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PubMed2004

Sample size calculations for surveys to substantiate freedom of populations from infectious agents.

We develop a Bayesian approach to sample size computations for surveys designed to provide evidence of freedom from a disease or from an infectious agent. A population is considered "disease-free" when the prevalence or probability of disease is less than some threshold value. Prior distributions are specified for diagnostic test sensitivity and specificity and we test the null hypothesis that the prevalence is below the threshold. Sample size computations are developed using hypergeometric sampling for finite populations and binomial sampling for infinite populations. A normal approximation is also developed. Our procedures are compared with the frequentist methods of Cameron and Baldock (1998a, Preventive Veterinary Medicine34, 1-17.) using an example of foot-and-mouth disease. User-friendly programs for sample size calculation and analysis of survey data are available at http://www.epi.ucdavis.edu/diagnostictests/.

Animals↗
PubMed1995

Modelling patterns of parasite aggregation in natural populations: trichostrongylid nematode-ruminant interactions as a case study.

The characteristically aggregated frequency distribution of macroparasites in their hosts is a key feature of host-parasite population biology. We begin with a brief review of the theoretical literature concerning parasite aggregation. Though this work has illustrated much about both the sources and impact of parasite aggregation, there is still no definite analysis of both these aspects. We then go on to illustrate the use of one approach to this problem--the construction of Moment Closure Equations (MCEs), which can be used to represent both the mean and second moments (variances and covariances) of the distribution of different parasite stages and phenomenological measures of host immunity. We apply these models to one of the best documented interactions involving free-living animal hosts--the interaction between trichostrongylid nematodes and ruminants. The analysis compares patterns of variability in experimental infections of Teladorsagia circumcincta in sheep with the equivalent wildlife situation--the epidemiology of T. circumcincta in a feral population of Soay sheep on St Kilda, Outer Hebrides. We focus on the relationship between mean parasite load and aggregation (inversely measured by the negative binomial parameter, k) for cohorts of hosts. The analysis and empirical data indicate that k tracks the increase and subsequent decline in the mean burden with host age. We discuss this result in terms of the degree of heterogeneity in the impact of host immunity or parasite-induced mortality required to shorten the tail of the parasite distribution (and therefore increase k) in older animals. The model is also used to analyse the relationship between estimated worm and egg counts (since only the latter are often available for wildlife hosts). Finally, we use these results to review directions for future work on the nature and impact of parasite aggregation.

Age Factors↗
PubMedDate not supplied

The distribution of psychiatric and somatic III health: associations with personality and socioeconomic status.

OBJECTIVE: Psychiatric and somatic disorders frequently co-occur in the same individuals. We examined whether this happens because these types of morbidity share risk factors or because they are risk factors for each other. METHODS: Negative binomial regression was used to examine, in a random sample of Dutch adults (N = 7076), cross-sectional associations of sociodemographic and personality variables like income and neuroticism with the presence, over 1 year, of 30 somatic and 13 psychiatric disorders, with the latter diagnosed by structured interview. We examined to what extent the links of these variables with these two morbidity types were independent of each other. RESULTS: This population experienced 5050 somatic and 2438 psychiatric disorders during the preceding year. Subjects reporting more somatic disorders had more psychiatric disorders. Neuroticism, followed closely by low educational attainment, was the strongest correlate of both morbidity types. After adjustment for all other covariates including somatic morbidity, the number of psychiatric diagnoses rose 1.84-fold (95% confidence interval = 1.74-1.94) per standard deviation increase in neuroticism. Likewise, adjusted for all other covariates including psychiatric diagnoses, 1.42 (95% confidence interval = 1.35-1.50) times more somatic disorders were reported per standard deviation increase in neuroticism. CONCLUSIONS: Personal features like neuroticism and low educational attainment are linked with psychiatric and with somatic morbidity. These links are largely independent. Although this study was cross-sectional, the results suggest that these different types of morbidity may have overlapping etiologies. Key words: Comorbidity, multimorbidity coefficient, negative binomial regression, epidemiology, neuroticism, social class.

