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PubMed1979

The estimation of mutation rates when premeiotic events are involved.

When mutation or recombination events occur premeiotically, the distribution of exceptional individuals among the offspring will be "clustered" as opposed to binomial. Even though the exact nature of the clustering is usually unknown, unbiased methods for measuring mutation rate and determining the precision of these measurements are given to replace a biased method now frequently used. When clustering is pronounced, the unweighted average mutation rate is found to be a more efficient estimator than the usual average weighted by family size. Methods of statistical inference and optimal experimental design in the absence of specific knowledge of the mechanism of clustering are also discussed.

Animals↗
PubMed2006

Generalizing the TITE-CRM to adapt for early- and late-onset toxicities.

Due to the staggered entry of subjects in phase I trials, some subjects will only be partially through the study when others are ready to be enrolled. Nonetheless, many phase I designs focus solely upon whether or not subjects experience toxicity, thereby determining the maximum tolerated dose (MTD) with a binomial likelihood using data from fully observed subjects. The time-to-event continual reassessment method (TITE-CRM) was the first attempt to incorporate information from partially observed subjects by using a weighted binomial likelihood in which the weights are based upon the actual toxicity time distribution. Unfortunately, it is difficult to accurately estimate the toxicity time distribution because only a small proportion of enrolled subjects will experience toxicity. Creators of the TITE-CRM propose the simple alternative of weighting subjects by the proportion of time observed, as well as two adaptive weights to adjust for late-onset toxicities. As a alternative to these approaches, we suggest assuming the toxicity times, as a proportion of the total time under observation, have a Beta distribution with parameters 1.0 and theta; we also allow theta to vary by dose. The value of theta allows us to reflect the occurrence of early- or late-onset toxicities without correctly specifying the actual distribution of toxicity times. Through this model, we do not necessarily expect to improve identification of the MTD, but rather hope to reduce the exposure of subjects to overly toxic doses. Through simulation, we examine how well our model identifies the MTD and allocates dose assignments in three scenarios investigated by previous publications.

Clinical Trials, Phase I as Topic↗
PubMedDate not supplied

Epidemiology of Ostertagia ostertagi in dairy cow from different breeding systems.

The epidemiology of Trichostrongylidae infections in three dairy cow groups reared under different conditions and in different habitats was studied with particular emphasis on Ostertagia ostertagi. In cows bred intensively in swampy lowlands (Po River Valley) the prevalence of infection was 43% and the mean intensity 567. In cows bred traditionally (Friuli, Northern-Eastern Italy), the prevalence in permanently housed cows was 24% (mean intensity: 13). In grazing cows, it was 68% (mean intensity: 120). The distribution of parasite numbers (O. ostertagi) per host was studied with the negative binomial model. The observed data were also compared by the method of cumulative relative frequencies. The results suggest that parasitism is also important in cows reared intensively.

Abomasum↗
PubMedDate not supplied

Can't miss: conquer any number task by making important statistics simple. Part 4. Confidence intervals with t distributions, standard error, and confidence intervals for proportions.

Healthcare quality professionals need to understand and use inferential statistics to interpret sample data from their organizations. Since in quality improvement and healthcare research studies, all the data from a population often are not available, investigators take samples and make inferences about that population using inferential statistics. This series of six articles will give readers an understanding of the concepts of inferential statistics, as well as the specific tools for calculating confidence intervals and tests of statistical significance for samples of data. The statistical principles are equally applicable to quality improvement and healthcare research studies. This article, Part 4, starts with a review of the information contained in Parts 1, 2, and 3, which appeared in the July/August 2003 issue of the Journal for Healthcare Quality. This article describes t distributions and how these are used to calculate confidence intervals for estimating a population mean based on a sample mean of a continuous variable. Part 4 concludes with a discussion of standard error, margin of error, and confidence intervals for estimating a population proportion based on a sample proportion from a binomial variable.

Confidence Intervals↗
PubMed1977

The formation and regression of synapses during the re-innervation of axolotl striated muscles.

