The distribution of births in some African populations: an empirical test of the adequacy of the negative binomial model.
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Africa↗
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Removing phenotypic distribution assumptions from tests of linkage disequilibrium for quantitative traits.
The transmission disequilibrium test (TDT) has become a family-based method of reference to search for linkage disequilibrium (LD). Although it was first developed for dichotomous traits, numerous approaches have extended the TDT to quantitative phenotypes that either rely on regression or variance component techniques. Both of these approaches are based on some phenotypic distribution assumptions, the violation of which can lead to inflation of type I error rates, and derive information from phenotypic variability, so that their power is very low under some selection schemes (e.g., one-tailed selection). We propose a new family-based test of association for quantitative traits, denoted maximum-likelihood-binomial (MLB)-QTDT, which addresses the two previous issues by incorporating a latent binary variable that captures the LD information between the marker allele and the quantitative phenotype. The method can be understood as a classical TDT for binary traits that would include pure affected and pure unaffected children, and the probability for a child to be affected or unaffected depends on his/her quantitative phenotypic value. Simulation studies under the null hypothesis show that the MLB-QTDT provides very consistent type I errors even in small and/or selected samples. Under the alternative hypothesis, the MLB-QTDT has good power to analyze one-tailed selected samples, and performs as well as a classical approach in other designs. The MLB-QTDT is a flexible distribution-free method to test for LD with quantitative phenotypes in nuclear families, and can easily incorporate previous extensions developed in the context of family-based association studies with binary traits.
Alleles↗
Monte Carlo models for nanoparticle formation in two microemulsion systems.
The process of formation of nanoparticles obtained by mixing two micellized, aqueous solutions has been simulated using the Monte Carlo technique. The model includes the phenomena of finite reaction, nucleation, and growth via intermicellar exchange. This exploratory study examines the characteristic particle size distributions (PSDs) that result from using combinations of different initial reactant distributions (Poissonian and geometric) and different types of intermicellar exchange protocols (random, cooperative, and binomial). It is observed that the PSDs obtained using an initial Poissonian distribution of reactants and random exchange rules are similar to reported experimental results for CdS nanoparticles. The effect of exchange efficiency and reaction rate has also been studied. It is seen that a high exchange efficiency leads to relatively larger particle sizes. Also, a slow reaction rate has been shown to lead to the formation of larger nanoparticles.
Journal Article↗
The binomial model in fluctuation analysis of quantal neurotransmitter release.
The mathematics of the binomial model for quantal neurotransmitter release is considered in general terms, to explore what information might be extractable from statistical aspects of data. For an array of N statistically independent release sites, each with a release probability p, the compound binomial always pertains, with = N , p' identical to 1 - var(m)/ = (1 + cvp2) and n' identical to /p' = N/(1 + cvp2), where m is the output/stimulus and cvp2 is var(p)/ 2. Unless n' is invariant with ambient conditions or stimulation paradigms, the simple binomial (cvp = 0) is untenable and n' is neither N nor the number of "active" sites or sites with a quantum available. At each site p = popA, whereas po is the output probability if a site is "eligible" or "filled" despite previous quantal discharge, and pA (eligibility probability) depends at least on the replenishment rate, po, and interstimulus time. Assuming stochastic replenishment, a simple algorithm allows calculation of the full statistical composition of outputs for any hypothetical combinations of po's and refill rates, for any stimulation paradigm and spontaneous release. A rise in n' (reduced cvp) tends to occur whenever po varies widely between sites, with a raised stimulation frequency or factors (tending to increase po's. Unlike and var(m) at equilibrium, output changes early in trains of stimuli, and covariances, potentially provide information about whether changes in reflect change in or in . Formulae are derived for variance and third moments of postsynaptic responses, which depend on the quantal mix in the signals. A new, easily computed function, the area product, gives noise-unbiased variance of a series of synaptic signals and its peristimulus time distribution, which is modified by the unit channel composition of quantal responses and if the signals reflect mixed responses from synapses with different quantal time course.
