Search PubMed⌕ Search

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.

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

At least 1,477 records · Page 82Linked to original sources
PubMed2004

Bayesian model accounting for within-class biological variability in Serial Analysis of Gene Expression (SAGE).

BACKGROUND: An important challenge for transcript counting methods such as Serial Analysis of Gene Expression (SAGE), "Digital Northern" or Massively Parallel Signature Sequencing (MPSS), is to carry out statistical analyses that account for the within-class variability, i.e., variability due to the intrinsic biological differences among sampled individuals of the same class, and not only variability due to technical sampling error. RESULTS: We introduce a Bayesian model that accounts for the within-class variability by means of mixture distribution. We show that the previously available approaches of aggregation in pools ("pseudo-libraries") and the Beta-Binomial model, are particular cases of the mixture model. We illustrate our method with a brain tumor vs. normal comparison using SAGE data from public databases. We show examples of tags regarded as differentially expressed with high significance if the within-class variability is ignored, but clearly not so significant if one accounts for it. CONCLUSION: Using available information about biological replicates, one can transform a list of candidate transcripts showing differential expression to a more reliable one. Our method is freely available, under GPL/GNU copyleft, through a user friendly web-based on-line tool or as R language scripts at supplemental web-site.

Astrocytoma↗
PubMed2002

An evaluation of spatio-temporal models for the estimation of the mortality relative risk from breast cancer in Galicia, Spain.

BACKGROUND: Disease mapping is now a big focus of interest in the area of Public Health, and the geographical distribution of a disease has an important role in understanding its origin or its causes. The purpose of this work is to review and evaluate different techniques to map the mortality risk of a disease in small geographical areas. METHODS: Three different methods have been studied. The first one is a classical approach consisting of mapping SMRs, which are maximum likelihood estimates of the relative risk under a Poisson model of death counts. In a second step we consider Poisson and negative binomial regression to fit the rates and finally we use a Bayesian approach that assumes a hierarchical model where the death counts follow a Poisson distribution conditioned by the prior information. These methods have been applied to the study of geographical variation in female breast cancer mortality from 1976 to 1999 in the districts of Galicia, Spain. RESULTS: Mapping the SMRs using the first method has important drawbacks and there are difficulties to distinguish the mortality pattern. With the second method we achieved some improvements. The Bayesian methodology produces smoother maps with a clear mortality pattern. DISCUSSION: These methods are powerful tools for identifying areas with elevated risk. The Bayesian methodology has many advantages over the other methods that had been analysed in this work.

Adult↗
PubMed2005

An application of bootstrap resampling method to obtain confidence interval for percentile fatness cutoff points in childhood and adolescence overweight diagnoses.

OBJECTIVE: To present a resampling approach to obtain confidence intervals (CIs) and the empirical distributions for the studentized regression residuals percentiles when used as cutoff points for overweight and obesity diagnosis in children and adolescents. METHOD: A tutorial for the nonparametric bootstrap with bias accelerating correction is presented. A classical method, the Binomial interpretation, is used as comparing criterion. SUBJECTS: A case study comprising 418 randomly selected subjects from a private secondary school (age: 10-17 y, boys: 52%). MEASUREMENTS: Body fat percentage (by), age (y) and Tanner criteria. RESULTS: The empirical distributions presented skewness suggesting that the CIs should not be symmetric. CIs obtained by the proposed approach were more realistic than the classical ones. CONCLUSIONS: We propose a simple and efficient way to obtain the interval estimates and the distribution properties of cutoff points for overweight and obese classification using a sample-based method that allows the comparison of cutoffs among many subpopulations.

Adipose Tissue↗
PubMed2004

Likelihood-based inference for stochastic models of sexual network formation.

