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 19 recordsLinked to original sources
PubMed1988

[An analysis of transmission in the interneuronal synapses using a convolution of binomial distributions].

The convolution of two binomial distributions has been used for the analysis of the discrete distributions of the elementary EPSPs amplitude in the sensorimotor, proprio- and reticulo-motoneuronal synapses of the frog. It is shown that the quantity of the working transmitter release sites is higher than that estimated by the binomial distribution. The probability of the release sites response to the single action potential was unequal. In most sites they did not exceed 0.1-0.3 and were supported on the constant level. The effect on the transmitter release mechanism induced blocking of the release sites. The disturbance of preparation to the transmitter release sharply decreased the probability of the release sites response.

Animals↗
PubMed2026

SNP genotyping in Pseudotsuga menziesii and Pinus radiata using targeted genotyping-by-sequencing (GBS): improved Bayesian SNP calling using a beta-binomial distribution and other optimized input parameters.

BACKGROUND: Single-nucleotide polymorphism markers (SNPs) have important applications in gene conservation, breeding, and fundamental genetics research. Our long-term goal is to develop routine approaches for SNP genotyping in forest trees. Ideally, these approaches would be inexpensive, able to accommodate a wide range of samples and SNPs, available through commercial providers, and produce high-quality SNP data. RESULTS: Using targeted genotyping-by-sequencing (GBS), we developed SNP assays for two highly heterozygous tree species, Douglas-fir (Pseudotsuga menziesii) and radiata pine (Pinus radiata). Using Douglas-fir haploid and diploid data, we optimized Bayesian SNP calling by testing four input parameters: (1) allele and genotype prior probabilities, (2) Rho, the beta-binomial dispersion parameter, (3) estimated read error (BayesReadError), and (4) the logPO cutoff used to filter low confidence SNP calls. logPO is the Bayesian posterior odds ratio for a called SNP. Compared to assuming a binomial distribution of read counts (Rho = 0), the beta-binomial distribution (Rho = 0.33) substantially reduced call error and heterozygote undercalling. Compared to the other Bayesian parameters, genotype priors had little effect on genotyping success. For Douglas-fir, we tested 5,360 SNP assays, and then studied the performance of the best 4,000. For radiata pine, we tested 6,000 SNP assays, and then studied the performance of the best 4,570. In Douglas-fir and radiata pine, our Bayesian approach resulted in median call rates of 95% to 98% for the top-ranked SNPs, with an estimated call error of 1.60% for known homozygous genotypes and 2.27% for known heterozygotes. In radiata pine, median and mean call rates were above 91% for GBS and SNP genotyping using an Axiom fixed genotyping array. Additionally, the median correspondence between the GBS and Axiom genotypes was about 98% overall (mean 96%). CONCLUSIONS: By optimizing Bayesian SNP calling, selecting the best 4-5 K SNPs, and excluding samples with low DNA amounts, we substantially reduced call error and heterozygote undercalling, resulting in SNP genotypes that were nearly identical to genotypes obtained using the Axiom array. Furthermore, genotyping performance should increase even further if our SNP rankings were used to develop less complex probe pools that target fewer SNPs.

Pinus↗
PubMed1989

Tutorial on large deviations for the binomial distribution.

We present, in an easy to use form, the large deviation theory of the binomial distribution: how to approximate the probability of k or more successes in n independent trials, each with success probability p, when the specified fraction of successes, a identical to k/n, satisfies 0 less than p less than a less than 1.

Amino Acid Sequence↗
PubMed1990

Segregation ratios within Segregation Distorter lines of Drosophila melanogaster conform to a beta-binomial distribution.

