A note on the local power of the LR, Wald, score and gradient tests

This paper examines the local power of the likelihood ratio, Wald, score and gradient tests under the presence of a scalar parameter, phi say, that is orthogonal to the remaining parameters. We show that some of the coefficients that define the local powers remain unchanged regardless of whether phi is known or needs to be estimated, where as the others can be written as the sum of two terms, the first of which being the corresponding term obtained as if phi were known, and the second, an additional term yielded by the fact that phi is unknown. The contribution of each set of parameters on the local powers of the tests can then be examined. Various implications of our main result are stated and discussed. Several examples are presented for illustrative purposes

Local power properties of some asymptotic tests in symmetric linear regression models

In this paper we obtain asymptotic expansions, up to order n(-1/2) and under a sequence of Pitman alternatives, for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the class of symmetric linear regression models. This is a wide class of models which encompasses the t model and several other symmetric distributions with longer-than normal tails. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters. Furthermore, in order to compare the finite-sample performance of these tests in this class of models, Monte Carlo simulations are presented. An empirical application to a real data set is considered for illustrative purposes. (C) 2011 Elsevier B.V. All rights reserved.

The new class of Kummer beta generalized distributions

Ng and Kotz (1995) introduced a distribution that provides greater flexibility to extremes. We define and study a new class of distributions called the Kummer beta generalized family to extend the normal, Weibull, gamma and Gumbel distributions, among several other well-known distributions. Some special models are discussed. The ordinary moments of any distribution in the new family can be expressed as linear functions of probability weighted moments of the baseline distribution. We examine the asymptotic distributions of the extreme values. We derive the density function of the order statistics, mean absolute deviations and entropies. We use maximum likelihood estimation to fit the distributions in the new class and illustrate its potentiality with an application to a real data set.

Assessment of variance components in nonlinear mixed-effects elliptical models

The issue of assessing variance components is essential in deciding on the inclusion of random effects in the context of mixed models. In this work we discuss this problem by supposing nonlinear elliptical models for correlated data by using the score-type test proposed in Silvapulle and Silvapulle (1995). Being asymptotically equivalent to the likelihood ratio test and only requiring the estimation under the null hypothesis, this test provides a fairly easy computable alternative for assessing one-sided hypotheses in the context of the marginal model. Taking into account the possible non-normal distribution, we assume that the joint distribution of the response variable and the random effects lies in the elliptical class, which includes light-tailed and heavy-tailed distributions such as Student-t, power exponential, logistic, generalized Student-t, generalized logistic, contaminated normal, and the normal itself, among others. We compare the sensitivity of the score-type test under normal, Student-t and power exponential models for the kinetics data set discussed in Vonesh and Carter (1992) and fitted using the model presented in Russo et al. (2009). Also, a simulation study is performed to analyze the consequences of the kurtosis misspecification.

A Single Statistic for Monitoring the Covariance Matrix of Bivariate Processes

In this article, we present a new control chart for monitoring the covariance matrix in a bivariate process. In this method, n observations of the two variables were considered as if they came from a single variable (as a sample of 2n observations), and a sample variance was calculated. This statistic was used to build a new control chart specifically as a VMIX chart. The performance of the new control chart was compared with its main competitors: the generalized sampled variance chart, the likelihood ratio test, Nagao's test, probability integral transformation (v(t)), and the recently proposed VMAX chart. Among these statistics, only the VMAX chart was competitive with the VMIX chart. For shifts in both variances, the VMIX chart outperformed VMAX; however, VMAX showed better performance for large shifts (higher than 10%) in one variance.

Local power and size properties of the LR, Wald, score and gradient tests in dispersion models

We derive asymptotic expansions for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the class of dispersion models, under a sequence of Pitman alternatives. The asymptotic distributions of these statistics are obtained for testing a subset of regression parameters and for testing the precision parameter. Based on these nonnull asymptotic expansions, the power of all four tests, which are equivalent to first order, are compared. Furthermore, in order to compare the finite-sample performance of these tests in this class of models, Monte Carlo simulations are presented. An empirical application to a real data set is considered for illustrative purposes. (C) 2012 Elsevier B.V. All rights reserved.