Sexually-transmitted diseases (STDs) constitute a major public health concern. Mathematical models for the transmission dynamics of STDs indicate that heterogeneity in sexual activity level allow them to persist even when the typical behavior of the population would not support endemicity. This insight focuses attention on the distribution of sexual activity level in a population. In this paper, we develop several stochastic process models for the formation of sexual partnership networks. Using likelihood-based model selection procedures, we assess the fit of the different models to three large distributions of sexual partner counts: (1) Rakai, Uganda, (2) Sweden, and (3) the USA. Five of the six single-sex networks were fit best by the negative binomial model. The American women's network was best fit by a power-law model, the Yule. For most networks, several competing models fit approximately equally well. These results suggest three conclusions: (1) no single unitary process clearly underlies the formation of these sexual networks, (2) behavioral heterogeneity plays an essential role in network structure, (3) substantial model uncertainty exists for sexual network degree distributions. Behavioral research focused on the mechanisms of partnership formation will play an essential role in specifying the best model for empirical degree distributions. We discuss the limitations of inferences from such data, and the utility of degree-based epidemiological models more generally.

Databases as Topic↗
PubMed2001

On small-sample confidence intervals for parameters in discrete distributions.

The traditional definition of a confidence interval requires the coverage probability at any value of the parameter to be at least the nominal confidence level. In constructing such intervals for parameters in discrete distributions, less conservative behavior results from inverting a single two-sided test than inverting two separate one-sided tests of half the nominal level each. We illustrate for a variety of discrete problems, including interval estimation of a binomial parameter, the difference and the ratio of two binomial parameters for independent samples, and the odds ratio.

Biometry↗
PubMedDate not supplied

[The problem of repeated measurements. Longitudinal analysis in epidemiology].

In longitudinal analyses subjects are repeatedly measured along time. They are mixed designs, characterised for their simultaneous consideration of two or more dimensions of analysis, in which time is one of the dimensions.Longitudinal analyses have important advantages with respect other designs. The most important is that they are more efficient, since they allow to distinguish between-individual and within-individual variation.Longitudinal analyses can be approached marginal and conditionally. Whereas the former allows to draw poblational, or average, inferences, the latter permits to draw individual inferences.The statistical models to use depend on the type of response variable. If the dependent variable is normally distributed one will use linear mixed models. When the response is a count one will use mixed Poisson regressions. Mixed binomial or multinomial logistic regressions should be used when the response would be categorical.

Epidemiologic Studies↗
PubMedDate not supplied

Empirical Bayes estimation of small area prevalence of non-rare conditions.

Geographical studies are becoming increasingly common in epidemiology. The problems of small area investigations are well known, and several methods are available for the estimation and mapping of disease risk across small areas, with the emphasis mainly on applications concerning rare disease incidence or mortality. An empirical Bayes method is proposed for small area estimation of the prevalence of non-rare conditions, whose variability is binomial and cannot be approximated by a Poisson model. It is the direct equivalent of a semi-parametric non-iterative moment estimation method proposed in the Poisson case. As an example, the geographical distribution of the prevalence of respiratory symptoms in schoolchildren across 71 small areas in Huddersfield, Northern England is studied. Whereas random variability causes the crude area-specific prevalences to be unstable, the posterior estimates, corrected towards overall or local means, are capable of highlighting genuine extra-binomial variability. The method is very simple and can readily be applied to the study of a number of common conditions.

Air Pollution↗
PubMed2005

Generics market in Greece: the pharmaceutical industry's beliefs.

The aim of this study was to investigate the beliefs and perspectives of the pharmaceutical industry on generic medication in Greece. Questionnaires were mailed to all 58 members of the Hellenic Association of Pharmaceutical Companies from November 2002 to February 2003. The response rate was 52%, namely 30 questionnaires were completed and returned. The questionnaire requested information on companies' involvement in generics, their opinion on generics' characteristics and on public policies affecting the demand and supply of generic medication. A descriptive analysis of the outcomes, that is percentage comparison through binomial tests and Fisher tests, was performed. According to our findings, 43% of the respondents were involved in the production and distribution of generics and the mean period of their involvement was 12 years. The majority of the respondents were in favor of their companies' involvement in generics, despite the relatively small market share of generics in Greece; 9.7% of total pharmaceutical market in 2003. Bearing in mind that in Greece the promotion of generics is not encouraged, pharmaceutical companies believe that the mandatory introduction of bioequivalence studies is an indirect promotional strategy towards generics. Additionally, the majority declared that their main competitive advantages are their safety, efficacy and effectiveness as well as their economic benefit to the society. Finally, the respondents expressed their preference for the introduction of pharmacoeconomic submissions for drugs' reimbursement by social insurance funds.