Adult↗
PubMed2007

Analysis on binary responses with ordered covariates and missing data.

We consider the situation of two ordered categorical variables and a binary outcome variable, where one or both of the categorical variables may have missing values. The goal is to estimate the probability of response of the outcome variable for each cell of the contingency table of categorical variables while incorporating the fact that the categorical variables are ordered. The probability of response is assumed to change monotonically as each of the categorical variables changes level. A probability model is used in which the response is binomial with parameters p(ij) for each cell (i, j) and the number of observations in each cell is multinomial. Estimation approaches that incorporate Gibbs sampling with order restrictions on p(ij) induced via a prior distribution, two-dimensional isotonic regression and multiple imputation to handle missing values are considered. The methods are compared in a simulation study. Using a fully Bayesian approach with a strong prior distribution to induce ordering can lead to large gains in efficiency, but can also induce bias. Utilizing isotonic regression can lead to modest gains in efficiency, while minimizing bias and guaranteeing that the order constraints are satisfied. A hybrid of isotonic regression and Gibbs sampling appears to work well across a variety of scenarios. The methods are applied to a pancreatic cancer case-control study with two biomarkers.

Algorithms↗
PubMed2001

The inheritance of genes in mitochondria and chloroplasts: laws, mechanisms, and models.

The inheritance of mitochondrial and chloroplast genes differs from that of nuclear genes in showing vegetative segregation, uniparental inheritance, intracellular selection, and reduced recombination. Vegetative segregation and some cases of uniparental inheritance are due to stochastic replication and partitioning of organelle genomes. The rate and pattern of vegetative segregation depend partly on the numbers of genomes and of organelles per cell, but more importantly on the extent to which genomes are shared between organelles, their distribution in the cell, the variance in number of replications per molecule, and the variance in numerical and genotypic partitioning of organelles and genomes. Most of these parameters are unknown for most organisms, but a simple binomial probability model using the effective number of genomes is a useful substitute. Studies using new cytological, molecular, and genetic methods are shedding some light on the processes involved in segregation, and also on the mechanisms of intracellular selection and uniparental inheritance in mammals. But significant issues remain unresolved, notably about the extent of paternal transmission and mitochondrial fusion in mammals.

Animals↗
PubMed1987

Spontaneous quantal currents in a central neuron match predictions from binomial analysis of evoked responses.

Inhibitory postsynaptic currents occurring spontaneously in the teleost Mauthner cell were analyzed with the single-electrode voltage-clamp technique. They were collected during depolarizing steps and were outward-going; this procedure allowed them to be isolated from possible excitatory currents flowing in the opposite direction. Their amplitude histograms were found to exhibit regularly spaced multiple peaks, each of which had a Gaussian distribution of the same width. These compound inhibitory postsynaptic currents represent responses evoked by background firing of presynaptic neurons, and when tetrodotoxin was applied topically, only the first peak in the frequency histogram, which can be attributed to single exocytotic events, remained. The mean conductance of this quantal unit equalled 46.0 nS, which corresponds to the opening of 1000-2000 Cl- channels activated by glycine--the transmitter at these synapses. Its waveform and those of the larger units were essentially the same. Furthermore, in each set of data provided by a given Mauthner cell, the size of a quantum was quite constant, with its variance and those of further peaks being equivalent to that of background noise. These properties, which characterize the quantal events on the basis of spontaneous synaptic activity, were strikingly similar to those of the basic units derived by the simple binomial to those of the basic units derived by the simple binomial analysis of unitary postsynaptic potentials, thus validating the use of this statistical model to quantify the quantal nature of release at central connections. The quite straightforward method used here to extract single miniature currents from complex signals should be applicable to the other systems of the central nervous system, where the pertinence of this probabilistic model of release has yet to be demonstrated.