Optimierungen des Nachweises von Supernovae in IceCube

Kernkollaps-Supernovae werden von einem massiven Ausbruch niederenergetischer Neutrinos begleitet. Sie zählen zu den energiereichsten Erscheinungen im Universum und stellen die derzeit einzig bekannte Quelle extrasolarer Neutrinos dar.rnDie Detektion einer solchen Neutrinosignatur würde zu einem tieferen Verständnis des bislang unzureichend bekannten stellaren Explosionsmechanismus führen. rnDarüber hinaus würden neue Einblicke in den Bereich der Teilchenphysik und der Supernova-Modellierung ermöglicht. Das sich zur Zeit am geographischen Südpol im Aufbau befindliche Neutrinoteleskop IceCube wird 2011 fertig gestellt sein.rnIceCube besteht im endgültigen Ausbau aus 5160 Photovervielfachern, die sich in gitterförmiger Anordnung in Tiefen zwischen 1450m und 2450m unter der Eisoberfläche befinden. Durch den Nachweis von Tscherenkow-Photonenrnim antarktischen Gletscher ist es in der Lage, galaktische Supernovae über einen kollektiven Anstieg der Rauschraten in seinen Photonenvervielfachern nachzuweisen.rnIn dieser Arbeit werden verschiedene Studien zur Implementierung einer künstlichen Totzeit vorgestellt, welche korreliertes Rauschen unterdrücken und somit das Signal-Untergund-Verhältnis maximieren würden.rnEin weiterer Teil dieser Dissertation bestand in der Integration der Supernova-Datenakquise eine neue Experiment-Steuerungssoftware.rnFür den Analyseteil der Arbeit wurde ein Monte-Carlo für IceCube entwickelt und Neutinooszillations-Mechanismen und eine Reihe von Signalmodellen integriert. Ein Likelihoodhypothesen-Test wurde verwendet, um die Unterscheidbarkeit verschiedener Supernova- beziehungsweise Neutrinooszillations-Szenarien zu untersuchen. Desweiteren wurde analysiert inwieweit sich Schock-Anregungen und QCD-Phasenübergnag im Verlauf des Explosionsprozesses detektieren lassen.

Fitting of Mixtures with Unspecified Number of Components Using Cross Validation Distance Estimate

Estimation of the number of mixture components (k) is an unsolved problem. Available methods for estimation of k include bootstrapping the likelihood ratio test statistics and optimizing a variety of validity functionals such as AIC, BIC/MDL, and ICOMP. We investigate the minimization of distance between fitted mixture model and the true density as a method for estimating k. The distances considered are Kullback-Leibler (KL) and “L sub 2”. We estimate these distances using cross validation. A reliable estimate of k is obtained by voting of B estimates of k corresponding to B cross validation estimates of distance. This estimation methods with KL distance is very similar to Monte Carlo cross validated likelihood methods discussed by Smyth (2000). With focus on univariate normal mixtures, we present simulation studies that compare the cross validated distance method with AIC, BIC/MDL, and ICOMP. We also apply the cross validation estimate of distance approach along with AIC, BIC/MDL and ICOMP approach, to data from an osteoporosis drug trial in order to find groups that differentially respond to treatment.

Comparative phylogenies of the housekeeping genes atpD, infB and rpoB and the 16S rRNA gene within the Pasteurellaceae

Phylogenies of housekeeping gene and 16S rRNA gene sequences were compared to improve the classification of the bacterial family Pasteurellaceae and knowledge of the evolutionary relationships of its members. Deduced partial protein sequences of the housekeeping genes atpD, infB and rpoB were compared in 28, 36 and 28 representative taxa of the Pasteurellaceae, respectively. The monophyly of representatives of the genus Gallibacterium was recognized by analysis of all housekeeping genes, while members of Mannheimia, Actinobacillus sensu stricto and the core group of Pasteurella sensu stricto formed monophyletic groups with two out of three housekeeping genes. Representatives of Mannheimia, Actinobacillus sensu stricto, [Haemophilus] ducreyi and [Pasteurella] trehalosi formed a monophyletic unit by analysis of all three housekeeping genes, which was in contrast to the 16S rRNA gene-derived phylogeny, where these taxa occurred at separate positions in the phylogenetic tree. Representatives of the Rodent, Avian and Aphrophilus-Haemophilus 16S rRNA gene groups were weakly supported by phylogenetic analysis of housekeeping genes. Phylogenies derived by comparison of the housekeeping genes diverged significantly from the 16S rRNA gene-derived phylogeny as evaluated by the likelihood ratio test. A low degree of congruence was also observed between the individual housekeeping gene-derived phylogenies. Estimates on speciation derived from 16S rRNA and housekeeping gene sequence comparisons resulted in quite different evolutionary scenarios for members of the Pasteurellaceae. The phylogeny based on the housekeeping genes supported observed host associations between Mannheimia, Actinobacillus sensu stricto and [Pasteurella] trehalosi and animals with paired hooves.