1. A study has been made of the formation and regression of synapses formed by spinal nerves 16 and 17 in axolotl hind-limb flexor muscles following the severing of nerve 16, using histological, ultrastructural and electrophysiological techniques. 2. Axolotl hind-limb flexor myofibres possessed 'en plaque' end-plates from either spinal nerve 16 or 17 or both at intervals of about 1000 micronm along their length; the myofibre's length constant was about 700 micronm allowing electrophysiological observations of at least two of these synapses during a single impalement; transmitter release at these synapses could be described by binomial statistics and in a given set of ionic conditions the binomial statistic parameter n was directly proportional to the size of the nerve terminals whilst the binomial statistic parameter p was invariant to changes in nerve terminal size. 3. The distribution of synapses formed by spinal nerves 16 and 17 in different sectors of the axolotl hind-limb flexor muscles was determined from a study of evoked end-plate potentials; the middle and proximal sectors of the flexor muscles contained myofibres which received an innervation from nerve 16 only, whereas the sectors surrounding these contained myofibres innervated either by nerve 16 or nerve 17 or by both nerves. 4. Six days following the severing of spinal nerve 16, evoked transmitter release from the synapses formed by this nerve had failed; transmission was subsequently recorded at a few synapses formed by nerve 17 in the middle and proximal sectors of the flexor muscles which are not normally innervated by this nerve and these synapses had a low n; during the succeeding four weeks the value of n at the synapses increased to a size about 70% that of the terminals normally formed by nerve 16 at these sites. 5. Four weeks after severing nerve 16, myofibres which possessed synapses formed by nerve 17 also possessed synapses from re-innervating nerve 16 and these were sometimes formed at the same synaptic sites as those occupied by nerve 17. 6. In the subsequent sixteen weeks, the n value of synapses formed by nerve 17 declined whilst the n values of synapses formed by re-innervating nerve 16 on the same myofibres matured to their control size. 7. It is suggested that on severing nerve 16 collateral sprouting of nearby intact nerve 17 occurs and these collateral sprouts innervate the denervated synaptic sites, although the sprouts arenot as well matched to the denervated synaptic sites as are the original nerve terminals; thus if nerve 16 returns it preferentially forms synapses at its original synaptic sites, and the collateral synapses formed by nerve 17 regress.

Ambystoma↗
PubMed1981

Observations on the occurrence of Diplostomum spathaceum and Schistocephalus sp. in ninespine sticklebacks (Pungitius pungitius) from the Belcher Islands, Northwest Territories, Canada.

All 175 ninespine sticklebacks, Pungitius pungitius (Linné), collected from the Belcher Islands were parasitized by Diplostomum spathaceum (Rudolphi) and 43% by Schistocephalus sp. D. spathaceum metacercariae were mostly confined to a dorso-ventral band encircling the lens of the eye, and were concentrated in the anterio-dorsal sector of this band. The central area of the lens was thus relatively free of diplostomula, probably minimizing interference with the vision of the fish. The frequency distribution of D. spathaceum abundance in P. pungitius was closely approximated by a negative binomial, while that for Schistocephalus was best fitted by a Poisson. None of the fish condition factors examined appeared related to the intensity of the parasitic infections.

Animals↗
PubMed1985

Clonal analysis of intestinal crypt populations in mouse aggregation chimaeras.

The epithelium of each individual intestinal crypt in adult mouse aggregation chimaeras is composed of cells of a single parental genotype (Ponder et al. 1985). Using a carbohydrate polymorphism recognized by Dolichos biflorus agglutinin as a strain-specific marker on entire sheets of intestinal mucosa, we have analysed the two-dimensional mosaic patterns of patches of the chimaeric intestinal crypt population. The relative proportions of each genotype varied greatly along the length of any one intestine. In chimaeras with highly unbalanced proportions, the minority component occurred as discrete patches. Patches of single or a few crypts were most frequent, but a smaller number of much larger patches was always present. The size frequency distribution of discrete patches was highly concave and departed significantly from a geometric distribution (a model for non-differential proliferation), but fitted the more skewed negative binomial model. The data are consistent with the interpretation that most progenitor crypts never or rarely divide, while a minority proliferate to a greater extent. We discuss ways in which our system could be analysed further to examine this interpretation. Our results also support Whitten's (1978) conclusion from a computer simulation that the mean patch size, as it has previously been used in statistical analyses of chimaeric tissue, 'is not a reliable statistic on which to judge mosaicism'.

Animals↗
PubMed1999

Spatio-temporal dynamics of resident and immigrating populations of Carcinops pumilio (Coleoptera: Histeridae) in high-rise poultry facilities.