Animals↗
PubMed1978

Improvement of scintigrams by computer processing.

Computer processing can improve the quality of scintigrams in several ways. It can increase the accuracy with which the image approximates the activity distribution by reversing degradation. It can selectively enhance normal or abnormal structures of interest. It can optimize the use of the display system presenting the image. The usefulness of computer processing must be determined by observer testing and clinical experience. The need to correct distortion in both intensity (nonuniformity) and space can be avoided by attention to calibration and to the setup of the imaging device employed and by use of the sliding energy window technique. Nonuniformity correction, especially for quantitative studies, should not be done using a flood field as this may actually decrease accuracy. Instead, any necessary correction should employ the sensitivity matrix, which measures the variation of sensitivity to a point source with the position of the source. Statistical fluctuations (noise) and degradation of resolution are commonly corrected using linear, stationary techniques [concepts which are defined and developed in the text], but nonstationary techniques appear to be frequently more successful at the expense of increased processing time. Techniques of choice for pure smoothing are nine-point binomial smoothing and variable shape averaging, and those for both sharpening and smoothing (preferred for most modern, high-count scintigrams) are unsharp masking, Metz or Wiener filtering, and bi-regional sharpening. Structures of interest can be enhanced by methods which detect and emphasize changes in local distributions of slope and curvature of intensity. High quality display devices are essential to reap any benefits from degradation correction. Those devices, which must have appropriately high sensitivity and must avoid display artifacts, have become available only recently. Use of the display should be matched to the processing done. Contrast enhancement, e.g. by histogram qualization, for optimal use for each image of the display intensity range, is often helpful. Most scintigram processing is done using computers with about 32K 16-bit words. Floating point hardware is often useful. Most processing methods require 1-30 seconds on such computers and usually under 15 seconds. Processing time tends to be negligible compared to time for user specification of the processing to be done, so the quality of command languages should be of concern. Careful observer studies using phantoms have shown processing to improve detectability of lesions when a single display is used for both processed and unprocessed images, but not when unprocessed images on standard analog displays are compared to processed images on common computer displays...

Computers↗
PubMed1991

An aggregate accident model based on pooled, regional time-series data.

The determinants of personal injury road accidents and their severity are studied by means of generalized Poisson regression models estimated on the basis of combined cross-section/time-series data. Monthly data have been assembled for 18 Norwegian counties (every county but one), covering the period from January 1974 until December 1986. A rather wide range of potential explanatory factors are taken into account, including road use (exposure), weather, daylight, traffic density, road investment and maintenance expenditure, accident reporting routines, vehicle inspection, law enforcement, seat belt usage, proportion of inexperienced drivers, and alcohol sales. Separate probability models are estimated for the number of personal injury accidents, fatal accidents, injury victims, death victims, car occupants injured, and bicyclists and pedestrians injured. The fraction of personal injury accidents that are fatal is interpreted as an average severity measure and studied by means of a binomial logit model.

Accidents, Traffic↗
PubMed2004

A Reed-Frost model taking into account uncertainties in the diagnostic of the infection.

In this paper, we model the epidemic course of a pathogen infection within a semi-closed group which generates clinical signals which do not necessarily permit its ready and certain identification. Typical examples of such a pathogen are influenza-type viruses. We allow for time-varying infectivity levels among individuals, and model the probability of infection per contact as a function of the clinical signals. In order to accomplish this, we introduce a modified chain-binomial Reed-Frost model. We obtain an expression for the basic reproduction ratio and determine conditions which guarantee that the epidemic does not survive in the long-term. These conditions being functions of the signal's distribution, they can be used to design and evaluate interventions, such as treatment protocols.

Disease Outbreaks↗
PubMed2003

Comparison of road crashes incidence and severity between some French counties.

