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PubMed1993

Confidence intervals for a binomial proportion.

Thirteen methods for computing binomial confidence intervals are compared based on their coverage properties, widths and errors relative to exact limits. The use of the standard textbook method, x/n +/- 1.96 square root of [(x/n)(1-x/n)/n], or its continuity corrected version, is strongly discouraged. A commonly cited rule of thumb stating that alternatives to exact methods may be used when the estimated proportion p is such that np and n(1(-)p) both exceed 5 does not ensure adequate accuracy. Score limits are easily calculated from closed form solutions to quadratic equations and can be used at all times. Based on coverage functions, the continuity corrected score method is recommended over exact methods. Its conservative nature should be kept in mind, as should the wider fluctuation of actual coverage that accompanies omission of the continuity correction.

Binomial Distribution↗
PubMed1993

A conditional analysis for two-treatment multiple-period crossover designs with binomial or poisson outcomes and subjects who drop out.

We propose a conditional analysis for outcome data on numbers of recurrent symptoms arising in a two-treatment, multiple-period crossover trial. Conditioning on subject-specific totals removes any dependence on mean subject-specific symptom rates and permits the use of standard software to perform regression analysis to examine treatment, period, carryover and interaction effects. The addition of offsets to the regression equations allows the incorporation of data from subjects who do not complete all periods in the trial. We apply the proposed method to data from a crossover trial and discuss its advantages and disadvantages.

Adult↗
PubMed1994

Deviance estimates of sample size for equivalence tests in vaccine trials.

This paper proposes a sample size procedure for both equivalence and conventional tests for the comparison of two binomial proportions, based on the signed square root of the deviance. When the comparison is based on the odds ratio, I describe an alternate 'close' conditional exact method that gives results that support those given by the deviance method. I summarize the advantages of the deviance-based method and also show that in general equivalence situations the sample size estimate depends upon the measure of comparison selected, odds ratio, risk ratio or risk difference.

Binomial Distribution↗
PubMedDate not supplied

Bayesian predictive approach for inference about proportions.

This paper investigates the Bayesian procedures for comparing proportions. These procedures are especially suitable for accepting (or rejecting) the equivalence of two population proportions. Furthermore the Bayesian predictive probabilities provide a natural and flexible tool in monitoring trials, especially for choosing a sample size and for conducting interim analyses. These methods are illustrated with two examples where antithrombotic treatments are administrated to prevent further occurrences of thromboses.

Bayes Theorem↗
PubMed1995

A hybrid paired and unpaired analysis for the comparison of proportions.

A method is presented for making inferences about the difference between two binomial proportions when there is partial overlap of the two samples. The method will simplify to the usual cases of two independent samples or paired samples (McNemar's method) depending on whether there is no or complete overlap. The method is used to compare sensitivities, specificities and Youden indices from a comparative study of trauma triage (screening) instruments.

Algorithms↗
PubMed1995

Comparison of tests and sample size formulae for proving therapeutic equivalence based on the difference of binomial probabilities.

To prove the hypothesis that a new treatment is as effective as a standard one, a possibility is to test the one-sided null hypothesis of a clear inferiority of the new treatment against the alternative hypothesis that, if at all, it is only negligibly inferior. Such a problem is of clinical relevance if, for instance, a new treatment with an effectiveness which is comparable to that of the standard one would be preferred if it is less toxic. If the difference between the two treatments is measured by the difference of failure rates, approximate statistical tests and sample size formulae have to be used. This paper reports the results of an extensive empirical investigation comparing the well known calculations proposed by Blackwelder, Rodary, ComNougue and Tournade, which propose a sample size formula for the test of Dunnett and Gent, and Farrington and Manning. The investigation was conducted in order to allow more comprehensive conclusions than those which may be drawn from the limited examples given by the last authors. For the usual settings in clinical trials, the formulae of Farrington and Manning are recommended. However, there are combinations of statistical parameters for which they are not preferred.

Binomial Distribution↗
PubMed1995

On the sample size for one-sided equivalence of sensitivities based upon McNemar's test.

In this paper we formalize the problem of testing the one-sided equivalence in the sensitivities of two medical diagnostic tests under a matched-pair study design. We derive conditional and unconditional sample size formulae which are decreasing functions of the probability of being diagnosed by both tests. We calculate upper boundary and midpoint sample sizes. Results of a Monte Carlo simulation study that compares the proposed sample size formulae with that of Lachenbruch suggest that our midpoint conditional sample size is the best choice to obtain the desired power for the type of equivalence studies discussed in the paper.

Binomial Distribution↗
PubMed1996

Simple robust procedures for combining risk differences in sets of 2 x 2 tables.