Binomial Distribution↗
Improved detection of event-related functional MRI signals using probability functions.
Selecting an optimal event distribution for experimental use in event-related fMRI studies can require the generation of large numbers of event sequences with characteristics hard to control. The use of known probability distributions offers the possibility to control event timing and constrain the search space for finding optimal event sequences. We investigated different probability distributions in terms of response estimation (estimation efficiency), detectability (detection power, parameter estimation efficiency, sensitivity to true positives), and false-positive activation. Numerous simulated event sequences were generated selecting interevent intervals (IEI) from the uniform, uniform permuted, Latin square, exponential, binomial, Poisson, chi(2), geometric, and bimodal probability distributions and fixed IEI. Event sequences from the bimodal distribution, like block designs, had the best performance for detection and the poorest for estimation, while high estimation and detectability occurred for the long-decay exponential distribution. The uniform distribution also yielded high estimation efficiency, but probability functions with a long tail toward higher IEI, such as the geometric and the chi(2) distributions, had superior detectability. The distributions with the best detection performance also had a relatively high incidence of false positives, in contrast to the ordered distributions (Latin square and uniform permuted). The predictions of improved sensitivities for distributions with long tails were confirmed with empirical data. Moreover, the Latin square design yielded detection of activated voxels similar to the chi(2) distribution. These results indicate that high detection and suitable behavioral designs have compatibility for application of functional MRI methods to experiments requiring complex designs.
Adult↗
Mixture models for estimating the size of a closed population when capture rates vary among individuals.
We develop a parameterization of the beta-binomial mixture that provides sensible inferences about the size of a closed population when probabilities of capture or detection vary among individuals. Three classes of mixture models (beta-binomial, logistic-normal, and latent-class) are fitted to recaptures of snowshoe hares for estimating abundance and to counts of bird species for estimating species richness. In both sets of data, rates of detection appear to vary more among individuals (animals or species) than among sampling occasions or locations. The estimates of population size and species richness are sensitive to model-specific assumptions about the latent distribution of individual rates of detection. We demonstrate using simulation experiments that conventional diagnostics for assessing model adequacy, such as deviance, cannot be relied on for selecting classes of mixture models that produce valid inferences about population size. Prior knowledge about sources of individual heterogeneity in detection rates, if available, should be used to help select among classes of mixture models that are to be used for inference.
Animal Identification Systems↗
Bayesian analysis for a single 2 x 2 table.
The simple comparison of two binomial populations is frequently of interest in epidemiology when the domains are large. For small domains, however, there are no exact methods except Fisher's exact test. A basic problem, therefore, is to compare two populations by assessing the difference between the proportions of individuals who possess a characteristic in the first and second populations. When there is prior information, we take the proportions to have independent conjugate beta distributions with known parameters, thereby facilitating a Bayesian analysis. We consider Bayesian inference on functions of the proportions, and the three most common scalar measures used in epidemiology and health services research, namely relative risk, odds ratio and attributable risk. We develop the highest density regions (both exact and approximate) for relative risk, odds ratio and attributable risk. In addition, we consider the Bayes factor for testing whether the model with a common proportion holds rather than one with distinct proportions. Using data from the population-based Worcester Heart Attack Study, we apply our methodology to study gender differences in the therapeutic management of patients with acute myocardial infarction (AMI) by selected demographic and clinical characteristics. The Bayes factor, the approximate and exact intervals generally suggest that there are no substantial differences in the pharmacologic management of males and females hospitalized with AMI.
Adult↗
Separation of asymmetrical hybrid hemoglobins by anaerobic cation-exchange high-performance liquid chromatography.