Our aim is to compare traffic safety among several counties in France, and explore whether observed differences can be explained by differences in road types distribution and by differences in socio-economic characteristics between counties. Traffic safety is measured by incidence and severity, where incidence is defined by the ratio of counts of injury accidents and exposure, measured by the amount of kilometres driven. Severity is measured by the ratio between fatal and injury accidents. These indexes are analysed in the framework of Generalised Linear Models: counts of injury accidents are analysed with a Negative Binomial regression, which accounts for over-dispersion. Severity being the proportion of fatal accidents among injury accidents corresponds to the probability of a Binomial setting and this is modelled by a logistic regression. This modelling provides an easy way to adjust for covariates such as road type, environment (urban/rural) and evolution over time, and to test their possible interactions. We find that the time trend of each indice (incidence and severity) is the same across counties and across road types. There is a significant interaction between county and road type, meaning that, first, differences in traffic safety between counties are not fully explained by different road type distributions, and second, that the "ranking" of counties in term of incidence or severity varies according to the road type considered, and vice-versa. It was planned to explore global characteristics of the counties (driving and socio-economic data) as possible explanatory factors of differences between counties, but the existence of an interaction of county with road types shows the necessity of collecting and exploring characteristics of the sub-levels of road type within county.

Accidents, Traffic↗
PubMed1979

The effect of calcium ions on the secretion of quanta evoked by an impulse at nerve terminal release sites.

A study has been made of the effects of calcium ions on the number of quanta secreted from all the release sites at an amphibian motor nerve terminal recorded with an intracellular microelectrode (m) compared with the number secreted simultaneously from a small number of release sites recorded with an extracellular microelectrode (me). If the endplate potential was made subthreshold by lowering the external calcium concentration ([Ca]o less than or equal to 0.4 mM), it was possible to find small groups of release sites for which me was comparable to m, indicating considerable nonuniformity in the probability of release of a quantum at different groups of release sites (Pe) in a given [Ca]o. Increasing [Ca]o in the range from 0.25 to 0.4 mM increased the probability of release of a quantum at groups of release sites (Pe), independent of the initial value of Pe, and the dependence of Pe on [Ca]o followed a fourth power relationship. A conditioning impulse enhanced the probability of release of a quantum by a subsequent test impulse at release sites, if Pe was less than 1.0 during the conditioning impulse. It is shown that the present observations regarding the dependence of Pe on [Ca]o and on conditioning impulses can be quantitatively predicted from previous observations regarding the dependence of the binomial parameters m, p, and n on [Ca]o and on conditioning impulses determined with intracellular electrodes, if the probability of secretion of a quantum at a release site (Pj) is different for different release sites and Pj is distributed as a beta random variable.

Action Potentials↗
PubMed2006

Enrichment or depletion of a GO category within a class of genes: which test?

MOTIVATION: A number of available program packages determine the significant enrichments and/or depletions of GO categories among a class of genes of interest. Whereas a correct formulation of the problem leads to a single exact null distribution, these GO tools use a large variety of statistical tests whose denominations often do not clarify the underlying P-value computations. SUMMARY: We review the different formulations of the problem and the tests they lead to: the binomial, chi2, equality of two probabilities, Fisher's exact and hypergeometric tests. We clarify the relationships existing between these tests, in particular the equivalence between the hypergeometric test and Fisher's exact test. We recall that the other tests are valid only for large samples, the test of equality of two probabilities and the chi2-test being equivalent. We discuss the appropriateness of one- and two-sided P-values, as well as some discreteness and conservatism issues. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Data Interpretation, Statistical↗
PubMed2000

Analysis and implications of equivalent uniform approximations of nonuniform unitary synaptic systems.

