SEARCH · Search PubMed

Results for “Binomial Distribution”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,513 records · Page 84Linked to original sources

PubMed2003

A cautionary note on exact unconditional inference for a difference between two independent binomial proportions.

Fisher's exact test for comparing response proportions in a randomized experiment can be overly conservative when the group sizes are small or when the response proportions are close to zero or one. This is primarily because the null distribution of the test statistic becomes too discrete, a partial consequence of the inference being conditional on the total number of responders. Accordingly, exact unconditional procedures have gained in popularity, on the premise that power will increase because the null distribution of the test statistic will presumably be less discrete. However, we caution researchers that a poor choice of test statistic for exact unconditional inference can actually result in a substantially less powerful analysis than Fisher's conditional test. To illustrate, we study a real example and provide exact test size and power results for several competing tests, for both balanced and unbalanced designs. Our results reveal that Fisher's test generally outperforms exact unconditional tests based on using as the test statistic either the observed difference in proportions, or the observed difference divided by its estimated standard error under the alternative hypothesis, the latter for unbalanced designs only. On the other hand, the exact unconditional test based on the observed difference divided by its estimated standard error under the null hypothesis (score statistic) outperforms Fisher's test, and is recommended. Boschloo's test, in which the p-value from Fisher's test is used as the test statistic in an exact unconditional test, is uniformly more powerful than Fisher's test, and is also recommended.

Humans↗

PubMed2004

Statistical models for protein validation using tandem mass spectral data and protein amino acid sequence databases.

The purpose of this work is to develop and verify statistical models for protein identification using peptide identifications derived from the results of tandem mass spectral database searches. Recently we have presented a probabilistic model for peptide identification that uses hypergeometric distribution to approximate fragment ion matches of database peptide sequences to experimental tandem mass spectra. Here we apply statistical models to the database search results to validate protein identifications. For this we formulate the protein identification problem in terms of two independent models, two-hypothesis binomial and multinomial models, which use the hypergeometric probabilities and cross-correlation scores, respectively. Each database search result is assumed to be a probabilistic event. The Bernoulli event has two outcomes: a protein is either identified or not. The probability of identifying a protein at each Bernoulli event is determined from relative length of the protein in the database (the null hypothesis) or the hypergeometric probability scores of the protein's peptides (the alternative hypothesis). We then calculate the binomial probability that the protein will be observed a certain number of times (number of database matches to its peptides) given the size of the data set (number of spectra) and the probability of protein identification at each Bernoulli event. The ratio of the probabilities from these two hypotheses (maximum likelihood ratio) is used as a test statistic to discriminate between true and false identifications. The significance and confidence levels of protein identifications are calculated from the model distributions. The multinomial model combines the database search results and generates an observed frequency distribution of cross-correlation scores (grouped into bins) between experimental spectra and identified amino acid sequences. The frequency distribution is used to generate p-value probabilities of each score bin. The probabilities are then normalized with respect to score bins to generate normalized probabilities of all score bins. A protein identification probability is the multinomial probability of observing the given set of peptide scores. To reduce the effect of random matches, we employ a marginalized multinomial model for small values of cross-correlation scores. We demonstrate that the combination of the two independent methods provides a useful tool for protein identification from results of database search using tandem mass spectra. A receiver operating characteristic curve demonstrates the sensitivity and accuracy level of the approach. The shortcomings of the models are related to the cases when protein assignment is based on unusual peptide fragmentation patterns that dominate over the model encoded in the peptide identification process. We have implemented the approach in a program called PROT_PROBE.

Amino Acid Sequence↗

PubMedDate not supplied

Comparing methods for calculating confidence intervals for vaccine efficacy.

A method is introduced for computing a Bayesian 95 per cent posterior probability region for vaccine efficacy. This method assumes independent vague gamma prior distributions for the incidence rates on each arm of the trial, and a Poisson likelihood for the counts of incident cases of infection. The approach is similar in spirit to the Bayesian analysis of the binomial risk ratio described by Aitchison and Bacon-Shone. However, the focus of our interest is not on incorporating prior information into the design of trials for efficacy, but rather on evaluating whether or not the Bayesian approach with vague prior information produces comparable results to a frequentist approach. A review of methods for constructing exact and large sample intervals for vaccine efficacy is provided as a framework for comparison. The confidence interval methods are assessed by comparing the size and power of tests of vaccine efficacy in proposed intermediate sized randomized double blinded placebo controlled trials.

