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PubMed2007

Bivariate random-effects meta-analysis and the estimation of between-study correlation.

BACKGROUND: When multiple endpoints are of interest in evidence synthesis, a multivariate meta-analysis can jointly synthesise those endpoints and utilise their correlation. A multivariate random-effects meta-analysis must incorporate and estimate the between-study correlation (rhoB). METHODS: In this paper we assess maximum likelihood estimation of a general normal model and a generalised model for bivariate random-effects meta-analysis (BRMA). We consider two applied examples, one involving a diagnostic marker and the other a surrogate outcome. These motivate a simulation study where estimation properties from BRMA are compared with those from two separate univariate random-effects meta-analyses (URMAs), the traditional approach. RESULTS: The normal BRMA model estimates rhoB as -1 in both applied examples. Analytically we show this is due to the maximum likelihood estimator sensibly truncating the between-study covariance matrix on the boundary of its parameter space. Our simulations reveal this commonly occurs when the number of studies is small or the within-study variation is relatively large; it also causes upwardly biased between-study variance estimates, which are inflated to compensate for the restriction on rhoB. Importantly, this does not induce any systematic bias in the pooled estimates and produces conservative standard errors and mean-square errors. Furthermore, the normal BRMA is preferable to two normal URMAs; the mean-square error and standard error of pooled estimates is generally smaller in the BRMA, especially given data missing at random. For meta-analysis of proportions we then show that a generalised BRMA model is better still. This correctly uses a binomial rather than normal distribution, and produces better estimates than the normal BRMA and also two generalised URMAs; however the model may sometimes not converge due to difficulties estimating rhoB. CONCLUSION: A BRMA model offers numerous advantages over separate univariate synthesises; this paper highlights some of these benefits in both a normal and generalised modelling framework, and examines the estimation of between-study correlation to aid practitioners.

CD4 Lymphocyte Count↗
PubMed2001

Viral risks associated with wastewater reuse: modeling virus persistence on wastewater irrigated salad crops.

A model for virus decay on lettuce and carrot crops has been derived as part of a comprehensive wastewater irrigation microbial risk assessment model under development. Results from the decay modeling indicated the presence of a very persistent sub-population of viruses evidenced by an initial rapid phase of decay followed by a very slow phase. In addition, virus counts fitted a negative binomial rather than Poisson distribution indicating over-dispersion. Hence the data indicated that viruses were not uniformly distributed over the surfaces of both crops. The aim of this paper was to investigate the implications of over-dispersion and the presence of a very persistent sub-population of viruses for assessing viral illness from the consumption of lettuces and carrots irrigated with secondary treated effluent. When over-dispersion or clumping of viruses was accounted for, a significant increase in the heterogeneity in the risk estimates arose. In addition, predicted infection rates were significantly underestimated if the presence of a persistent sub-population of viruses was not considered in the decay kinetics of the risk model. Hence, both viral clumping and persistence sub-populations should be accounted for in future risk assessments of enteric viruses associated with wastewater reuse.

Agriculture↗
PubMed1976

Effects of physiologic alterations on binomial transmitter release at magnesium-depressed neuromuscular junctions.

1. Transmitter release from Mg2+-treated frog neuromuscular junctions can be described by binomial statistics. Good agreement between the observed amplitude-frequency distribution of e.p.p.s. and that predicted by binomial statistics is observed with relatively low concentrations of Mg2+. Conversely, good agreement is found with Poisson predictions when higher concentrations of Mg2+ are used to depress transmission. 2. Binomial analysis at these junctions shows that Mg2+ reduces quantal content (m), the probability of release (p) and to a lesser extent the available stores of transmitter (n). Raising Ca2+ causes an increase in n and p and a small but significant increase in n. K+ increases m and p but not n. 3. During 'frequency-facilitation' (1-6 Hz), e.p.p.s., m and n are increased but p is unaffected. 4. It is concluded that binomial statistics can be used to estimate the quantal parameters of transmitter release and that these parameters can be identified as discrete entities.

Animals↗
PubMed2000

Stochastic focusing: fluctuation-enhanced sensitivity of intracellular regulation.