Meta-analyses often use a random-effects model to incorporate unexplained heterogeneity of study results. Trimmed versions of meta-analytic estimators for the risk difference, adapted from procedures designed for a random-effects analysis, can resist the impact of a few anomalous studies. A simulation study compared untrimmed and trimmed versions of four meta-analytic procedures that give weighted averages of risk differences. An adaptation of Winsorized estimates of components of variance gains some resistance to anomalous studies when estimating variability. The simulations found that a modified version of the DerSimonian-Laird estimator is attractive when risk differences reveal the added variability described by a random-effects model, and that a 20 per cent trimmed, weighted version of this procedure offers resistance against the impact of highly anomalous results. Among four trimmed procedures considered, the trimmed version of the modified DerSimonian-Laird estimator offers the best performance over a wide range of simulation designs and sample sizes. None of the methods, whether trimmed or untrimmed, is uniformly preferable. A published meta-analysis of a vaccination against TB provides data that serve to illustrate differences among the eight procedures.

BCG Vaccine↗
PubMed1994

Quantal analysis of presynaptic inhibition, low [Ca2+]0, and high pressure interactions at crustacean excitatory synapses.

The cellular mechanisms underlying the effects of high pressure, GABAergic presynaptic inhibition, and low [Ca2+]0 on glutamatergic excitatory synaptic transmission were studied in the opener muscle of the lobster walking leg. Excitatory postsynaptic currents (EPSCs) were recorded with or without prior stimulation of the inhibitor using a loose macropatch clamp technique at atmospheric pressure and at 6.9 MPA helium pressure. High pressure reduced the mean EPSC amplitude and variance, decreased the quantal content (m), but did not affect the quantum current (q). Pressure shifted the median of the amplitude histogram to the left by 1-2 q. Under normal pressure conditions, presynaptic inhibition and low [Ca2+]0 induced similar effects. However, quantal analysis using a binomial frequency distribution model revealed that high pressure and low [Ca2+]0 diminished n (available active zones) and slightly increased p (probability of release), but presynaptic inhibition reduced p and slightly increased n. At high pressure, presynaptic inhibition was reduced, at which time the major contributor to the inhibitory process appeared to be reduction in n and not p. The similarity of the alterations in quantal parameters of release at high pressure, low [Ca2+]0, and in some conditions of presynaptic inhibition is consistent with the hypothesis that pressure reduces Ca2+ inflow into the presynaptic nerve terminals to affect the Ca(2+)-dependent quantal release parameters n and p.

Animals↗
PubMed1999

A study of dipolar interactions and dynamic processes of water molecules in tendon by 1H and 2H homonuclear and heteronuclear multiple-quantum-filtered NMR spectroscopy.

The effect of proton exchange on the measurement of 1H-1H, 1H-2H, and 2H-2H residual dipolar interactions in water molecules in bovine Achilles tendons was investigated using double-quantum-filtered (DQF) NMR and new pulse sequences based on heteronuclear and homonuclear multiple-quantum filtering (MQF). Derivation of theoretical expressions for these techniques allowed evaluation of the 1H-1H and 1H-2H residual dipolar interactions and the proton exchange rate at a temperature of 24 degrees C and above, where no dipolar splitting is evident. The values obtained for these parameters at 24 degrees C were 300 and 50 Hz and 3000 s-1, respectively. The results for the residual dipolar interactions were verified by repeating the above measurements at a temperature of 1.5 degrees C, where the spectra of the H2O molecules were well resolved, so that the 1H-1H dipolar interaction could be determined directly from the observed splitting. Analysis of the MQF experiments at 1.5 degrees C, where the proton exchange was in the intermediate regime for the 1H-2H dipolar interaction, confirmed the result obtained at 24 degrees C for this interaction. A strong dependence of the intensities of the MQF signals on the proton exchange rate, in the intermediate and the fast exchange regimes, was observed and theoretically interpreted. This leads to the conclusion that the MQF techniques are mostly useful for tissues where the residual dipolar interaction is not significantly smaller than the proton exchange rate. Dependence of the relaxation times and signal intensities of the MQF experiments on the orientation of the tendon with respect to the magnetic field was observed and analyzed. One of the results of the theoretical analysis is that, in the fast exchange regime, the signal decay rates in the MQF experiments as well as in the spin echo or CPMG pulse sequences (T2) depend on the orientation as the square of the second-rank Legendre polynomial.

Achilles Tendon↗
PubMed1995

Statistical properties of segregating sites.

A mutation leading to a segregating site of a sample can be classified by the number of sequences in the sample that inherits the mutant nucleotide; it can also be classified by the frequencies of the two segregating nucleotides at the resulting segregating side. We define the size of a mutation to be the number of sequences in the sample that inherits the mutant nucleotide and the type of mutation (segregating site) to be the smallest value of the frequencies of segregating nucleotides. Each of these two classifications of mutations is analogous to allelic types in a sample of genes. Assuming the neutral Wright-Fisher model, we derived in this paper the mean and variance of the frequency of mutations of each size and type, and the covariance between the numbers of mutations of two different sizes and two different types. Potential applications of these results are discussed.

Analysis of Variance↗
PubMed1996

Discrete clutch sizes, local mate competition, and the evolution of precise sex allocation.