Adaptive Molecular Evolution in the Opsin Genes of Rapidly Speciating Cichlid Species

Cichlid fish inhabit a diverse range of environments that vary in the spectral content of light available for vision. These differences should result in adaptive selective pressure on the genes involved in visual sensitivity, the opsin genes. This study examines the evidence for differential adaptive molecular evolution in East African cichlid opsin genes due to gross differences in environmental light conditions. First, we characterize the selective regime experienced by cichlid opsin genes using a likelihood ratio test format, comparing likelihood models with different constraints on the relative rates of amino acid substitution, across sites. Second, we compare turbid and clear lineages to determine if there is evidence of differences in relative rates of substitution. Third, we present evidence of functional diversification and its relationship to the photic environment among cichlid opsin genes. We report statistical evidence of positive selection in all cichlid opsin genes, except short wavelength–sensitive 1 and short wavelength–sensitive 2b. In all genes predicted to be under positive selection, except short wavelength–sensitive 2a, we find differences in selective pressure between turbid and clear lineages. Potential spectral tuning sites are variable among all cichlid opsin genes; however, patterns of substitution consistent with photic environment–driven evolution of opsin genes are observed only for short wavelength–sensitive 1 opsin genes. This study identifies a number of promising candidate-tuning sites for future study by site-directed mutagenesis. This work also begins to demonstrate the molecular evolutionary dynamics of cichlid visual sensitivity and its relationship to the photic environment.

Genome-wide association study of survival from sepsis due to pneumonia: an observational cohort study.

BACKGROUND Sepsis continues to be a major cause of death, disability, and health-care expenditure worldwide. Despite evidence suggesting that host genetics can influence sepsis outcomes, no specific loci have yet been convincingly replicated. The aim of this study was to identify genetic variants that influence sepsis survival. METHODS We did a genome-wide association study in three independent cohorts of white adult patients admitted to intensive care units with sepsis, severe sepsis, or septic shock (as defined by the International Consensus Criteria) due to pneumonia or intra-abdominal infection (cohorts 1-3, n=2534 patients). The primary outcome was 28 day survival. Results for the cohort of patients with sepsis due to pneumonia were combined in a meta-analysis of 1553 patients from all three cohorts, of whom 359 died within 28 days of admission to the intensive-care unit. The most significantly associated single nucleotide polymorphisms (SNPs) were genotyped in a further 538 white patients with sepsis due to pneumonia (cohort 4), of whom 106 died. FINDINGS In the genome-wide meta-analysis of three independent pneumonia cohorts (cohorts 1-3), common variants in the FER gene were strongly associated with survival (p=9·7 × 10(-8)). Further genotyping of the top associated SNP (rs4957796) in the additional cohort (cohort 4) resulted in a combined p value of 5·6 × 10(-8) (odds ratio 0·56, 95% CI 0·45-0·69). In a time-to-event analysis, each allele reduced the mortality over 28 days by 44% (hazard ratio for death 0·56, 95% CI 0·45-0·69; likelihood ratio test p=3·4 × 10(-9), after adjustment for age and stratification by cohort). Mortality was 9·5% in patients carrying the CC genotype, 15·2% in those carrying the TC genotype, and 25·3% in those carrying the TT genotype. No significant genetic associations were identified when patients with sepsis due to pneumonia and intra-abdominal infection were combined. INTERPRETATION We have identified common variants in the FER gene that associate with a reduced risk of death from sepsis due to pneumonia. The FER gene and associated molecular pathways are potential novel targets for therapy or prevention and candidates for the development of biomarkers for risk stratification. FUNDING European Commission and the Wellcome Trust.

Effectiveness of meticillin-resistant Staphylococcus aureus decolonization in long-term haemodialysis patients: a systematic review and meta-analysis.

BACKGROUND Chronic haemodialysis patients are a high-risk population for meticillin-resistant Staphylococcus aureus (MRSA) colonization, which is a precursor of infection. AIM To summarize the effect of nasal (± whole-body wash) MRSA decolonization in haemodialysis patients by means of a systematic review and meta-analysis. METHODS We identified eligible studies using Medline, Embase, the Cochrane database, clinicaltrials.org, and conference abstracts investigating the success of MRSA decolonization in haemodialysis patients. For the statistical analysis, we used Stata 13 to express study-specific proportions with 95% confidence intervals. A likelihood ratio test was used to assess inter-study heterogeneity. FINDINGS Six published prospective cohort studies and one study described in a conference abstract met our inclusion criteria. From 1150 haemodialysis patients enrolled in these studies, MRSA was isolated from nasal swabs of 147 (12.8%) patients. Six of the trials used mupirocin nasal ointment and combined it with chlorhexidine body washes for decolonization. The most widely used protocol was a five-day course of mupirocin nasal ointment application three times a day, and chlorhexidine body wash once daily. The pooled success rate of decolonization was 0.88 (95% confidence interval: 0.75-0.95). A likelihood ratio test of the fixed versus the random-effects model showed significant inter-study heterogeneity (P = 0.047). Four of seven studies determined subsequent MRSA infections in 94 carriers overall, two (2%) of which experienced infection. CONCLUSION The use of mupirocin together with whole-body decolonization is highly effective in eradicating MRSA carriage in haemodialysis patients. The current literature, however, is characterized by a lack of comparative effectiveness studies for this intervention.