Many regulatory molecules are present in low copy numbers per cell so that significant random fluctuations emerge spontaneously. Because cell viability depends on precise regulation of key events, such signal noise has been thought to impose a threat that cells must carefully eliminate. However, the precision of control is also greatly affected by the regulatory mechanisms' capacity for sensitivity amplification. Here we show that even if signal noise reduces the capacity for sensitivity amplification of threshold mechanisms, the effect on realistic regulatory kinetics can be the opposite: stochastic focusing (SF). SF particularly exploits tails of probability distributions and can be formulated as conventional multistep sensitivity amplification where signal noise provides the degrees of freedom. When signal fluctuations are sufficiently rapid, effects of time correlations in signal-dependent rates are negligible and SF works just like conventional sensitivity amplification. This means that, quite counterintuitively, signal noise can reduce the uncertainty in regulated processes. SF is exemplified by standard hyperbolic inhibition, and all probability distributions for signal noise are first derived from underlying chemical master equations. The negative binomial is suggested as a paradigmatic distribution for intracellular kinetics, applicable to stochastic gene expression as well as simple systems with Michaelis-Menten degradation or positive feedback. SF resembles stochastic resonance in that noise facilitates signal detection in nonlinear systems, but stochastic resonance is related to how noise in threshold systems allows for detection of subthreshold signals and SF describes how fluctuations can make a gradual response mechanism work more like a threshold mechanism.

Animals↗
PubMed1996

Sr2+ and quantal events at excitatory synapses between mouse hippocampal neurons in culture.

1. Whole-cell recording from pairs of adjacent mouse hippocampal neurons in culture was used to study the quantal properties of action potential-evoked excitatory synaptic transmission and to demonstrate the use of Sr2+ in quantifying those properties. 2. In the presence of extracellular Sr2+, excitatory postsynaptic currents (EPSCs) were followed by an after-discharge of miniature excitatory postsynaptic currents (mEPSCs) lasting 1-2 s and generated by evoked asynchronous release of presynaptic quanta of transmitter. Like the EPSC of which it is thought to be an extension, the after-discharge was modulated by procedures expected to modulate Sr2+ influx into the nerve terminal. The number of mEPSCs in the after-discharge was decreased by increasing extracellular [Mg2+], and increased by increasing extracellular [Sr2+] or increasing the number of action potentials used to evoke the after-discharge. 3. EPSCs recorded in media containing either 1 mM Ca2+ or 6 mM Sr2+ were of similar amplitude. Adding Sr2+ to low-Ca2+ media increased EPSC amplitude, while adding Sr2+ to high-Ca2+ media lowered EPSC amplitude. These results suggest that extracellular Sr2+ is less effective than Ca2+ in supporting quantal release. 4. The levels of extracellular Ca2+, Mg2+ and Sr2+ were adjusted so that most after-discharge mEPSCs were discrete and comparable in numbers to the quantal events that contributed to the corresponding evoked EPSCs. In a series of twenty-five pairs of neurons, the mean amplitude of mEPSCs recorded at -80 mV was 35 +/- 10 pA and the mean coefficient of variation was 0.50 +/- 0.10 (range, 0.26-0.62). The mEPSC amplitude histogram was positively skewed. 5. In ten pairs of neurons, the mean and variance of EPSCs and mEPSCs and quantal content were determined from samples of more than 100 evoked events (in superfusion solutions containing (mM): 0.5 Ca2+, 2 Sr2+ and 10 Mg2+) and mean quantal content was determined from the ratio of amplitudes of the mean EPSC and mEPSC. A binomial quantal analysis produced values of 2-12 for Napp (apparent number of independent synapses) and 0.25-0.75 for Papp (apparent probability of releasing a quantum at one of those synapses). These parameters predicted the number of observed failures. The observed coefficient of variation for quantal content predicted the observed coefficient of variation of the EPSC amplitude when the coefficient of variability of quantal amplitude of after-discharge mEPSCs was taken into account. 6. In six pairs of neurons, where more than 250 evoked events were recorded, the observed amplitude histogram for EPSCs could be approximated by a predicted amplitude distribution generated from the estimated binomial parameters and an empirical function describing the amplitude distribution of after-discharge mEPSCs. 7. The observation that parameters derived from mEPSCs that contribute to the Sr(2+)-generated after-discharge can predict the shape of the EPSC amplitude distribution and a quantal content consistent with the observed failure rate and EPSC amplitude variance, suggests that this subset of mEPSCs has the same properties as the quantal events released around the time of the peak of the corresponding EPSCs. The use of Sr2+ to evoke after-discharges of mEPSCs should allow unambiguous determination of the extent to which modification of synaptic strength is pre- or postsynaptic.

Animals↗
PubMed1977

[Intersatellite connections of the human acrocentric chromosomes that participate in associations].