Segregation Distorter (SD) chromosomes are preferentially recovered from SD/SD+ males due to the dysfunction of sperm bearing the SD+ chromosome. The proportion of offspring bearing the SD chromosome is given the symbol k. The nature of the frequency distribution of k was examined by comparing observed k distributions produced by six different SD chromosomes, each with a different mean, with k distributions predicted by two different statistical models. The first model was one where the k of all males with a given SD chromosome were considered to be equal prior to the determination of those gametes which produce viable zygotes. In this model the only source of variation of k would be binomial sampling. The results rigorously demonstrated for the first time that the observed k distributions did not fit the prediction that the only source of variation was binomial sampling. The next model tested was that the prior distribution of segregation ratios conformed to a beta distribution, such that the distribution of k would be a beta-binomial distribution. The predicted distributions of this model did not differ significantly from the observed distributions of k in five of the six cases examined. The sixth case probably failed to fit a beta-binomial distribution due to a major segregating modifier. The demonstration that the prior distribution of segregation ratios of SD lines can generally be approximated with a beta distribution is crucial for the biometrical analysis of segregation distortion.

Animals↗
PubMed1978

Use of the beta-binomial distribution in dominant-lethal testing for "weak mutagenic activity: part 2.

Experiments in Dominant-Lethal Testing have been simulated on the computer to estimate the type I error rates and the power of the Beta-Binomial test under various models. (1) The mating ratio is one; and p, the probability that an implant will die, is distributed over the couples. (2) The mating ratio is larger than one; and p is distributed over the males, the females mated to the same male being binomial observations of the value p supplied by the male. (3) The mating ratio is larger than one; and p is distributed over the females. The average rates of dead implants have been set at 0.08 and 0.10 for the control and treatment groups, respectively, and a nominal level of significance equal to 0.05 has been chosen. The type I error rate of the traditional chi-square test has also been estimated. A by-product of these simulations is the behaviour of the estimates alpha and beta of the beta-distribution parameters, which discloses that, in the actual experiments with mice, p is distributed over the females. Our results lead to the recommendations that, for a given number of animals per group, a mating ratio larger than one should be adopted and that the males should be considered as the experimental units for the calculations. With 300 and 450 animals per group, average powers of 0.72 and 0.85 are reached, respectively, for the chosen increment of 2% in the rate of dead implants. Under these models, the type I error rate of the traditional chi-square test may grow to 0.30 for the nominal level of 0.05.

Genes, Dominant↗
PubMed1975

[The result-sequence method (sequence analysis) in leptospira research. 3. Communication: The bilateral sequential test (de Boer, Armitage) for testing the difference of mean values of two binomial distributions (author's transl)].

The influence of the liver-activated and non-activated cytostatic drug Cyclophosphamid on the respiration of Leptospira biflexa semaranga Veldrat S 173 was tested in three different concentrations by group-sequential testing of two relative frequencies in a two-sided test-reading. The conditioned probability theta = 0.82 results from thetan = 0.40 and thetaa = 0.75. On account of a practicable sample size, we choose theta' = 0.80 (activated form superior) and theta'' = 0.20 (non-activated form superior). The test-adjusted level of significance is alpha = 0.05 less than beta = 0.10. The expected values for the number of discordant pairs are Etheta' = Etheta'' = 13, Etheta = 1/1 = 14 and Ethetamax = 16. The acceptance inspection performed by control chart and tabulated reference figures results - in comparison with conventional procedures - in savings of discordant pairs of 65 per cent (concentration 10(-4) g/ml) in a decision in favour of activated form, of 65 per cent (concentration 10(-8) g/ml) in an equal efficiency of both states of Cyclophosphamid and of 10 per cent (concentration 10(-11) g/ml) in a non-significant difference. Taking into consideration all unrestrictedly selected pairs, the duration of the experiment takes only 4.25 months instead of 6.75 if the statistical data analysis is not performed conventionally, but group-sequentially instead.

Cyclophosphamide↗
PubMed1976

An approach to numerical identification of bacterial species.