The histerid beetle Carcinops pumilio (Erichson) is an important natural predator of the house fly, Musca domestica L., in accumulated poultry house manure. We examined the spatio-temporal dynamics of establishing adult C. pumilio in high-rise poultry facilities using conventional and geostatistical approaches. The growth curves of resident and immigrating populations followed logistic and exponential equations, respectively, and their rates of establishment were statistically the same. Frequency distributions for both populations were strongly positively skewed, and approximately 53% of sampling intervals were significantly modeled by the negative binomial. Taylor's power law indicated both populations to be aggregated, and gave excellent least squares regression fits to both populations. Correlograms, a geostatistical tool, suggested little local spatial structure (e.g., 2nd order effects) for either population. The resident population was 'randomly' aggregated: beetles were clustered around randomly distributed aggregations of house fly immatures. The immigrating population exhibited significant spatial trends (e.g., 1st order effects) consistently seen at all sampling intervals. C. pumilio spatial structure was represented primarily by this spatial trend; thus, immigration of C. pumilio may have been either a singular event in time, or initiating at 1 or multiple times from a singular location.

Animal Husbandry↗
PubMed1996

Analysis and Modeling of Time-Dose-Mortality of Melanoplus sanguinipes, Locusta migratoria migratorioides, and Schistocerca gregaria (Orthoptera: Acrididae) from Beauveria, Metarhizium, and Paecilomyces Isolates from Madagascar

A complementary log-log (CLL) model was used to model time-dose-mortality relationships from bioassay tests of 26 fungal isolates mostly from Madagascar, Africa, against three acridid species, all referred to here as "grasshoppers." The fungal pathogens included 15 isolates of Beauveria bassiana, 9 isolates of Metarhizium flavoviridae, and 2 isolates of Paecilomyces spp. Grasshopper species tested included Melanoplus sanguinipes, Locusta migratoria migratorioides, and Schistocerca gregaria. The scaled deviance, mean deviance, Pearson X2 statistic, Hosmer-Lemeshow (H-L) C statistic, and three-dimensional time-dose-mortality graphs were used to assess extra-binomial variation, data points that were potential outliers, conformance of the scaled deviance statistic and Pearson's X2 statistic to a chi2 distribution, and the fit of the CLL model. The H-L C statistic also was found to be useful in showing the goodness of fit of the CLL model for the fungal isolates prior to modeling the extra-binomial variation. After the extra-binomial variation was modeled using Williams' method, the slope from maximum likelihood estimation, modified log(LD50) estimates (which were corrected for background mortality using the CLL model), a dynamic ranking of the log(LD50) values over time, and a three-dimensional plot of time, dose, and mortality of the three grasshopper species were used to evaluate the effectiveness of the fungal isolates. In general, the CLL model provided a rather poor fit of the fungal isolates which had a large number of replicate trials in the bioassay tests (i.e., a large sample size) due to extra-binomial variation. The CLL model provided an excellent fit of the time-dose-mortality relationships of such isolates after the extra-binomial variation was modeled and included in the CLL model. Metarhizium isolates MFV and SP5 were found to be the most virulent isolates tested against M. sanguinipes, followed by Metarhizium isolates: SP8, SP7, SP9, SP6, and SP1, and Beauveria isolate S33B. Metarhizium isolates SP3, SP5, SP6, and SP9, and Beauveria isolates SP11, SP12, SP13, and SP16 showed higher levels of virulence against L. migratoria migratorioides over more of the time periods tested than the other pathogen isolates examined. Metarhizium isolates SP9 and SP5 were the most effective isolates tested against S. gregaria. In general, the Metarhizium isolates were more virulent against the grasshoppers than the Beauveria isolates, which were more virulent than the Paecilomyces isolates. The CLL model was found to be very useful in describing grasshopper mortality as a function of time and dose. This approach combined with model and fungal isolate assessment statistics will be helpful for determining which pathogen isolates have the greatest potential for controlling grasshoppers and other pests in the future.

Journal Article↗
PubMed2002

A modification of Peto's nonparametric estimation of survival curves for interval-censored data.

Peto (1973, Applied Statistics, 22, 86-91) gave a nonparametric generalized maximum-likelihood estimate of the survival function for interval-censored data. His method has a tendency to concentrate probability masses at the endpoints of the intervals, even for the ordinary grouped data, instead of spreading them through the intervals, as one might expect them to be in the underlying distribution. We describe a modification that overcomes this. The new estimate reduces to the standard binomial estimate when applied to grouped data. It also reduces to the Kaplan-Meier estimate when applied to survival data that consist of only exact or right-censored observations. Both estimates are maximum-likelihood estimates but are based on different interpretations of the endpoints of the intervals.

Biometry↗
PubMedDate not supplied

CAN'T MISS--conquer any number task by making important statistics simple. Part 1. Types of variables, mean, median, variance, and standard deviation.