Intersatellite connections between acrocentric chromosomes in associations were revealed by the method of thermal ammoniacal silver staining. The associations were allotted to the corresponding groups on the basis of the number of chromosomes. Distribution of D- and G-chromosomes in associations was studied on the basis of 714 associations from 500 metaphase plates of 10 normal individuals. The hypotheses of hypergeometric, binomial, Poisson, uniform and exponential distribution laws of D- and G-chromosomes in associations were rejected. The hypothesis of normal distribution was not rejected. The principal characteristics of normal distribution law were found. The distribution law of the number of D- and G-chromosomes in associations was written analytically; the central moments and other characteristics were presented.

Adult↗
PubMed1991

Quantal components of the synaptic potential induced in hippocampal neurons by activation of granule cells, and the effect of 2-amino-4-phosphonobutyric acid.

The probabilistic nature of excitatory postsynaptic potentials (EPSPs) induced monosynaptically in CA3 neurons by impulses of granule cells was studied in thin transverse sections of the guinea pig hippocampus. More than 600 EPSPs were recorded under several conditions, their amplitudes were measured, and histograms representing the EPSP amplitude distribution were constructed. Quantal parameters were estimated by the method of maximum likelihood. Of 9 neurons examined in the control solution, one neuron showed an exceptionally large number of transmission failures. The amplitude distribution of EPSPs recorded from this neuron could be described by Pascal statistics, but not by binomial or Poisson statistics. The EPSP amplitude distribution from the other neurons could be described by either binomial, Poisson, or Pascal predictions with a minor preference for the last statistic. When an apparently homogeneous group of data was divided into two subgroups and parameters were estimated separately, inconsistent values were obtained in some neurons with no failures. 2-Amino-4-phosphonobutyric acid (APB) suppressed the EPSPs reversibly at relatively low concentrations. Theoretical curves calculated according to the Pascal statistics fit quite well to the entire amplitude distribution of EPSPs recorded under the action of APB. The suppression of EPSPs by APB was accompanied by a marked decrease in mean quantal content (m) with no significant reduction in mean quantal amplitude (q). A quantum induced an increase in membrane conductance of about 150 pS. These results suggest that the release probability of the mossy fiber terminal fluctuates temporally according to a gamma distribution, and that APB reduces the liberation of the transmitter from mossy fiber terminals, thereby suppressing transmission between mossy fibers and CA3 neurons.

Aminobutyrates↗
PubMed1983

Analysis of polymorphic variation in different types of habitat.

A correlation between the distribution of an organism and features of its environment can be taken as indirect evidence of natural selection. Biologists may therefore collect samples from polymorphic populations at a number of locations, classify the locations into habitat types, and consider whether the distribution of morphs varies with the habitat. Statistical aspects of this type of study are discussed in this paper. A randomization test for habitat effects is proposed and a negative binomial model is suggested for the distribution of morphs from random locations within one type of habitat. Data on the distribution of Cepaea hortensis and C. nemoralis snails in southern England provide an example. For both species there is clear evidence of differences between habitats, although the morph distributions are rather variable within habitats. The negative binomial model suggests that, for the snail data, variation in morph proportions is mainly due to location differences. The binomial sampling error is relatively unimportant unless the sample size at a location is very small. Therefore it is reasonable to analyse morph proportions by standard methods without giving different weights to data from different locations. The snail data are analysed in this way. Discriminant function analyses are used to test for habitat effects. The relationships between C. hortensis and C. nemoralis morph frequencies within one habitat are examined by a canonical correlation analysis.

Animals↗
PubMed2001

Exploring extra-binomial variation in teratology data using continuous mixtures.

Discrete data from animal teratology experiments are known to exhibit extra-binomial variation. For example, we discuss a dominant lethal assay experiment in which male mice are exposed to various levels of radiation and are then mated to females. The response of interest is the number of resorptions out of the number of implantations. Most statistical work on analyzing such data has focused on modeling response rates as a function of dose of a suspected teratogen (radiation in this case) while accounting for the extra-binomial variability when calculating standard errors of the regression coefficients. Sometimes, however, when an unobserved genetic or exposure variable is suspected, the shape of the mixing distribution is of interest. We propose a mixture of beta-binomials (MBB) family of distributions that includes the non-parametric mixture of binomials model of Laird (1978) as a special case. The MBB family can accommodate a mixing distribution with one or more modes, and we develop a bootstrap test for multimodality. We apply the method to data from a dominant lethal teratology experiment.