Asymmetrical hybrid hemoglobins formed from mixtures of two structurally different hemoglobins were found to be readily separated by cation-exchange high-performance liquid chromatography under anaerobic conditions. When oxyhemoglobins A and S were mixed and deoxygenated, the resulting HPLC chromatogram showed three peaks. The distribution of the three components follow the binomial expansion a2 + 2 ab + b2 = 1, where a and b are the initial fractions of parent hemoglobins. The middle peak was collected in a test tube saturated with CO gas and reanalyzed under the same experimental conditions. This middle component gave two peaks of equal areas with retention times identical to those of the CO-form of the parent hemoglobins without the appearance of the hybrid hemoglobin band. No intermediate peak was observed in solutions of mixtures of liganded hemoglobins under aerobic conditions. Hybrid hemoglobins AC and SC were also formed when oxyhemoglobins A and C,S and C were mixed, respectively. The separation and the identification of hemoglobins and hybrid hemoglobin employing cation-exchange HPLC can be achieved within 30 min by gradient elution. In addition, the ability to isolate hybrid hemoglobins may be a valuable tool for the study of physical and chemical properties of hybrid hemoglobins.
Chromatography, High Pressure Liquid↗
Evidence that each nerve varicosity on the surface of the mouse vas deferens secretes ATP.
The secretion of ATP from visualised varicosities on the surface of the mouse vas deferens was determined. Small diameter microelectrodes (about 6 microns and 20 microns) were placed over a set of 2 to 5 varicosities visualised with DiOC2(5) in order to record excitatory junctional currents (e.j.c.s') arising from the evoked secretion of quanta. In high external calcium concentrations, [Ca2+]o, the amplitude-frequency distribution of e.j.c.s' was well described by binomial statistics in which binomial parameter n and the number of varicosities were approximately the same. Idazoxan (1 microM) had no effect on the e.j.c.s' or the binomial parameters p and n. Suramin (100 microM) blocked the e.j.c.s' as well as the spontaneous e.j.c.s' (s.e.j.c.s') in all cases, reducing n and p to zero. These results indicate that all varicosities secrete the transmitter blocked by suramin, presumably ATP.
Adenosine Triphosphate↗
Multiple coronary angioplasty: a model to discriminate systemic and procedural factors related to restenosis.
To assess the interrelation of clinical and procedural factors responsible for restenosis, 119 patients undergoing coronary arteriography were studied a mean of 5.8 +/- 3 months after successful multiple percutaneous transluminal coronary angioplasty. In all clinical, angiographic and procedural variables, the 119 patients undergoing repeat catheterization were similar to the 87 patients that did not. Overall, restenosis occurred in 74 (34%) of 215 lesions. Sixty-three patients had no restenosis, 44 had at least one restenosis and 12 had restenosis at all angioplasty sites. The statistical distribution of restenoses did not follow a binomial model, suggesting that restenosis is more than a lesion-specific phenomenon. Of all the clinical and procedural variables assessed by multivariate logistic regression analysis, only percent stenosis before angioplasty (p less than 0.01), diabetes mellitus (p less than 0.01) and percent stenosis after angioplasty (p less than 0.05) were predictive of restenosis in the entire group. Patients with no restenosis and patients with restenosis at all sites were not different with respect to procedural variables; however, patients with restenosis at all sites more often (p less than 0.05) had diabetes and recent onset angina. In contrast, patients with no restenosis differed from patients with isolated restenosis with respect to procedural variables: severity of stenosis before and after angioplasty, balloon/artery lumen ratio and maximal inflation pressure. Thus, procedural factors may be more related to isolated restenosis, but patient-related factors such as diabetes and recent onset angina may play a more important role in patients with multiple restenoses.
Aged↗
Statistical distribution of hydrophobic residues along the length of protein chains. Implications for protein folding and evolution.
