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PubMed1987

Population biology of hookworms in west Bengal: analysis of numbers of infective larvae recovered from damp pads applied to the soil surface at defaecation sites.

The aims of this study were to analyze the seasonal distribution of infective larvae on the soil surface, to determine whether numbers of infective larvae near faeces were related to the faecal egg count of individuals, and to relate the distribution of larvae to environmental characteristics. Larvae were recovered from damp pads, applied to the soil surface in an annulus around fresh, identified stools of individuals who were participating in a larger epidemiological study. This provided an estimate of exposure to infection at the time of defaecation. Transmission was restricted to the rainy season and large aggregations of larvae were encountered earlier rather than later in the rainy season. Frequency distributions for the number of larvae extracted from each pad showed a high degree of aggregation, with most monthly counts showing good fits to the negative binomial probability distribution. Despite variations in monthly sampling means, the degree of aggregation in the population of larvae was remarkably stable over the 18 month sampling period (k of negative binomial = 0.01 to 0.08). Estimates of the degree of aggregation of the parasites in the human population were also available, and comparisons suggest that the infective larvae were much more aggregated than the parasitic stages. There was no relationship between the mean daily egg output of individuals and the number of larvae which developed and were recovered from the soil surface near the faeces. Thus, people who contribute large numbers of eggs to the environment are not necessarily those who are the greatest source of infection for others.(ABSTRACT TRUNCATED AT 250 WORDS)

Ancylostoma↗
PubMed1991

Epidemic curve characteristics for the Reed-Frost model.

Some useful approximations are developed in this paper that describe large-scale epidemic phenomena for the deterministic and stochastic Reed-Frost model. These characteristics provide an a priori quantitative description of the epidemic curve for the deterministic case, such as a threshold requirement, the total size of the epidemic, and the degree of skewness in the epidemic curve. A Poisson distribution asymptotically describes the distribution of the total size of an epidemic when the relative removal rate is well below threshold for the Reed-Frost chain binomial model. These properties are established by an extension of the large-scale epidemic phenomena of the Kermack-McKendrick model.

Binomial Distribution↗
PubMedDate not supplied

A model for intra-familial distribution of an infectious disease (Chagas' disease).

A probabilistic model for intra-familial distribution of infectious disease is proposed and applied to the prevalence of positive serology for Trypanosoma cruzi infection in a Northeastern Brazilian sample. This double binomial with one tail excess model fits satisfactorily to the data and its interpretation says that around 51% of these 982 families are free of infection risk; among those that are at risk, 3% have a high risk (0.66), probably due to high domestic infestation of the vector bug; while 97% show a small risk (0.11), probably due to accidental, non-domestic transmission.

Binomial Distribution↗
PubMed1997

A formula for the probability of discordant classification in method comparison studies.

Method comparison studies are often reported in terms of the "limits of agreement' between the methods. Many clinical applications use the measurements simply to classify patients, for example, whether or not they are hypoglycaemic. In such circumstances it may be useful to present an estimate of the probability of discordant classification based on the bivariate Normal distribution. This paper provides as accurate and easily calculated approximation to this quantity.

Bias↗
PubMed1993

Aggregated distributions in models for patchy populations.

We investigate a model describing immigration, birth, and death of parasites on a dynamic host population. The model can also be interpreted as describing a herbivore population distributed on discrete patches of vegetation. We derive differential equations for the total number of hosts/patches and the mean number of parasites/herbivores per host/patch. The equations explicitly involve the variance-to-mean ratio of the distribution. It is shown that the positive equilibrium is stable if and only if the variance-to-mean ratio as a function of the mean increases with increasing mean. Thus aggregation of the parasites alone is not sufficient to stabilize the system; it is rather the density-dependent increase in parasite mortality due to a higher aggregation at higher mean parasite loads that causes stability. From this it follows that introducing a distribution with a constant clumping parameter into the model artificially stabilizes the steady state. We derive a three-dimensional model based on an assumption about the form of the distribution of the parasites on the hosts, but without introducing additional parameters into the model. We compare stability results for this model for different types of aggregated distributions and show that the underlying distribution determines the qualitative results about the stability of the equilibrium.