Animals↗
PubMed1988

[Quantal analysis of the postsynaptic potentials in interneuronal synapses: the recovery of the signal from the noise].

Discrete distributions of the elementary EPSP amplitude in the interneuronal synapses of vertebrates were obtained by the maximum likelihood method. The equality of the intervals between values of the computed densities testifies to the quantal nature of the signal. The binomial model approximating the empirical distributions is revealed to be able to distinguish quantal levels of the nerve impulse transmission. These levels are conditioned by the structural organization of the interneuronal connections. Systematical differences between empirical distributions and the model necessitate generalization of the latter.

Animals↗
PubMed2003

Isochores merit the prefix 'iso'.

The isochore concept in the human genome sequence was challenged in an analysis by the International Human Genome Sequencing Consortium (IHGSC). We argue here that a statement in the IHGSC's analysis concerning the existence of isochores is misleading, because the homogeneity was not examined at a large enough length scale and consequently an inappropriate statistical test was applied. A test of the existence of isochores should be equivalent to a test of homogeneity or equality of windowed GC%. The statistical test applied in the IHGSC's analysis, the binomial test, is a test of whether individual bases are independent and identically-distributed (iid). For testing the existence of isochores, or homogeneity in windowed GC%, we propose to use another statistical test: the analysis of variance (ANOVA). It can be shown that DNA sequences that are rejected by the binomial test may not be rejected by the ANOVA test.

Analysis of Variance↗
PubMed2005

Responder cell frequency estimation and binomial three-level nonlinear mixed effects model in limiting dilution assays.

Responder cell frequencies (RCF), which describe vaccine-boosted immune responses in herpes zoster (HZ) prevention studies, have been estimated by using limiting dilution assays (LDA). The theoretical linearity assumption between the logarithm of the proportion of nonresponding wells (s) and the cell concentration (N) (or dilution level) in LDA, based on the single-hit Poisson model, is often violated with observed data resulting in biased estimates of RCF. In this article, the Poisson assumption is modified by applying a mixture of Poisson and gamma distributions, resulting in a negative binomial assumption, which presents a better fit between s and N. In LDA for HZ prevention studies, binary responses (responder or non-responder wells) are measured repeatedly at different cell concentrations and over time. To account for the correlation between responses to varying dilution levels from individuals, and the correlation between repeated assays of individuals over time simultaneously, a binomial three-level nonlinear mixed-effects model is proposed. For parameter estimation, a maximum likelihood method is applied via adaptive Gaussian quadrature. There is a lack of non-Gaussian multilevel nonlinear mixed-effects software, which can execute such a complicated fit. In this article, an algorithm for the three-level nonlinear mixed-effects model, which can be inserted into the code in the SAS procedure NLMIXED, is suggested.

Cell Count↗
PubMed1991

[Statistics (4). Tossing for decision making: one sample, dichotomy].

A coin, suspected to be biased, may be distinguished from a fair one by tossing it a number of times and applying the binomial test. Taking into account the probabilities of all possible outcomes (the theoretical sampling distribution), a too large occurrence of heads (or tails) will lead to rejection of the null hypothesis implying that the coin is not fair.

Binomial Distribution↗
PubMed1996

The homogenetic estimate for the variance of survival rate.

The homogenetic estimate for the variance of survival rate is proposed based on generalization and reduction between the complement of the empirical distribution function and the Kaplan--Meier or Berkson--Gage estimate. It reduces to the binomial variance estimate when there is no censoring. A Monte Carlo simulation study was carried out under various sample sizes, survival and censoring configurations, number of tied observations, and confidence levels with 2000 replications. It verifies that the commonly employed Greenwood estimate understimates, and the Simon and Lee expression for the Peto estimate strictly overestimates, the variance of survival rate to an extent dependent on the censoring distributions. The conclusions are identical with those of Peto et al. (1977) and Slud et al. (1984). The bias of the homogenetic estimate is less than that of both the Greenwood estimate and the Simon and Lee expression for the Peto estimate. The homogenetic estimate slightly overestimates when there are no ties and becomes unbiased and then slightly underestimates as the number of tied observations increases.

Analysis of Variance↗
PubMed1996

Does license disqualification reduce reoffence rates?