We consider in this paper the statistical distribution of hydrophobic residues along the length of protein chains. For this purpose we used a binary hydrophobicity scale which assigns hydrophobic residues a value of one and non-hydrophobes a value of zero. The resulting binary sequences are tested for randomness using the standard run test. For the majority of the 5,247 proteins examined, the distribution of hydrophobic residues along a sequence cannot be distinguished from that expected for a random distribution. This suggests that (a) functional proteins may have originated from random sequences, (b) the folding of proteins into compact structures may be much more permissive with less sequence specificity than previously thought, and (c) the clusters of hydrophobic residues along chains which are revealed by hydrophobicity plots are a natural consequence of a random distribution and can be conveniently described by binomial statistics.
Amino Acids↗
A stochastic branching model with formation of subunits applied to the growth of intestinal crypts.
The intestinal epithelium is one of the most rapidly regenerating tissues in mammals. Cell production takes place in the intestinal crypts which contain about 250 cells. Only a minority of 1-60 proliferating cells are able to maintain a crypt over a long period of time. However, so far attempts to identify these stem cells were unsuccessful. Therefore, little is known about their cellular growth and selfmaintenance properties. On the other hand, the crypts appear to exhibit a life cycle which starts by fission of existing crypts and ends by fission or extinction. Data on these processes have recently become available. Here, we demonstrate how these data on the life cycle of the macroscopic crypt structure can be used to derive a quantitative model of the microscopic process of stem cell growth. The model assumptions are: (1) stem cells undergo a time independent supracritical Markovian branching process (Galton-Watson process); (2) a crypt divides if the number of stem cells exceeds a given threshold and the stem cells are distributed to both daughter crypts according to binomial statistics; (3) the size of the crypt is proportional to the stem cell number. This model combining two different stochastic branching processes describes a new class of processes whose stationary stability and asymptotic behavior are examined. This model should be applicable to various growth processes with formation of subunits (e.g. population growth with formation of colonies in biology, ecology and sociology). Comparison with crypt data shows that intestinal stem cells have a probability of over 0.8 of dividing asymmetrically and that the threshold number should be 8 or larger.
Animals↗
Human immunodeficiency virus type 1 may preferentially integrate into chromatin occupied by L1Hs repetitive elements.
Human DNA flanking sites of eight human immunodeficiency virus type 1 (HIV-1) proviral integrations have been analyzed in isolates derived both from integrations in an infected individual and from tissue culture. Sequence analysis encompassing 80-3000 bp of human DNA on one or both sides of the site of integration revealed that seven of the eight HIV-1 proviruses had integrated directly into or within one nucleosome's distance from an L1Hs or Alu repetitive element. To compare this with the frequency at which human L1 or Alu elements sharing > or = 70% identity with L1Hs and Alu consensus sequences would be encountered at random, > 200 bp from each of 82 individual anonymously cloned segments of human DNA were sequenced: L1Hs elements were encountered in 8.5% of the 82 clones and Alu elements were encountered in 13.4+ by using these homology windows. From these data it appears that HIV-1 integrates into or near L1Hs elements with an approximately 6-fold higher frequency than would be expected if HIV-1 integration events were distributed uniformly throughout the genome. A cumulative binomial probability test shows that there is a 0.26% chance that one would arrive at these figures by chance and puts the data well within a 99% confidence interval. We propose that sites of L1Hs and Alu insertions originally occurred in regions of chromatin that were more easily accessible to the retroposon machinery and that these regions are now acting as preferred integration sites for HIV-1.
Base Sequence↗
Conformation and structural fluctuations of a 218 nucleotides long rRNA fragment: 4-thiouridine as an intrinsic photolabelling probe.