AIDS Vaccines↗

PubMed2001

The statistical analysis of truncated data: application to the Sverdlovsk anthrax outbreak.

An outbreak of anthrax occurred in the city of Sverdlovsk in Russia in the spring of 1979. The outbreak was due to the inhalation of spores that were accidentally released from a military microbiology facility. In response to the outbreak a public health intervention was mounted that included distribution of antibiotics and vaccine. The objective of this paper is to develop and apply statistical methodology to analyse the Sverdlovsk outbreak, and in particular to estimate the incubation period of inhalational anthrax and the number of deaths that may have been prevented by the public health intervention. The data available for analysis from this common source epidemic are the incubation periods of reported deaths. The statistical problem is that incubation periods are truncated because some individuals may have had their deaths prevented by the public health interventions and thus are not included in the data. However, it is not known how many persons received the intervention or how efficacious was the intervention. A likelihood function is formulated that accounts for the effects of truncation. The likelihood is decomposed into a binomial likelihood with unknown sample size and a conditional likelihood for the incubation periods. The methods are extended to allow for a phase-in of the intervention over time. Assuming a lognormal model for the incubation period distribution, the median and mean incubation periods were estimated to be 11.0 and 14.2 days respectively. These estimates are longer than have been previously reported in the literature. The death toll from the Sverdlovsk anthrax outbreak could have been about 14% larger had there not been a public health intervention; however, the confidence intervals are wide (95% CI 0-61%). The sensitivity of the results to model assumptions and the parametric model for the incubation period distribution are investigated. The results are useful for determining how long antibiotic therapy should be continued in suspected anthrax cases and also for estimating the ultimate number of deaths in a new outbreak in the absence of any public health interventions.

Journal Article↗

PubMed1989

Testing for non-randomness of events in sparse data situations.

In experiments involving cytogenetic assays or mutation assays it is often of interest to determine if there are hot spots for certain events, that is, to determine if the events occur more often at certain sites than would be expected under the assumption of randomness. In examining chromosome aberrations using banded chromosome preparations, for example, it may be of interest to determine if a particular type of aberration occurs more often in a particular band than would be expected given the relative length of the band. In a mutation assay it may be of interest to determine if a mutation occurs more often at a particular nucleotide in a given sequence than would be expected given the length of the sequence in question. Such experiments typically result in data following a multinomial distribution with a large number of classes and relatively few observations. For such data, De Braekeleer & Smith (1988) have suggested analysis of the frequencies in individual classes using an exact binomial test. Two cautions are noted for application of the binomial analysis in the usual situation in which the locations of potential hot spots are not specified beforehand.

Biometry↗

PubMed1983

On estimating the difference between two probabilities, with special reference to clinical trials.

The problem of estimating the difference between the probabilities of 'success' for two binomial experiments is considered. Confidence intervals based on large-sample theory are constructed and some of their properties are compared with those of a simple technique based on exact distributions. It is shown that the former method is superior to the latter, both theoretically and practically.

Biometry↗

PubMed2026

The spatial and temporal distribution of Staphylococcus aureus along a tropical Hawaiian watershed.