Healthcare quality improvement professionals need to understand and use inferential statistics to interpret sample data from their organizations. In quality improvement and healthcare research studies all the data from a population often are not available, so investigators take samples and make inferences about the population by using inferential statistics. This three-part series will give readers an understanding of the concepts of inferential statistics as well as the specific tools for calculating confidence intervals for samples of data. This article, Part 1, presents basic information about data including a classification system that describes the four major types of variables: continuous quantitative variable, discrete quantitative variable, ordinal categorical variable (including the binomial variable), and nominal categorical variable. A histogram is a graph that displays the frequency distribution for a continuous variable. The article also demonstrates how to calculate the mean, median, standard deviation, and variance for a continuous variable.

Analysis of Variance↗
PubMed1993

Determination of the center of pressure of the hoofs of the forelimbs of horses standing on a flat level surface.

The pressure exerted on a flat level surface by recently trimmed, unshod hoofs of the front limbs of 23 sound, adult horses was measured using pressure-sensitive film and a specially built cassette. The horses were tranquilized and stood with one foot on the 2.9-cm-thick cassette and the other on a block of equal height. The hoofs were observed for motion during the measurement, and the developed film was examined for improper alignment of the film or slipping of the hoof. The center of pressure was located using the method of weighted proportions of Barrey. This static measurement system with a long measurement time and the number of measurements reduced the influence of variables inherent in the horses' behavior and the measuring system. The calculated point was recorded as falling medial to, lateral to or on a line bisecting the central sulcus of the frog. In the dorsal to palmar orientation the point was classified with reference to a line drawn halfway between the most dorsal and the most palmar mark on the film. Forty-six percent of the calculated centers of pressure were located in the medial heel area. Binomial analysis for large samples indicates that this was a significant variation from a random distribution. Seventy-six percent of the centers were located in or on the borders of the medial heel.

Animals↗
PubMed1988

Two methods for measuring the non-randomness of chromosome abnormalities.

Applying conventional statistical techniques to cytogenetic data usually faces the problem of working with small numbers and many classes. We describe two techniques, one based on a binomial test procedure, the other on Monte Carlo simulations, aimed at studying the non-randomness of chromosomal aberrations. Both techniques were used to study the distribution of breakpoints involved in variant Philadelphia translocations in chronic myeloid leukaemia. The results showed that 28 bands were non-randomly rearranged (P less than or equal to 0.05). Furthermore, the probabilities calculated from the binomial test procedure were close to those calculated from the Monte Carlo simulations.

Chromosome Aberrations↗
PubMed2003

Unitary EPSCs of corticogeniculate fibers in the rat dorsal lateral geniculate nucleus in vitro.

To investigate unitary corticogeniculate excitatory postsynaptic currents (EPSCs), whole cell patch-clamp recordings were obtained from 20 principal cells in slices of the dorsal lateral geniculate nucleus (dLGN) of DA-HAN rats. EPSCs, evoked by electrical stimulation of corticogeniculate axons, had size distributions with one or more quantal peaks. Gaussian curves fitted to such distributions gave a mean quantal size (q) of -5.0 +/- 0.7 (SD) pA for the EPSCs. Paired-pulse ratio (EPSC2/EPSC1) was 3.3 +/- 0.9 for stimuli separated by 40 ms. The mean quantal size was similar for facilitated EPSCs (-5.2 +/- 0.8 pA), implying an increase in mean quantal content (m). Most corticogeniculate axons were capable of releasing only one or two quanta onto individual principal cells. Mean resting release probability (p) was low, 0.09 +/- 0.04. Binomial models, with the same n but increased p, could account for both the basal and facilitated EPSC size distributions in 6/8 cells. It is suggested that the low resting efficacy of corticogeniculate synapses serves to stabilize this excitatory feedback system. The pronounced facilitation in conjunction with large convergence from many corticogeniculate cells would provide a transient, potent excitation of dLGN cells, compliant with the idea of a visually driven neuronal amplifier.

Animals↗
PubMed1998

Recent developments in computer-assisted analysis of mixtures.

This paper reviews recent developments in the area of computer-assisted analysis of mixture distributions (C.A.MAN). Given a biometric situation of interest in which, under homogeneity assumptions, a certain parametric density occurs, such as the Poisson, the binomial, the geometric, the normal, and so forth, then it is argued that this situation can easily be enlarged to allow a variation of the scalar parameter in the population. This situation is called unobserved heterogeneity. This naturally leads to a specific form of nonparametric mixture distribution that can then be assumed to be the standard model in the biometric application of interest (since it also incorporates the homogeneous situations as a special case). Besides developments in theory and algorithms, the work focuses on developments in biometric applications such as meta-analysis, fertility studies, estimation of prevalence under clustering, and estimation of the distribution function of survival time under interval censoring. The approach is nonparametric for the mixing distribution, including leaving the number of components (subpopulations) of the mixing distribution unknown.