Administrative Personnel↗
PubMed1999

Practical considerations in using calculated healthy-tissue complication probabilities for treatment-plan optimization.

PURPOSE: Healthy and neoplastic tissues are generally exposed nonuniformly to ionizing radiation. It is thus useful to develop algorithms that predict the probability of tumor control or normal tissue complication probability (NTCP) for any given spatial pattern of dose delivery. The questions addressed here concern: (a) the sensitivity of the NTCP predictions to the actual model used for extrapolation from uniform irradiation (where some clinical data exist) to nonuniform exposures, (b) its dependence on tissue type, and (c) consequences for treatment-plan optimization. METHODS AND MATERIALS: Two (of several possible) NTCP formulations are used here: the Lyman model and a binomial equation. The effective volume-reduction scheme of Kutcher and Burman is used to obtain the NTCP for an arbitrary distribution of dose. NTCP was calculated for seven organs by postulating a dose distribution of maximum nonuniformity. RESULTS: Both models fit available NTCP data well, but have very different extrapolations for exposures of small tissue volumes and very low values of NTCP (e.g., < 5%) where no data exist. Organs with pronounced volume effects (lung, kidneys) show substantial NTCP differences between the two models. Even in organs where the volume effect is small (e.g., spinal cord, brain), differences in NTCP due to the model selected may still have serious clinical consequences, as an actual example (for the spinal cord) indicates. CONCLUSIONS: NTCP calculations based on extrapolations to volume fractions and/or NTCP levels for which reliable data do not exist depend on the model used to fit the data and the degree of dose nonuniformity. If NTCP is to be used in treatment-plan optimization, the prudent approach is to design plans that reproduce the conditions under which available dose-volume data were taken (e. g., uniform dose distributions).

Algorithms↗
PubMed2006

Multivariate extensions of McNemar's test.

This article considers global tests of differences between paired vectors of binomial probabilities, based on data from two dependent multivariate binary samples. Difference is defined as either an inhomogeneity in the marginal distributions or asymmetry in the joint distribution. For detecting the first type of difference, we propose a multivariate extension of McNemar's test and show that it is a generalized score test under a generalized estimating equations (GEE) approach. Univariate features such as the relationship between the Wald and score tests and the dropout of pairs with the same response carry over to the multivariate case and the test does not depend on the working correlation assumption among the components of the multivariate response. For sparse or imbalanced data, such as occurs when the number of variables is large or the proportions are close to zero, the test is best implemented using a bootstrap, and if this is computationally too complex, a permutation distribution. We apply the test to safety data for a drug, in which two doses are evaluated by comparing multiple responses by the same subjects to each one of them.

Biometry↗
PubMedDate not supplied

Testing deviation for a set of serial dilution most probable numbers from a Poisson-binomial model.

A serial dilution experiment estimates the microbial concentration in a broth by inoculating several sets of tubes with various amounts of the broth. The estimation uses the Poisson distribution and the number of tubes in each of these sets that show growth. Several factors, such as interfering microbes, toxins, or disaggregation of adhering microbes, may distort the results of a serial dilution experiment. A mild enough distortion may not raise suspicion with a single outcome. The test introduced here judges whether the entire set of serial dilution outcomes appears unusual. This test forms lists of the possible outcomes. The set of outcomes is declared unusual if any occurrence of an observed outcome is on the first list, or more than one is on the first or second list, etc. A similar test can apply when there are only a finite number of possible outcomes, and each outcome has a calculable probability, and few outcomes have tied probabilities.

Chemistry↗
PubMed1977

Significance testing to establish equivalence between treatments, with special reference to data in the form of 2X2 tables.

In this paper, the role of significance testing in establishing equivalence between treatments is described. In place of the more customary null hypothesis of no difference between treatments, the hypothesis that the true difference is equal to a specified delta is tested. The particular case of comparing two binomial samples is described in detail. Results using a method due to Gart and approximations based on the chi2 and normal distributions are compared. It is found that the test based upon chi2 with continuity correction agrees best overall with Gart's (1971) test and is therefore recommended for use when computational facilities needed for carrying out the latter are not available.