Real synaptic systems consist of a nonuniform population of synapses with a broad spectrum of probability and response distributions varying between synapses, and broad amplitude distributions of postsynaptic unitary responses within a given synapse. A common approach to such systems has been to assume identical synapses and recover apparent quantal parameters by deconvolution procedures from measured evoked (ePSC) and unitary evoked postsynaptic current (uePSC) distributions. Here we explicitly consider nonuniform synaptic systems with both intra (type I) and intersynaptic (type II) response variability and formally define an equivalent system of uniform synapses in which both uePSC and ePSC amplitude distributions best approximate those of the actual nonuniform synaptic system. This equivalent system has the advantage of being fully defined by just four quantal parameters: ñ, the number of equivalent synapses;p, the mean probability of quantal release; mu, mean; and sigma(2), variance of the uePSC distribution. We show that these equivalent parameters are weighted averages of intrinsic parameters and can be approximated by apparent quantal parameters, therefore establishing a useful analytical link between the apparent and intrinsic parameters. The present study extends previous work on compound binomial analysis of synaptic transmission by highlighting the importance of the product of p and mu, and the variance of that product. Conditions for a unique deconvolution of apparent uniform synaptic parameters have been derived and justified. Our approach does not require independence of synaptic parameters, such as p and mu from each other, therefore the approach will hold even if feedback (i.e., via retrograde transmission) exists between pre and postsynaptic signals. Using numerical simulations we demonstrate how equivalent parameters are meaningful even when there is considerable variation in intrinsic parameters, including systems where subpopulations of high- and low-release probability synapses are present, therefore even under such conditions the apparent parameters estimated from experiments would be informative.

Animals↗
PubMed2006

A demonstration of modeling count data with an application to physical activity.

Counting outcomes such as days of physical activity or servings of fruits and vegetables often have distributions that are highly skewed toward the right with a preponderance of zeros, posing analytical challenges. This paper demonstrates how such outcomes may be analyzed with several modifications to Poisson regression. Five regression models 1) Poisson, 2) overdispersed Poisson, 3) negative binomial, 4) zero-inflated Poisson (ZIP), and 5) zero-inflated negative binomial (ZINB) are fitted to data assessing predictors of vigorous physical activity (VPA) among Latina women. The models are described, and analytical and graphical approaches are discussed to aid in model selection. Poisson regression provided a poor fit where 82% of the subjects reported no days of VPA. The fit improved considerably with the negative binomial and ZIP models. There was little difference in fit between the ZIP and ZINB models. Overall, the ZIP model fit best. No days of VPA were associated with poorer self-reported health and less assimilation to Anglo culture, and marginally associated with increasing BMI. The intensity portion of the model suggested that increasing days of VPA were associated with more education, and marginally associated with increasing age. These underutilized models provide useful approaches for handling counting outcomes.

Journal Article↗
PubMed1972

Quantal components of the inhibitory synaptic potential in spinal mononeurones of the cat.

1. Monosynaptic i.p.s.p.s were produced in spinal motoneurones of the cat by stimulation of a pool of interneurones following chronic degeneration of descending tracts and primary afferent fibres in the lumbosacral cord.2. Monosynaptic i.p.s.p.s so evoked by supramaximal stimuli often showed a fluctuation in amplitude with occasional failures of response.3. When two successive stimuli were applied at a short interval, the mean amplitude of the second i.p.s.p.s was greater than that of the first. This facilitation was associated with a decrease in the number of failures, a decrease in the coefficient of variation of the amplitude distribution and an increase in the probability of occurrences of large i.p.s.p.s.4. A statistical analysis of the i.p.s.p. amplitude fluctuation showed that the monosynaptic i.p.s.p. is composed of discrete unit potentials evoked with a certain probability in a manner described by a binomial law.5. The application of strychnine decreased the mean amplitude of i.p.s.p.s with little change in the coefficient of variation of the i.p.s.p. amplitude distribution.6. It is concluded that the release of inhibitory transmitter occurs in quantal steps and that strychnine blocks primarily the post-synaptic receptors for the inhibitory transmitter.

Animals↗
PubMed1990

Probability of transmission of Chagas disease by Triatoma infestans (Hemiptera: Reduviidae) in an endemic area of Santiago del Estero, Argentina.