Animals↗
PubMed1992

Testing the null hypothesis in small area analysis.

The goal of small area analysis is often to demonstrate that hospital admission rates or procedure rates vary greatly among regions, suggesting the occurrence of unnecessary admissions or procedures in some regions. Recent articles have shown that such variation may be largely due to chance, even if no underlying differences exist among the small areas; thus, it is important to test if the observed variation is larger than expected by chance. In this article we discuss how the appropriate method for testing the null hypothesis depends on the distribution of the number of admissions at the person level. If it is not possible for an individual to have more than one admission for a given procedure, the appropriate test is a simple chi-square test. If multiple admissions are possible, a modified chi-square test can be used to account for the excess variability due to multiple admissions. Failure to make the correct modification to the chi-square test in this latter case can result in spurious results. This underscores the importance of collecting data on multiple admissions in order to estimate the distribution of the number of admissions at the individual-patient level.

Analysis of Variance↗
PubMed1994

Intrafusal motor innervation: a quantitative histological analysis of tenuissimus muscle spindles in the cat.

A quantitative analysis of the motor innervation of intrafusal muscle fibres is described, based on teased silver-impregnated spindles of the tenuissimus muscle of the cat. Included in the analysis are the number and distribution of intrafusal branches of both skeletofusimotor (beta) and purely fusimotor (gamma) axons, and the form of their endings. The number of axonal branches per spindle was found to follow binomial probability distributions, as had previously been shown for the afferent axons. There was a strong correlation between the numbers of gamma intrafusal branches and afferent axons, but none for the intrafusal branches of beta axons. The degree of segregation of gamma input to bag2 and chain fibres was assessed and was found, among other things, to be related to the presence of secondary sensory endings in the same pole. In this and other respects it did not appear to have the properties that would be expected if independent activation of the bag2 and chain fibres were to be functionally important. Morphometric analysis of the motor endings supplied to bag2 or chain fibres by gamma axons revealed some differences between those of intrafusal branches with segregated as opposed to unsegregated distributions, but this cannot be taken as evidence of more than one type of static gamma motoneuron because of the likely contribution of other influential factors such as fibre size. Finally, the relevance of studies on intrafusal motor innervation to the concept of the motor unit and its development are discussed.

Animals↗
PubMed1992

Multiple-trait restricted maximum likelihood for simulated measures of ovulation rate with underlying multivariate normal distributions.

A data set that was used to estimate covariance components with REML for an animal model with eight measures of ovulation rate treated as separate traits was used as a template to simulate data sets of eight multivariate normal traits that were then truncated to binomial traits. The model for simulation included eight measures on 610 animals with 1,071 animals in the numerator relationship matrix. Heritabilities were equal for the eight measures, and both genetic and phenotypic correlations among the measures were equal. Ten replications for each combination of heritability (.15, .25, and .35) and genetic correlation (.50, .66, and .90) were simulated on the normal scale. For each replicate, estimates of the eight heritabilities and 28 genetic correlations were obtained by multiple-trait REML. The usual transformation of heritability estimated on the binomial scale overestimated heritability on the normal scale. Genetic correlations on the binomial scale seriously underestimated the correlations on the normal scale. Standard errors of the estimates obtained by replication were somewhat larger than the approximate SE from REMLPK (the multi-trait REML program of K. Meyer). A final set of 10 simulated replications with heritability of .25 and genetic correlation of 1.00 resulted in average estimates of .18 for heritability and of .66 for genetic correlation that agree closely with those from the analysis of measures of ovulation at eight estrous cycles used as a template; averages for heritability of .16 and for genetic correlation of .66 were obtained.

Animals↗
PubMed2005

Exact asymptotic results for the Bernoulli matching model of sequence alignment.

Finding analytically the statistics of the longest common subsequence (LCS) of a pair of random sequences drawn from c alphabets is a challenging problem in computational evolutionary biology. We present exact asymptotic results for the distribution of the LCS in a simpler, yet nontrivial, variant of the original model called the Bernoulli matching (BM) model. We show that in the BM model, for all c , the distribution of the asymptotic length of the LCS, suitably scaled, is identical to the Tracy-Widom distribution of the largest eigenvalue of a random matrix whose entries are drawn from a Gaussian unitary ensemble.