Biometry↗
PubMed2025

Sex Distributions in the Most Frequent Autosomal Genetic Causes of Retinitis Pigmentosa.

PURPOSE: The purpose of this study was to explore whether sex imbalances are detectable in the most frequent genetic causes of retinitis pigmentosa (RP). METHODS: Databases from centers in three countries (Moorfields Eye Hospital, London; Hospital for Sick Children, Toronto; and Australian Inherited Retinal Disease Registry, Perth, Australia) were searched, quantifying numbers of male and female patients with disease attributed to variants in the six most frequently involved autosomal RP genes. Proportions of female patients (with 95% confidence intervals [CIs]) were calculated for each gene. Two-tailed binomial testing was performed (Bonferroni corrected threshold, P = 0.008) to investigate whether proportions differed significantly from an underlying male:female ratio of 1:1. For genes where the 95% CI did not include 50%, sex distributions were also explored in previously published cohorts. RESULTS: Our search yielded 1454 patients with disease attributable to variants in USH2A (n = 550), RP1 (n = 277), RHO (n = 246), PRPF31 (n = 158), EYS (n = 124), and MYO7A (n = 99). Proportions of female patients (95% CI) for each gene were 46.2% (42.0-50.5%), 49.5% (43.4-55.5%), 55.3% (48.8-61.6%), 63.9% (55.9-71.3%), 39.5% (31.0-48.7%), and 42.4% (32.7-52.8%), respectively. The 95% CI did not include 50% for PRPF31 and EYS; binomial testing revealed P values of 6.24 &#xd7; 10-4 and 0.025, respectively. Combining with data extracted from previously published cohorts yielded P values of 1.62 &#xd7; 10-6 and 0.0084, respectively. CONCLUSIONS: We observed a significant preponderance of female patients for PRPF31-associated RP and a preponderance of male patients in those with EYS-associated RP. Our findings suggest that sex is likely to be a modifier affecting penetrance in PRPF31-associated disease and might act in the opposite direction in disease associated with EYS.

Humans↗
PubMed2002

Egg distributions and the information a solitary parasitoid has and uses for its oviposition decisions.

Approximately three decades ago the question was first answered "whether parasitoids are able to assess the number or origin of eggs in a host" for a solitary parasitoid, Leptopilina heterotoma, by fitting theoretically derived distributions to empirical ones. We extend the set of different theoretically postulated distributions of eggs among hosts by combining searching modes and abilities in assessing host quality. In the models, parasitoids search either randomly (Poisson) (1) or by vibrotaxis (Negative Binomial) (2). Parasitoids are: (a) assumed to treat all hosts equally, (b) able to distinguish them in unparasitised and parasitised hosts only, (c) able to distinguish them by the number of eggs they contained, or (d) able to recognise their own eggs. Mathematically tractable combinations of searching mode (1 and 2) and abilities (a,b,c,d) result in seven different models (M1a, M1b, M1c, M1d, M2a, M2b and M2c). These models have been simulated for a varying number of searching parasitoids and various mean numbers of eggs per host. Each resulting distribution is fitted to all theoretical models. The model with the minimum Akaike's information criterion (AIC) is chosen as the best fitting for each simulated distribution. We thus investigate the power of the AIC and for each distribution with a specified mean number of eggs per host we derive a frequency distribution for classification. Firstly, we discuss the simulations of models including random search (M1a, M1b, M1c and M1d). For M1a, M1c and M1d the simulated distributions are correctly classified in at least 70% of all cases. However, in a few cases model M1b is only properly classified for intermediate mean values of eggs per host. The models including vibrotaxis as searching behaviour (M2a, M2b and M2c) cannot be distinguished from those with random search if the mean number of eggs per host is low. Among the models incorporating vibrotaxis the three abilities are detected analogously as in models with random search. Experiments with two species of solitary parasitoids (L. heterotoma and Asobara tabida) are conducted. All theoretically postulated distributions are separately fitted to the resulting experimental egg distributions. The AIC criterion is used to choose the best fitting theoretical distribution. For both parasitoid species the frequency distribution of best fitting models for experimental data is compared to the classification of distributions generated by simulations. This leads to the conclusion that both L. heterotoma and A. tabida are able to distinguish between parasitised and unparasitised hosts. For L. heterotoma the results point to an ability to assess the number of eggs in a host, whereas A. tabida does not seem to have this ability. This difference suggests that an egg is more valuable for L. heterotoma than for A. tabida.