Staphylococcus aureus is a leading cause of community-acquired skin and soft-tissue infections worldwide. One major route of exposure is recreating in marine waters, but knowledge is limited regarding the drivers of S. aureus in surface waters that discharge into marine environments. This study explores spatial and temporal distributions of S. aureus, including antimicrobial-resistant and virulence genes, using both culture-dependent and molecular techniques across a tropical Hawaiian watershed with a gradient of human influence. Negative binomial generalized linear mixed models revealed that the interaction between spatial and temporal factors was the strongest predictor of S. aureus and associated genes. Cultured S. aureus was highest at mid-watershed sites in summer, which included a popular swimming hole, suggesting human shedding as a significant source. Molecular detection of S. aureus (femA gene) yielded concentrations two orders of magnitude higher than cultured concentrations and peaked at estuarine sites with the greatest nutrients and water residence times. In the winter at upstream sites with no public access, staphylococci antibiotic-resistant (mecA) and S. aureus virulence gene (etb) were elevated, indicating highly pathogenic S. aureus strains in surface waters may originate from zoonotic sources. Our findings indicate that human and zoonotic sources contribute antibiotic-resistant and virulent S. aureus to watersheds, with streams facilitating environmental transmission to marine waters. This watershed-scale assessment enables the prediction of spatial and temporal conditions associated with elevated S. aureus concentrations, thereby reducing exposure and infections.

Staphylococcus aureus↗

PubMed2002

An algorithm for assessing the risk of traffic accident.

INTRODUCTION: This study is aimed at developing an algorithm to estimate the number of traffic accidents and assess the risk of traffic accidents in a study area. METHOD: The algorithm involves a combination of mapping technique (Geographical Information System (GIS) techniques) and statistical methods (cluster analysis and regression analysis). Geographical Information System is used to locate accidents on a digital map and realize their distribution. Cluster analysis is used to group the homogeneous data together. Regression analysis is performed to realize the relation between the number of accident events and the potential causal factors. Negative binomial regression model is found to be an appropriate mathematical form to mimic this relation. Accident risk of the area, derived from historical accident records and causal factors, is also determined in the algorithm. The risk is computed using the Empirical Bayes (EB) approach. A case study of Hong Kong is presented to illustrate the effectiveness of the proposed algorithm. RESULTS: The results show that the algorithm improves accident risk estimation when comparing to the estimated risk based on only the historical accident records. The algorithm is found to be more efficient, especially in the case of fatality and pedestrian-related accident analysis. IMPACT ON INDUSTRY: The output of the proposed algorithm can help authorities effectively identify areas with high accident risk. In addition, it can serve as a reference for town planners considering road safety.

Accidents, Traffic↗

PubMed2005

Geographic prediction of human onset of West Nile virus using dead crow clusters: an evaluation of year 2002 data in New York State.

The risk of becoming a West Nile virus case in New York State, excluding New York City, was evaluated for persons whose town of residence was proximal to spatial clusters of dead American crows (Corvus brachyrhynchos). Weekly clusters were delineated for June-October 2002 by using both the binomial spatial scan statistic and kernel density smoothing. The relative risk of a human case was estimated for different spatial-temporal exposure definitions after adjusting for population density and age distribution using Poisson regression, adjusting for week and geographic region, and conducting Cox proportional hazards modeling, where the week that a human case was identified was treated as the failure time and baseline hazard was stratified by region. The risk of becoming a West Nile virus case was positively associated with living in towns proximal to dead crow clusters. The highest risk was consistently for towns associated with a cluster in the current or prior 1-2 weeks. Weaker, but positive associations were found for towns associated with a cluster in just the 1-2 prior weeks, indicating an ability to predict onset in a timely fashion.

Animals↗

PubMedDate not supplied

The hyphomycete Teberdinia hygrophila gen. nov., sp. nov. and related anamorphs of Pseudeurotium species.

A hyphomycetous fungus isolated from montane fen soil in the Caucasus Mountains, Russia, had obscurely sympodial conidiogenous cells that suggested a link to the heterogeneous genus Leptodontidium. Sequence analysis of the nuclear ribosomal small subunit and internal transcribed spacer region, however, disclosed that the fungus was an anamorphic member of a clade containing the cleistothecial ascomycetous genus Pseudeurotium. Teberdinia, gen. nov., is proposed for the blastic, generally sympodially proliferating anamorphs in this group, and Teberdinia hygrophila, sp. nov., is proposed for the species from upland fens. Binomials are not proposed for the remaining Teberdinia anamorphs of Pseudeurotium species. Purely anamorphic isolates in this clade are difficult to recognize using current morphological keys and might be more widely distributed and ecologically significant than is currently evident.