Binomial Distribution↗
PubMed1994

Log-normal distribution of physiological parameters and the coherence of biological systems.

The well-known fact that biological parameters, randomly selected, are distributed according to log-normal frequency curves instead of normal ones, has been traced back to a 'multiplicative Gestaltungs-principle of nature'. A further analysis shows that the basis of this principle can be assigned to the optimization of connections in a network of circuit elements, or, even more profoundly, to the formation of coherent states in living systems. The diagnosis of patients based on physiological frequency distributions provides a new powerful tool of understanding sickness in terms of deviations from a basic regulation principle.

Animals↗
PubMed1997

Risk analysis in relation to the importation and exportation of animal products.

The design of a quantitative risk analysis model has to be dictated by the questions it seeks to answer. The model should also be as objective as the available data will allow. Animal and animal product import risks usually have three characteristics which make the design of a good quantitative risk analysis model quite difficult, namely:--the probabilities of the steps leading to the undesired outcome are frequently inter-related--the probability of the undesired outcome itself is in many cases very small, making direct simulation impractical--important variables within the model often cannot be quantified through analysis of data, thus these variables must be modelled with probability distributions to reflect the degree of uncertainty, usually determined by expert opinion. This paper provides a tutorial on some modelling techniques which are essential to the risk assessment of animal and animal product imports and which help overcome these problems. A number of probability distributions, their uses and inter-relationships, are examined. The application of these distributions, coupled with some general modelling techniques, is then demonstrated to produce rigorous and transparent animal import risk analyses.

Animal Diseases↗
PubMed1977

Estimates of quantal-release and binomial statistical-release parameters at rat neuromuscular junction.

Quantal-release and binomial statistical-release parameters were examined in the isolated rat diaphragm phrenic nerve preparation. The muscle resting potentials were reduced by cutting the muscle fibers to prevent muscle action potentials and contractions. The cutting technique was modified to allow persistent observation of miniature end-plate potentials (MEPPs) and end-plate potentials (EPPs) with intracellular recording techniques. Direct estimates of quantal release were examined and compared with predicted binomial and Poisson distributions. The results indicate that release is binomial when the nerve is stimulated with low- or high-frequency stimuli. The indirect method of estimating quantal release (variance method), which assumes release is described by a Poisson distribution, seriously overestimates quantal release. The binomial analysis indicates that the statistical store is small (less than 90 quanta) and that most of these quanta are released with each nerve impulse.

Animals↗
PubMed2002

Quantifying dental inequality--developing the methodology.

OBJECTIVE: To develop a simple quantitative measure of dental health inequality. METHOD: Define equality based on statistical theory and construct a formula to compare actual and theoretical disease distributions. RESULT: A new index (DHII) is proposed, based on the ratio of the distribution of the actual disease to a (theoretical) Poisson distribution. An example using caries data is provided. CONCLUSION: Use of DHII will allow quantitative measurement of dental health inequality.

Binomial Distribution↗
PubMed2003

Exact unconditional tests for a 2 x 2 matched-pairs design.

The problem of comparing two proportions in a 2 x 2 matched-pairs design with binary responses is considered. We consider one-sided null and alternative hypotheses. The problem has two nuisance parameters. Using the monotonicity of the multinomial distribution, four exact unconditional tests based on p-values are proposed by reducing the dimension of the nuisance parameter space from two to one in computation. The size and power of the four exact tests and two other tests, the exact conditional binomial test and the asymptotic McNemar's test, are considered. It is shown that the tests based on the confidence interval p-value are more powerful than the tests based on the standard p-value. In addition, it is found that the exact conditional binomial test is conservative and not powerful for testing the hypothesis. Moreover, the asymptotic McNemar's test is shown to have incorrect size; that is, its size is larger than the nominal level of the test. Overall, the test based on McNemar's statistic and the confidence interval p-value is found to be the most powerful test with the correct size among the tests in this comparison.