The structure in solution of an RNA fragment (218 nucleotides long) containing part of E. coli 16S rRNA domain 2 has been studied using the intrinsic photoaffinity probe 4-thiouridine (s4U). In vitro transcription with T7 polymerase, in the presence of s4U triphosphate yielded complete RNA molecules. An affinity electrophoresis system based on Phenylmercuric substituted polyacrylamide (APM) gels allows separation of the RNA chains as a function of their s4U content. Distribution of s4U within chains follows a binomial law indicating that (i) substitution is close to random, (ii) efficiency of s4U incorporation is 0.22 times that of U. The monothiolated RNA fraction isolated from APM gel was irradiated at 366 nm under native conditions and the intramolecularly crosslinked molecules, (34%), were separated on denaturing polyacrylamide gel according to loop size. The positions of the two partners of bridges were identified by mean of reverse transcription and RNA sequencing. 17 of the 41 possible s4U positions lead to detectable bridges. These crosslinks formed efficiently at the border of bihelical regions or when structural mobility is allowed. The pattern of crosslinks is in agreement with the previously proposed secondary structure but indicates that it is much more flexible than expected.
Base Sequence↗
On testing departure from the binomial and multinomial assumptions.
This paper is concerned with testing the multinomial (binomial) assumption against the Dirichlet-multinomial (beta-binomial) alternatives. In particular, we discuss the distribution of the asymptotic likelihood ratio (LR) test and obtain the C(alpha) goodness-of-fit test statistic. The inadequacy of the regular chi-square approximation to the LR test is supported by some Monte Carlo experiments. The C(alpha) test is recommended based on empirical significance level and power and also computational simplicity. Two examples are given.
Computer Simulation↗
Sequential clinical trials for normal variates using interval composite hypotheses.
Sequential methods have become increasingly important for the monitoring of patient safety during clinical trials. However, the typical Wald sequential probability ratio test (SPRT), which compares two simple hypotheses, often presents anomalies which can be attributed to an inadequate representation of the parameter space. The use of composite null and alternative hypothesis in sequential clinical trials is explored and the resulting sequential rules are examined. It is shown that the SPRT and the Bayes formulations using Bayes odds ratios are equivalent in terms of the weighted likelihood ratio (WLR). The WLR is obtained for normal variates when the null hypothesis restricts the mean to (i) an interval and (ii) a point, in each case with complementary alternatives, as well as the one-sided formulation with a half-open interval. Applications to clinical trials include large-samples procedures, the comparative binomial trial and the comparison of survival distributions. Illustrative sequential boundaries are presented and the features of these different formulations are compared and discussed. Mixed sequential rules are considered within the framework for ethical stopping rules proposed by Meier (1979, Clinical Pharmacology and Therapeutics 25, 633--640).
Bayes Theorem↗
[Switching on sequence of lactate dehydrogenase loci in the early embryonic development of the mouse].
The dynamics of changes in the spectrum of lactate dehydrogenase was studied in the early pre- and postimplantation development in the CBA mice by the method of ultramicrophoresis. In the preimplantation embryos only LDH-1 was found during the first 5 days of development. The LDH-5 first appears by the 5th day of development and is preserved at all subsequent stages. The LDH spectrum of 5--7 days old embryos is represented by LDH-1 and LDH-5 and a very small amount of hybrid forms. The distribution of isozymes in the spectrum does not correspond to the binomial one. The LDH-1 is completely absent from 8--11 days old embryos and reappears in some tissues beginning from the 13th day of development. The distribution of isozymes in the LDH spectra from the 8th day of development is close to the binomial one.
Animals↗
Tests for 2 x K contingency tables with clustered ordered categorical data.
Ordered categorical data summarized in a 2 x K table usually consist of two-sample multinomial or K-sample binomial observations. In analysing these data, we usually assign scores to the K columns and perform a testing for the equality of two multinomial distributions in the former case and no trend among K binomial proportions in the latter case. Among the most popular score tests are the Wilcoxon rank sum test and the Armitage's linear trend test. In this paper we extend the score tests to be used for clustered data under diverse study designs. Our methods do not require correct specification of the dependence structure within clusters. The proposed tests are based on the asymptotic normality for large number of clusters and are a generalization of the standard tests used for independent data. Simulation studies are conducted to investigate the finite-sample performance of the new methods. The proposed methods are applied to real-life data.
Amoxicillin↗