The daily probability (P) of transmission of Trypanosoma cruzi to a noninfected human host by an infected Triatoma infestans bug was estimated using field data from a 2-year longitudinal study carried out in a rural settlement of 20 households in Amamá, Santiago del Estero, Argentina. The following information was used for this purpose: the bug density and the proportion of infected bugs; the bug biting rate and the distribution of bites between humans and animals; the age-specific seropositivity to T. cruzi of the human population; and the actual number of new cases of human infection. The 2-year accumulated number of infective contacts per house estimated using a binomial model shows a statistically significant logistic correlation with the observed proportion of new cases per house. An average house where new cases of human infection were registered in the 2-year period had a P value of 0.0012, while an average general house (i.e., with and without new cases) had a P value of 0.0009. The observed range of P is discussed in terms of the chain of factors that affects the individual human risk of acquiring the infection and the possible entomological sampling errors.

Adolescent↗
PubMed2025

Estimating Re and overdispersion in secondary cases from the size of identical sequence clusters of SARS-CoV-2.

The wealth of genomic data that was generated during the COVID-19 pandemic provides an exceptional opportunity to obtain information on the transmission of SARS-CoV-2. Specifically, there is great interest to better understand how the effective reproduction number [Formula: see text] and the overdispersion of secondary cases, which can be quantified by the negative binomial dispersion parameter k, changed over time and across regions and viral variants. The aim of our study was to develop a Bayesian framework to infer [Formula: see text] and k from viral sequence data. First, we developed a mathematical model for the distribution of the size of identical sequence clusters, in which we integrated viral transmission, the mutation rate of the virus, and incomplete case-detection. Second, we implemented this model within a Bayesian inference framework, allowing the estimation of [Formula: see text] and k from genomic data only. We validated this model in a simulation study. Third, we identified clusters of identical sequences in all SARS-CoV-2 sequences in 2021 from Switzerland, Denmark, and Germany that were available on GISAID. We obtained monthly estimates of the posterior distribution of [Formula: see text] and k, with the resulting [Formula: see text] estimates slightly lower than estimates obtained by other methods, and k comparable with previous results. We found comparatively higher estimates of k in Denmark which suggests less opportunities for superspreading and more controlled transmission compared to the other countries in 2021. Our model included an estimation of the case detection and sampling probability, but the estimates obtained had large uncertainty, reflecting the difficulty of estimating these parameters simultaneously. Our study presents a novel method to infer information on the transmission of infectious diseases and its heterogeneity using genomic data. With increasing availability of sequences of pathogens in the future, we expect that our method has the potential to provide new insights into the transmission and the overdispersion in secondary cases of other pathogens.

COVID-19↗
PubMed1991

Measurement of sensitivity to adriamycin in hybrid spheroids.

Using the newly developed hybrid spheroid system, we have been able to measure sensitivities to adriamycin in two sublines of LoVo cells (a human colon adenocarcinoma line). Hybrid spheroids are composed of coagglomerated LoVo cells, and nonproliferating HeLa "feeder" cells, mimicking a population of minitumors. Spheroids of uniform size, but containing different numbers of LoVo cells, were incubated with various concentrations of adriamycin and after washing, plated for colony formation. Binomial counting statistics were achieved by marking surface-attached spheroids soon after plating, and scoring colonies one week later. From the fraction of noncolony formers, the average number of clonogens per spheroid (clonogenicity) was calculated using the zero term of the Poisson distribution. The effect of treatment with adriamycin was evaluated from the decrease in clonogenicity in parallel series of hybrid spheroids. Response to treatment was found to be independent of cellular clonogenicity in the control, untreated series. Dose-response curves were obtained for each of the two sublines after treatment for 1.5 h with various concentrations of adriamycin. The difference in the response to adriamycin between the two sublines amounted to a factor of 27 (deduced from D0 ratios; these are the same as isosurvival dose ratios).

Adenocarcinoma↗