, two test procedures are proposed for testing the hypothesis that an interclass correlation is equal to a specified value. To compare the properties of the tests, including a likelihood ratio test, Monte Carlo experiments are performed. Several test statistics are derived for testing whether two variables about a parent and child are uncorrelated. The proposed tests are compared with previous test procedures, using Monte Carlo simulation. A general procedure for finding confidence intervals for interclass correlations is also derived.     

以雾灵山夜蛾科为材料评估进化模型对DNA条码分类的影响

为了探究进化模型对DNA条形码分类的影响, 本研究以雾灵山夜蛾科44个种的标本为材料, 获得COI基因序列。使用邻接法（neighbor-joining）、 最大简约法（maximum parsimony）、 最大似然法（maximum likelihood）以及贝叶斯法（Bayesian inference）构建系统发育树, 并且对邻接法的12种模型、 最大似然法的7种模型、 贝叶斯法的2种模型进行模型成功率的评估。结果表明, 邻接法的12种模型成功率相差不大, 较稳定; 最大似然法及贝叶斯法的不同模型成功率存在明显差异, 不稳定; 最大简约法不基于模型, 成功率比较稳定。邻接法及最大似然法共有6种相同的模型, 这6种模型在不同的方法中成功率存在差异。此外, 分子数据中存在单个物种仅有一条序列的情况, 显著降低了模型成功率, 表明在DNA条形码研究中, 每个物种需要有多个样本。     

Incisor size and community structure in rodents: Two tests of the role of competition

We used two different approaches to test for the effect of interspecific competition on community-wide patterns in the size of the upper incisor in six rodent communities. One tests for constancy of size ratios between adjacent species (Barton and David's test), and the other tests for minimum mean size overlap between species pairs (randomization test). The results of the two tests were more congruent for the radius of the upper incisor than for its diameter. Although a number of tests gave significant results, they led to a consistent rejection of the null hypothesis of a randomly generated pattern only in two communities from an African rainforest. Many factors are likely to disturb community structure, among which we identify recent species introductions and the presence of rare species. Our results also show that Hutchinson's rule of a limiting size similarity does not hold; the mean size ratio between adjacent species was correlated with the overall size range and the number of species in a community.