Animals↗
PubMed2001

An exact trend test for correlated binary data.

The problem of testing a dose-response relationship in the presence of exchangeably correlated binary data has been addressed using a variety of models. Most commonly used approaches are derived from likelihood or generalized estimating equations and rely on large-sample theory to justify their inferences. However, while earlier work has determined that these methods may perform poorly for small or sparse samples, there are few alternatives available to those faced with such data. We propose an exact trend test for exchangeably correlated binary data when groups of correlated observations are ordered. This exact approach is based on an exponential model derived by Molenberghs and Ryan (1999) and Ryan and Molenberghs (1999) and provides natural analogues to Fisher's exact test and the binomial trend test when the data are correlated. We use a graphical method with which one can efficiently compute the exact tail distribution and apply the test to two examples.

Abnormalities, Drug-Induced↗
PubMed2005

Analysis of count data using poisson regression.

Nurses and other health researchers are often concerned with infrequently occurring, repeatable, health-related events such as number of hospitalizations, pregnancies, or visits to a health care provider. Reports on the occurrence of such discrete events take the form of non-negative integer or count data. Because the counts of infrequently occurring events tend to be non-normally distributed and highly positively skewed, the use of ordinary least squares (OLS) regression with non-transformed data has several shortcomings. Techniques such as Poisson regression and negative binomial regression may provide more appropriate alternatives for analyzing these data. The purpose of this article is to compare and contrast the use of these three methods for the analysis of infrequently occurring count data. The strengths, limitations, and special considerations of each approach are discussed. Data from the National Longitudinal Survey of Adolescent Health (AddHealth) are used for illustrative purposes.

Adolescent↗
PubMedDate not supplied

Investigations into parametric analysis of data from in vivo micronucleus assays by comparison with non-parametric methods.

Data from micronucleus assays of 6 compounds were analysed by 3 non-parametric and 3 parametric methods. Two of the latter involved transformation of the data so several transformation strategies were investigated. It was concluded that the non-parametric Kolmogorov-Smirnov two-sample test was the most reliable method of analysis. None of the parametric solutions was entirely satisfactory. The Bayesian solution to the Behrens-Fisher problem of normal distributions with differing variances was an acceptable compromise after the data had been transformed by the inverse hyperbolic sine method applicable to negative binomials.

Animals↗
PubMed1997

Evaluation and comparison of antibody ELISAs for serodiagnosis of bovine trypanosomosis.

A total of 457 serum samples from cattle kept under moderate tsetse challenge in Mukono County, Uganda, (79 of them with confirmed trypanosomosis) and 86 sera from cattle in Germany were tested for Trypanosoma antibodies using enzyme-linked immunosorbent assay (ELISA) with antigen obtained from blood stream form (BSF) and in vitro cultivated procyclic (PRO) trypanosomes. The BSF and PRO ELISA showed a moderate quantitative correlation. A difference plot revealed a slightly non-linear relation between the two methods. Cut-off values were established using (A) non-exposed controls, (B) exposed negative controls and (C) by mixture distribution analysis of the quantitative ELISA results for the sample from the endemic target population. The diagnostic agreement between both assays was significant (kappa, p < 0.05). The diagnostic accuracy of the two tests relative to standard parasitological detection methods was not markedly different as shown by the areas under the receiver operating characteristic (ROC) plots. In our study, neither non-exposed controls (cut-off A) nor exposed negative controls (cut-off B) were suitable for establishing cut-off values. Based on the cut-off value C, derived from mixture distribution analysis, the proportion of animals with elevated antibody levels in the study population was estimated by both assays at 45% (41-50% binomial 95% confidence interval). This can be regarded as an unbiased estimate of the proportion of 'sero-responders' and not necessarily as a proxy for infection prevalence in the target population. We recommend the PRO ELISA to be used for seroepidemiological surveys, since in vitro cultivation of procyclic trypanosomes allows a continuous and standardised preparation of test antigen.

Animals↗