The distribution of matching coefficients (M values) for strains of a species to their own 'hypothetical mean organism' (HMO) or to HMO patterns of other organisms was studied in 754 strains of 19 mycobacterial species, testing for 91 discriminating characters. The M values of strains of a species to the HMO of other species usually showed a normal distribution, and M values to their own HMO showed either a normal distribution of a binomial distribution, depending on the mean of M values. If the number of test characters was large, the binomial distribution usually resembled the normal distribution. After preparation of the HMO for every species and estimation of the mean of the M values (M) and the standard deviation (s), numerical identification could be carried out: if a test strain had an M value to the HMO of species chi that only fell within the range (M +/2s) for species chi, the strain would be identified as a member of that species.

Bacteria↗
PubMed1990

Multichannel 18-test panels: are 60% of panels abnormal by chance?

Current teaching concerning the frequency of abnormal results secondary to chance alone in a multichannel panel is theoretically based on the binomial distribution. However, this distribution can be used only when the probability of an abnormal result (pi) is the same for each test in the panel. In modern-day multichannel testing, pi varies from test to test and most often is less than the usually reported 0.05. On the other hand, a test such as cholesterol may have a pi level as high as 0.55. Theoretically the only distribution that can take this variability into consideration is the Lexis distribution, a form of the binomial distribution that allows for varying pi s. Since no formula is available to calculate this distribution, we wrote a computer program to generate it. We arranged 18-test panels from 203 normal patients in a frequency distribution. This was then compared with the theoretical Lexis and binomial distributions. This analysis showed that although there was a 50% chance of having one abnormality per panel and a 16% chance of having two abnormalities per panel, there was less than 4% chance of having three or more abnormalities per 18-test panel. In addition, most of the abnormalities noted were minor and were thought to be clinically unimportant.

Adult↗
PubMed1989

[Family clustering analysis of HBV infection].

A family clustering analysis of HBsAg, anti-HBs, anti-HBc positive and total infected persons in 148 families on a farm was carried out by the methods of G statistic, binomial distribution and negative binomial distribution. The results consistently showed that there was significant clustering of HBsAg carriers in families, whereas there were not clustering was seen an overall HBV infected persons in families. The clustering of HBsAg carriers in families is due probably to the effect of some genetic factors. The results of G statistic analysis indicate that anti-HBc also have significant clustering in families.

Carrier State↗
PubMed1979

The micronucleus test: statistical design and analysis.

Alternative statistical procedures are discussed which may be employed to compare the incidences among treatment groups of micronucleated polychromatic and normochromatic erythrocytes and their ratios. Comparison of incidences of micronucleated polychromatic erythrocytes using a sequential sampling strategy based on the negative binomial distribution is shown to require fewer animals for the same sensitivity of test than a similar procedure based on the binomial distribution. The sequential test is superior, both in power and number of animals required, to an alternative 1-stage test based on the same distribution. The procedure described permits the investigator to optimize the number of animals in each test group and the number of cells counted per animal to detect a predetermined increase in the incidence of micronucleated cells over that observed in the control population within chosen limits of type I and type II error. An alternative sequential approach based on the binomial distribution is presented, which is applicable when the number of cells analyzed per animal is variable.

Animals↗
PubMed1988

The distribution of numbers of open channels in multi-channel patches.

Assumptions inherent in use of the binomial distribution are relaxed in order to identify alternative distributions with different variances, for fitting to the frequency distributions of numbers of open channels in multi-channel patches. The variance is less than that for the binomial distribution with the same expectation when either there is a negative interaction between channels or channels have different probabilities of being open. When the variance is greater, this may be because of positive interaction between channels or non-stationary behaviour. Use of the distributions and lack-of-fit statistics is illustrated.

Ion Channels↗
PubMed1991

Frequency of elevated urinary beta 2-microglobulin levels in relatives of patients with asymptomatic low-molecular-weight proteinuria.