Binomial Distribution↗
PubMed2000

Conditional and exact tests in crossover trials.

Generalized linear models are developed for crossover trials with no carryover effects and fixed subject effects. A general multinominal model for the distribution of data is considered. This subsumes both binary and categorical data. Conditional inferences eliminate subject effects by conditioning on their sufficient statistics. For normal data, least-squares analysis is exact with identical treatment inferences from unconditional and conditional analyses. For Poisson data, unconditional and conditional analyses are also identical, but for multinomial data this is not the case and the unconditional analysis is invalid. For multinomial data, asymptotic tests of both treatment effects and goodness of fit are unreliable with small samples. Procedures for exact tests are developed to overcome such problems, using enumeration, random sampling, and a hybrid of importance sampling and enumeration. A four-period binary crossover trial is used to illustrate an exact test of treatment effects by a two-stage sampling procedure based on a factorization of the conditional distribution of the sufficient statistics. An exact test of goodness of fit on the same data illustrates a two-stage scheme mixing importance sampling and enumeration.

Binomial Distribution↗
PubMed2003

Power comparison of two-sided exact tests for association in 2 x 2 contingency tables using standard, mid p and randomized test versions.

Exact Pearson's chi square, likelihood ratio (LR), and Fisher's tests are obtained from the conditional distribution of its test statistic, given the row and column sums of the contingency table. The power and obtained significance level of the standard, mid p, and randomized versions of these tests are compared for two-sided tests in 2 x 2 tables, using binomial and multinomial sampling. The mid p type I error probabilities seldom exceed the nominal significance level. The mid p and randomized test versions have approximately the same power, and higher power than the standard test version. The power of the Pearson's chi square, LR and Fisher's test differ, and they differ in approximately the same way for standard, mid p and randomized test versions for any given set of parameters. There is no general ranking between the three tests. In many cases, Pearson's chi square and Fisher's tests have almost equal power, and higher power than LR. In a few cases, perhaps characterized by poorly balanced designs, LR performs best. Fisher's test seems to be slightly more robust even if the design is poor.

Binomial Distribution↗
PubMed1997

Bayesian and mixed Bayesian/likelihood criteria for sample size determination.

Sample size estimation is a major component of the design of virtually every experiment in medicine. Prudent use of the available prior information is a crucial element of experimental planning. Most sample size formulae in current use employ this information only in the form of point estimates, even though it is usually more accurately expressed as a distribution over a range of values. In this paper, we review several Bayesian and mixed Bayesian/likelihood approaches to sample size calculations based on lengths and coverages of posterior credible intervals. We apply these approaches to the design of an experiment to estimate the difference between two binomial proportions, and we compare results to those derived from standard formulae. Consideration of several criteria can contribute to selection of a final sample size.

Bayes Theorem↗
PubMed1994

Theoretical recombination processes incorporating interference effects.

With the acquisition of genetic, physical, and sequence maps, linkage relationships among genes (markers) may be more accurately approached in terms of global models for the distribution of recombination events that take into account interference. There are two principal analytical methods used for ascertaining linkage relationships. The first method, the Haldane-Kosambi differential equation approach, has the limitation that all of its calculations rest on consideration of only three gene markers, where recombination depends only on the physical distance between markers. In this formulation the resulting map function is in general not feasible for use with multiple markers. The second method starts with a model of the crossover process from which recombination values are determined. The best studied global recombination processes are based on sequential (renewal) crossover formation processes, the count-location crossover structure, and crossovers evolving by a cascade mechanism. This paper, containing both review and new results, concentrates on two aspects of recombination structures: (i) classifications and characterizations of multimarker crossover distributions; and (ii) analysis of regular and higher order crossover interference forms. In eucaryotic species, the general impression is that positive interference prevails, while in procaryotic and viral organisms, there may be circumstances of negative interference. We would propose in estimating the crossover formation process a binomial count distribution or any other count distribution satisfying property (a) of Theorem 9.1 and a location distribution fitted by the data. It is also reasonable to try one or more obligate crossover points superimposed on independent Poisson processes determining other crossover points. This latter model also generates a situation of positive interference (Theorem 3.1).

Animals↗