Ascomycota↗

PubMed2002

Habitat destruction, environmental catastrophes, and metapopulation extinction.

The extinction process of fragmented populations, characterized by a small number of conspecifics inhabiting each patch, is heavily affected by natural and human disturbance. To evaluate the risk of extinction we consider a network of identical patches connected by passive or active dispersal and hosting a finite, discrete number of individuals. We discuss three types of disturbance affecting the metapopulation: permanent loss of habitat patches, erosion of existing patches, and random catastrophes that wipe out the entire population of a patch. Starting from an infinite-dimensional Markov model that fully accounts for demographic stochasticity, we reduce it to finite dimension via moment closure with negative-binomial approximation. The compact models obtained in this way account for the dynamics of the fraction of empty patches, the average number of individuals in occupied patches, and the variance of their distribution. After comparing the performance of these compact models with that of the infinite-dimensional model in the case of no disturbances, we then proceed to computing persistence-extinction boundaries as bifurcation lines of the compact models in the space of demographic and disturbance parameters. We consider bifurcations with respect to demographic and environmental parameters and contrast our results with those of previous theories. We find out that environmental catastrophes increase the risk of extinction for both frequent and infrequent dispersers, while the random loss of patches has a much larger influence on frequent dispersers. This influence can be counterbalanced by active dispersal. Local erosion of habitat fragments has a larger influence on infrequent than on frequent dispersers. We finally discuss the important synergistic effects of disturbances acting simultaneously.

Disasters↗

PubMed1990

A generalized chain binomial model with application to HIV infection.

The original Reed-Frost formulation of the chain binomial model is mathematically equivalent to a stochastic model allowing a Poisson number of effective contacts in a time interval. Their formulation cannot accommodate survey data that necessarily correspond to more complex distributions of partners or contacts, or to large populations where complete random mixing is unlikely. This paper generalizes the Reed-Frost model to accommodate these situations in both the one- and two-population settings. The extension to multiple populations is also outlined. Using the model to predict HIV incidence in San Francisco's homosexual population, we show that the total number of contacts over all partners is more important than the distribution of contacts among partners in determining the number of infected.

HIV Infections↗

PubMed1988

Small-sample confidence limits for parameters under inequality constraints with application to quantal bioassay.

A family of methods is presented for constructing confidence limits for the parameters of a collection of distributions when a simple ordering is assumed among the parameters. The methods are shown to yield confidence limits that are exact or conservative for finite samples. For discrete distributions, one of the methods produces confidence limits that are at least as tight as the limits produced by a commonly used single-sample procedure. Confidence limits are demonstrated for a binomial quantal bioassay problem assuming a nondecreasing dose-response function. Results of a simulation study show that competing asymptotic methods can produce serious discrepancies between nominal and actual coverage probabilities for binomial samples of sizes up to 30, and demonstrate that the new approach can be competitive with the asymptotic methods when the latter maintain their nominal error rates.

Animals↗

PubMed1989

The influence of individual, social group and household factors on the distribution of Ascaris lumbricoides within a community and implications for control strategies.

The distribution of Ascaris lumbricoides within a community was examined at an initial mass anthelmintic treatment programme (January 1984) and following an 11-month period of reinfection (November 1984). Similar patterns of the negative binomial parameter kappa (an inverse measure of parasite aggregation) and the proportion of parasites within the most heavily infected quartile of the community were recorded at the two dates. The pattern of parasite aggregation within individuals, measured by parameter k, appears to be a stable characteristic of this host-parasite relationship. Significant variation in the intensity of infection was observed between households in the community. The number of family members living in the house strongly influenced the mean Ascaris burden and proportion of relatively heavy infections within adults and children. This finding suggests that the density of people in a house positively influences the frequency of exposure to infective stages of Ascaris, which in turn plays a major role in determining which individuals will harbour heavy infections. Positive correlations were recorded between the initial and reinfection burdens of individuals, relative to others in the community. The correlations were strongest in the youngest and oldest age groups and were more frequently significant among age-stratified groups of females, compared to males. A comparative examination of hypothetical treatment strategies suggests that for Ascaris infections in this community, targetting age groups with anthelmintic treatment would probably be more cost-effective in the long term in reducing the abundance of this parasite than selective treatment of individually identified heavy infections.