We studied urinary beta 2-microglobulin levels in a total of 29 apparently healthy relatives (aged 0.8-70 years) of 8 male patients with asymptomatic low-molecular-weight proteinuria in six families. The frequency of levels above the age- and sex-associated 95% confidence limit was 7 of 29 (24%), 4 of 12 (33%) in first-degree relatives, 2 of 6 (33%) fathers, and 2 of 6 (33%) mothers. These frequencies were significantly above those in the general population (P less than 0.01, by a normal distribution test, a binomial distribution, and Poisson distribution test for the sample proportion). The increased frequency in fathers argues against an X-linked pattern of inheritance for this entity, suggesting that there is heterogeneity in the inheritance.

Adolescent↗
PubMed1985

Characterization of a cation channel on the apical surface of the frog lens epithelium.

The properties of a single conductance pathway of the apical (fibre-facing) surface of the frog lens epithelium are reported. Using the patch-clamp technique (Hamill, Marty, Neher, Sakmann & Sigworth, 1981), the most common single-channel currents had an amplitude of 1.9 pA, the mean open time 2.1 ms and a conductance of 25 pS. One open-state time constant (to = 3.3 ms) and two closed-state time constants (tau c1 = 0.9 ms, tau c2 = 23.1 ms) were resolved. The channel current and the mean open time were both increased when Ca2+ was removed from the external solution and the open time distribution was no longer fitted by a single exponential. Multiple-channel events in cell-attached patches containing two or more identical channels were distributed in a binomial fashion and the probability that an individual channel was open, obtained by fitting the binomial distribution, was 0.039. The channel was found to have a Na+:K+ selectivity ratio of 3:1. When Ca2+ was removed from the pipette solution the probability that an individual channel was open increased to 0.137 and the Na+:K+ selectivity ratio increased to 4:1. Channel activity was observed in the presence of tetrodotoxin (10(-6) M) in the bathing medium and the pipette solution but was abolished by internal perfusion of the patch pipette with 0.5 x 10(-4) M amiloride. this apical conductance pathway is identified as an amiloride-sensitive cation channel. These channels are clustered in groups on the apical membrane, spontaneously active at the resting potential and with the possibility of altering their Na+:K+ selectivity. They represent a distinct type of channel, that differ from nerve and muscle Na+ channels in their manner of activation, but do share some common features with both Na+ and Ca2+ channels in excitable cells.

Amiloride↗
PubMed1989

[Natural microbial control of crickets populations (Orthoptera: Gryllotalpidae: Scapteriscus borellii): regulation of populations aggregated in time and space].

From 1983 through 1988, a total of 1,762 collections, containing 31,312 individuals of the mole cricket, Scapteriscus borellii, were made, principally in the State of São Paulo, Brazil. Collections were found to fit a negative binomial distribution both as whole and when divided into monthly collections. In these collections, an iridovirus, a entomogenous nematode, and the fungi Metarhizium anisopliae, Beauveria bassiana, Paecilomyces sp., and Entomophtora sp., were found to be agents of natural mortality, although usually as endozootics and relatively rarely as epizootics and panzootics. As a group, these diseases were also distributed in a binomial negative. These data suggest that the temporal and spatial aggregations of the mole crickets, produced by high rates of migration among suitable habitats, are adaptations to outbreaks of epidemics, which also serve as mole cricket population regulators. These ideas are develop and derived from simple mathematical models of population change.

Animals↗
PubMed1979

Predictive probability early termination plans for phase II clinical trials.

A phase II clinical trial is designed to gather data to help decide whether an experimental treatment has sufficient effectiveness to justify further study. In a one-arm trial with dichotomous outcome, we wish to test a simple null hypothesis on the Bernoulli parameter against a one-sided alternative in a sample of N patients. It is advisable to have a rule to terminate the trial early when evidence accumulates that the treatment is ineffective. Predictive probabilities based on the binomial distribution and beta and uniform prior distributions for the binomial parameter are found to be useful as the basis of group sequential designs. Size, power and average sample size for these designs are discussed. A process for the specification of an early termination plan, advice on the quantification of prior beliefs, and illustrative examples are included.

Antineoplastic Agents↗