Optimal sex allocation under a population structure with local mate competition has been studied mainly in deterministic models that are based on the assumption of continuous clutch sizes; Hamilton's (1967) model is the classic example. When clutch sizes are small, however, this assumption is not appropriate. When taking the discrete nature of eggs into account it becomes critically important whether females control only the mean sex ratio ("binomial" females) or the variance as well ("precise" females). As both types of sex ratio control have been found, it is of interest to investigate their evolutionary stability. In particular, it may be questioned whether perfect control of the sex ratio is always favoured by natural selection when mating groups are small. Models based on discrete clutch sizes are developed to determine evolutionarily stable (ES) sex ratios. It is predicted that when all females are of the binomial type they should produce a lower proportion of daughters than predicted by Hamilton's model, especially when clutch size and foundress number are small. When all females are of the precise type, the ES number of sons should generally be either a stable mixed strategy or a pure strategy, but there are special cases (for two foundresses and particular clutch sizes) where the ES number of sons lies in a trajectory of neutrally stable mixed strategies; the predicted mean sex ratios can be either higher or lower than predicted by Hamilton's model. The existence of ES mixed strategies implies that individual females do not necessarily have to produce sex ratios with perfect precision; some level of imperfection can be tolerated (i.e., will not be selected against). When the population consists of both binomial and precise females, the latter always have a selective advantage. This advantage of precision does not disappear when precision approaches fixation in the population. The latter result contradicts the conclusions of Taylor and Sauer (1980) which is due to their way of expressing selective advantage; they define selective advantage as the between-generation increase per allele, which will always become vanishingly small when an allele reaches fixation, irrespective of fitness differences.

Animals↗
PubMed1999

Stochastic effects in LMC models.

LMC (local mate competition) was first introduced by W. D. Hamilton to explain extraordinary female-biased sex ratios observed in a variety of insects and mites. In the original model, the population is subdivided into an infinite number of colonies founded by a fixed number of inseminated females producing the same very large number of offspring. The male offspring compete within the colonies to inseminate the female offspring and then these disperse at random to found new colonies. An unbeatable sex ratio strategy is found to be female-biased. In this paper, the effects of having colonies of random size and foundresses producing a random finite number of offspring are considered. The exact evolutionarily stable strategy (ESS) sex ratio is deduced and comparisons with previous approximate or numerical results are made. As the mean or the variance of brood size increases, the ESS sex ratio becomes more female-biased. An increase in the variance of colony size increases the ESS proportion of males when the mean brood size and colony size are both small, but decreases this proportion when the mean brood size or the mean colony size is large.

Animals↗
PubMed2000

Fixation probabilities when the population size undergoes cyclic fluctuations.

Let us assume that there is a monoecious random mating population that changes cyclically in size. Then, the probability that a nonrecessive favorable mutant is ultimately fixed, if it is originally present in a single heterozygote, is approximately proportional to the harmonic mean of the effective population sizes in the cycle and inversely proportional to the population size when the mutant appears. This approximation works well if the selective advantage s of the mutant is small and the length k of a cycle is small in comparison with the population sizes in a cycle. If k is large the harmonic mean is, in general, replaced by a weighted harmonic mean that puts the largest weights on reciprocals of effective population sizes in the first few generations after the mutant appears.

Alleles↗
PubMed1990

Quantitative in situ hybridization to measure single-cell changes in vasopressin and oxytocin mRNA levels after osmotic stimulation.

1. The measurement of cellular mRNA content by quantitative in situ hybridization is a valuable approach to the study of gene expression in brain since this tissue exhibits a high degree of phenotypic heterogeneity. 2. The cellular content of vasopressin and oxytocin mRNA in hypothalamo-neurohypophysial system neurons was altered by maintaining rats for 24 hr on 2% sodium chloride water. 3. Statistical and graphical techniques were then used to analyze cell by cell how mRNA levels were altered as a result of osmotic stimulation. We propose that the negative binomial probability distribution is a suitable model to describe how mRNA content varies across a defined cell population. For both measures of oxytocin and vasopressin mRNA levels, maximum-likelihood estimation indicated that this model adequately described empirical findings obtained from rats drinking tap water or salt water. 4. Both graphical and statistical analyses suggested how the defined neural system responds to osmotic stimulation: mRNA content was altered as a multiplicative function of "initial state." The utility and limitations of the quantitative approach are discussed.

Animals↗
PubMed1991

Practical identification of functional expansions of nonlinear systems submitted to non-Gaussian inputs.

Time-domain identification of nonlinear systems represented by functional expansions is considered. A general framework is defined for the analysis of three identification methods: the widely used cross-correlation method, Korenberg's method, and a suboptimal least-squares method based on a stochastic approximation algorithm. First, the major characteristics of the underlying estimation problem are pointed out. Then, the identification methods are interpreted as approximations to an optimal estimator, which helps gain insight into their internal functioning and to the investigation of their connections and differences. Examination of results previously published and of the simulations reported in this article indicate that stochastic approximation is an interesting alternative to other existing methods. Identification of a biological system stimulated by a non-Gaussian input confirms the practicality of this approach.

Binomial Distribution↗