A review was conducted of the subsequent driving records of over 25,000 Queensland drivers cited for a drink driving offence in 1988 who received at least one subsequent license restriction. The interval of follow-up was at least 3 years, average 3.9 years. Periods of driving disqualification were identified and, for each driver, the total amount of time during restricted and unrestricted driving was computed; the numbers of events, i.e. crashes and traffic offences, recorded during these periods were counted. Rates under disqualification and during legal driving, expressed per thousand person-years were derived by dividing total numbers of events by total time during which they could occur. Three categories of traffic violation were considered: drink driving offences; traffic offences unassociated with drink driving, and any offence involving driving. Since only 12% of the offenders and 9% of the reoffenders were female, detailed analyses are presented for men only; results for women were little different. Statistical inference assumed a Poisson model for crashes and a negative binomial model for offences, and analyses were performed after stratification by number of drink driving offences. Calculated rates during periods of disqualification were about one third of the rates during legal driving for crashes and all three categories of traffic offence, ranging from 25% in the case of unassociated offences to 35% for any driving offence. There were differences, some statistically significant, by age and between metropolitan, provincial city and rural regions of the State, but most were relatively minor. Drivers were apprehended more frequently earlier in the disqualification period than later. It is impossible from these data to distinguish between reduced driving levels and more cautious traffic behaviour during periods of license restriction. It is nonetheless clear that while such penalties are in operation, they substantially reduce the negative impact of convicted drink-drivers on the road. Unfortunately the data do not permit one to say whether or for how long the effect persists.

Accidents, Traffic↗
PubMed2001

Confidence of compliance: a Bayesian approach for percentile standards.

Rules for assessing compliance with percentile standards commonly limit the number of exceedances permitted in a batch of samples taken over a defined assessment period. Such rules are commonly developed using classical statistical methods. Results from alternative Bayesian methods are presented (using beta-distributed prior information and a binomial likelihood), resulting in "confidence of compliance" graphs. These allow simple reading of the consumer's risk and the supplier's risks for any proposed rule. The influence of the prior assumptions required by the Bayesian technique on the confidence results is demonstrated, using two reference priors (uniform and Jeffreys') and also using optimistic and pessimistic user-defined priors. All four give less pessimistic results than does the classical technique, because interpreting classical results as "confidence of compliance" actually invokes a Bayesian approach with an extreme prior distribution. Jeffreys' prior is shown to be the most generally appropriate choice of prior distribution. Cost savings can be expected using rules based on this approach.

Bayes Theorem↗
PubMed2003

Accurate confidence intervals for binomial proportion and Poisson rate estimation.

Estimates of proportion and rate-based performance measures may involve discrete distributions, small sample sizes, and extreme outcomes. Common methods for uncertainty characterization have limited accuracy in these circumstances. Accurate confidence interval estimators for proportions, rates, and their differences are described and MATLAB programs are made available. The resulting confidence intervals are validated and compared to common methods. The programs search for confidence intervals using an integration of the Bayesian posterior with diffuse priors to measure the confidence level. The confidence interval estimators can find one or two-sided intervals. For two-sided intervals, either minimal-length, balanced-tail probabilities, or balanced-width can be selected.

Binomial Distribution↗
PubMed2002

The use of negative binomial modelling in a longitudinal study of gastrointestinal parasite burdens in Canadian dairy cows.

The epidemiology of bovine gastrointestinal nematodes was investigated through a 1-year (October 1999 to September 2000) longitudinal study in 38 Canadian dairy herds from 4 different provinces (Prince Edward Island, Quebec, Ontario, Saskatchewan). For each herd, fecal egg counts from 8 randomly selected animals were performed on a monthly or quarterly basis. Larval cultures were performed once, to determine the species breakdown of the parasites. All producers were interviewed regarding herd management practices. The observed fecal egg counts were low in this study, with a range from 0 to 419 nematode eggs per 5 g of feces. The mean count was 9.8 and the median was 1. Standard transformations failed to normalize the data, which followed an over-dispersed Poisson distribution. A zero inflated negative binomial model was applied to assess factors that would influence the fecal egg counts. Identified associations were: egg counts were lowest in the winter and highest in the late spring; first-lactation cattle had higher counts than older cows; if manure was spread mechanically on pastures used by lactating cattle the egg counts were higher; and if manure was spread on heifer-pastures, the adult cows had lower counts. In herds where pasture use was more extensive, the cattle had higher fecal egg counts. The difference in pasture exposure was found to be a main contributor to an observed difference in fecal egg counts among herds in the 4 provinces.

Animal Husbandry↗