DNA nucleotide excision repair gene single nucleotide polymorphisms and hereditary nonpolyposis colorectal cancer

Hereditary nonpolyposis colorectal cancer (HNPCC) is an autosomal dominant disease caused by germline mutations in DNA mismatch repair(MMR) genes. The nucleotide excision repair(NER) pathway plays a very important role in cancer development. We systematically studied interactions between NER and MMR genes to identify NER gene single nucleotide polymorphism (SNP) risk factors that modify the effect of MMR mutations on risk for cancer in HNPCC. We analyzed data from polymorphisms in 10 NER genes that had been genotyped in HNPCC patients that carry MSH2 and MLH1 gene mutations. The influence of the NER gene SNPs on time to onset of colorectal cancer (CRC) was assessed using survival analysis and a semiparametric proportional hazard model. We found the median age of onset for CRC among MMR mutation carriers with the ERCC1 mutation was 3.9 years earlier than patients with wildtype ERCC1(median 47.7 vs 51.6, log-rank test p=0.035). The influence of Rad23B A249V SNP on age of onset of HNPCC is age dependent (likelihood ratio test p=0.0056). Interestingly, using the likelihood ratio test, we also found evidence of genetic interactions between the MMR gene mutations and SNPs in ERCC1 gene(C8092A) and XPG/ERCC5 gene(D1104H) with p-values of 0.004 and 0.042, respectively. An assessment using tree structured survival analysis (TSSA) showed distinct gene interactions in MLH1 mutation carriers and MSH2 mutation carriers. ERCC1 SNP genotypes greatly modified the age onset of HNPCC in MSH2 mutation carriers, while no effect was detected in MLH1 mutation carriers. Given the NER genes in this study play different roles in NER pathway, they may have distinct influences on the development of HNPCC. The findings of this study are very important for elucidation of the molecular mechanism of colon cancer development and for understanding why some mutation carriers of the MSH2 and MLH1 gene develop CRC early and others never develop CRC. Overall, the findings also have important implications for the development of early detection strategies and prevention as well as understanding the mechanism of colorectal carcinogenesis in HNPCC. ^

Outcome-based adaptive randomization for binary data in clinical trials---Compare and contrast

Monte Carlo simulation has been conducted to investigate parameter estimation and hypothesis testing in some well known adaptive randomization procedures. The four urn models studied are Randomized Play-the-Winner (RPW), Randomized Pôlya Urn (RPU), Birth and Death Urn with Immigration (BDUI), and Drop-the-Loses Urn (DL). Two sequential estimation methods, the sequential maximum likelihood estimation (SMLE) and the doubly adaptive biased coin design (DABC), are simulated at three optimal allocation targets that minimize the expected number of failures under the assumption of constant variance of simple difference (RSIHR), relative risk (ORR), and odds ratio (OOR) respectively. Log likelihood ratio test and three Wald-type tests (simple difference, log of relative risk, log of odds ratio) are compared in different adaptive procedures. ^ Simulation results indicates that although RPW is slightly better in assigning more patients to the superior treatment, the DL method is considerably less variable and the test statistics have better normality. When compared with SMLE, DABC has slightly higher overall response rate with lower variance, but has larger bias and variance in parameter estimation. Additionally, the test statistics in SMLE have better normality and lower type I error rate, and the power of hypothesis testing is more comparable with the equal randomization. Usually, RSIHR has the highest power among the 3 optimal allocation ratios. However, the ORR allocation has better power and lower type I error rate when the log of relative risk is the test statistics. The number of expected failures in ORR is smaller than RSIHR. It is also shown that the simple difference of response rates has the worst normality among all 4 test statistics. The power of hypothesis test is always inflated when simple difference is used. On the other hand, the normality of the log likelihood ratio test statistics is robust against the change of adaptive randomization procedures. ^