Animals↗
PubMed1997

Frequency distributions of fish parasites in the perch Perca fluviatilis L. from Lake Constance.

Seventy perch (Perca fluviatilis) caught in Lake Constance at Langenargen in May 1990 were examined for parasites. The frequency distributions of the eyefluke Diplostomum spathaceum (Rudolphi, 1819), and the tapeworms Proteocephalus percae (Müller, 1780) and Triaenophorus nodulosus (Pallas, 1781) fitted closely to a negative binomial. Only a few fish were highly parasitized. These fishes are devoured by the final hosts: gulls (Diplostomum spathaceum) or the pike (Triaenophorus nodulosus). The fish population was influenced negligibly and the parasite population stayed at a moderate level. During the spawning period female perch were infested with Proteocephalus percae more than the males. This may be because the females had a higher food consumption and became more infected by copepods (intermediate hosts). In contrast, Diplostomum spathaceum, Ichthyocotylurus variegatus, Triaenophorus nodulosus, and Tylodelphys clavata did not occur in different numbers in female and male perches. The frequency distribution of Ichthyocotylurus variegatus (Creplin, 1825) and Tylodelphys clavata (Nordmann, 1832) did not conform to a negative binomial.

Animals↗
PubMed1993

Probabilistic secretion of quanta from successive sets of visualized varicosities along single sympathetic nerve terminals.

Quantal secretion was recorded from adjacent sets of varicosities along the length of single sympathetic nerve terminals that had been visualized with the fluorescent dye, 3,3-diethyloxardicarbocyanine iodide (DiOC2(5)). Recordings were made with both small diameter microelectrodes (4-6 microns) placed over 1-3 varicosities and large diameter microelectrodes (20-50 microns) placed over 3-7 varicosities. The proportion of trials in which secretion occurred from sets of varicosities declined in general for the adjacent sets of varicosities along the length of single sympathetic nerve terminals. The amplitude-frequency distributions of excitatory junctional currents (EJCs) were in general predicted by Poisson statistics and occasionally by binomial statistics. The mean quantal content of the EJC in general declined over threefold along the length of single sympathetic nerve terminals for adjacent sets of varicosities.

Animals↗
PubMed1999

Analysis of an IFN-gamma gene (IFNG) polymorphism in multiple sclerosis in Europe: effect of population structure on association with disease.

An intronic dinucleotide polymorphism in the IFN-gamma gene (IFNG) was used as a marker for testing association with multiple sclerosis (MS). Disease association was analyzed in case-control sets sampled from four geographically separate European populations (Germany, Northern Italy, Sardinia, and Sweden). Only in the Swedish was a weak disease association of the IFNG allele pattern found, mainly due to a higher frequency of IFNG allele I1 in MS patients. No evidence for association was found in the German or Northern Italian populations. These results contrast with the situation in Sardinia. We have recently reported transmission disequilibrium of IFNG allele I2 in Sardinian MS siblings not carrying the predisposing DRB1 *03 or *04 alleles (Ann. Neurol. 44, 841-842, 1998). Further analysis now shows that I2 is significantly more often transmitted to DRB1 *03-/*04- males, than to DRB1 *03-/*04- females. The odds ratio (OR) for IFNG-associated susceptibility to MS in the total Sardinian DRB1*03-/*04- group was 1.88 for I2 heterozygotes but amounted to 8.235 for I2 homozygotes, suggestive of a recessive mode of inheritance. Score test-based statistics pointed to an I2 allele dosage effect acting in susceptibility. Comparison of the IFNG allele frequencies in seven European populations (Northern Finnish, Southern Finnish, Swedish, Danish, German, Italian, and Sardinian) revealed a highly different distribution pattern. We introduced latitude as a score variable in order to test for trend in binomial proportions. This test statistic showed that for both most common alleles, I1 and I2 (compiled allele frequency about 85%), a significant opposite north-to-south trend is seen throughout Europe. This effect is primarily due to the extreme values found in the outlier populations of Finland and Sardinia. Our findings are discussed with respect to recent literature pertinent to the role of the IFNG chromosome region in autoimmune diseases.

Alleles↗