Adolescent↗

PubMed2005

Bias-corrected maximum likelihood estimator of the negative binomial dispersion parameter.

We derive a first-order bias-corrected maximum likelihood estimator for the negative binomial dispersion parameter. This estimator is compared, in terms of bias and efficiency, with the maximum likelihood estimator investigated by Piegorsch (1990, Biometrics46, 863-867), the moment and the maximum extended quasi-likelihood estimators investigated by Clark and Perry (1989, Biometrics45, 309-316), and a double-extended quasi-likelihood estimator. The bias-corrected maximum likelihood estimator has superior bias and efficiency properties in most instances. For ease of comparison we give results for the two-parameter negative binomial model. However, an example involving negative binomial regression is given.

Animals↗

PubMed2004

An accident waiting to happen: a spatial approach to proactive pedestrian planning.

There are about 75,000 pedestrian crashes in the United States each year. Approximately 5000 of these crashes are fatal, accounting for 12% of all roadway deaths. On college campuses, pedestrian exposure and crash-risk can be quite high. Therefore, we analyzed pedestrian crashes on the campus of the University of North Carolina at Chapel Hill (UNC) as a test case for our spatially-oriented prototype tool that combines perceived-risk (survey) data with police-reported crash data to obtain a more complete picture of pedestrian crash-risk. We use spatial analysis techniques combined with regression models to understand factors associated with risk. The spatial analysis is based on comparing two distributions, i.e. the locations of perceived-risk with police-reported crash locations. The differences between the two distributions are statistically significant, implying that certain locations on campus are perceived as dangerous, though pedestrian crashes have not yet occurred there, and there are actual locations of police-reported crashes that are not perceived to be dangerous by pedestrians or drivers. Furthermore, we estimate negative binomial regression models to combine pedestrian and automobile exposure with roadway characteristics and spatial/land use information. The models show that high exposure, incomplete sidewalks and high crosswalk density are associated with greater observed and perceived pedestrian crash-risk. Additionally, we found that people perceive a lower risk near university libraries, stadiums, and academic buildings, despite the occurrence of crashes.

Accidents, Traffic↗

PubMedDate not supplied

Analysis of exacerbation rates in asthma and chronic obstructive pulmonary disease: example from the TRISTAN study.

Recurrent events in clinical trials have typically been analysed using either a multiple time-to-event method or a direct approach based on the distribution of the number of events. An area of application for these methods is exacerbation data from respiratory clinical trials. The different approaches to the analysis and the issues involved are illustrated for a large trial (n = 1465) in chronic obstructive pulmonary disease (COPD). For exacerbation rates, clinical interest centres on a direct comparison of rates for each treatment which favours the distribution-based analysis, rather than a time-to-event approach. Poisson regression has often been employed and has recently been recommended as the appropriate method of analysis for COPD exacerbations but the key assumptions often appear unreasonable for this analysis. By contrast use of a negative binomial model which corresponds to assuming a separate Poisson parameter for each subject offers a more appealing approach. Non-parametric methods avoid some of the assumptions required by these models, but do not provide appropriate estimates of treatment effects because of the discrete and bounded nature of the data.

Albuterol↗

PubMed1986

Threshold behaviour for a chain-binomial S-I-S infectious disease.

The present paper is concerned with a chain-binomial deterministic model for an infectious disease of the S-I-S type. The model extends the Cooke et al. (1977) and Longini (1980) model in the sense that it accounts for the distribution of the number of contacts made by each susceptible during an infectious period and for the probabilities of infection at the different contacts with infectives. The aim of the work is to investigate under which conditions the disease becomes endemic or not. Some partial results are first derived, but a complete analysis of the threshold behaviour seems very intricate. A more detailed discussion is then presented for the specific case where at least K + 1 contacts with infectives, K greater than or equal to 1 fixed, are required to make a susceptible infected.

Communicable Diseases↗