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PubMed1999

On testing equivalence of three populations.

We consider analysis of clinical trials in which the objective is to show that three populations are equivalent. Equivalence is defined in terms of delta, the maximum difference in population means; a one-sided hypothesis test of delta is considered. We provide the distribution of the maximum pairwise difference in sample means, and we use this distribution to find critical values for tests of size 0.100, 0.050, 0.025, and 0.010. When standard errors are not equal among the three treatments, a simple adjustment is proposed to control the type I error rate. These tests are applied to studying the equivalence of three binomial proportions. Test-based confidence intervals are discussed. Two examples illustrate the proposed methods.

Analysis of Variance↗
PubMed1993

Bayesian analysis of binary data from an audit of cervical smears.

A large data set of unsatisfactory smear rates from 629 different cervical smear takers is used to illustrate a Bayesian approach to the analysis of medical audit data with a binary outcome. It is shown that this gives more relevant results in terms of characterizing individual smear takers than frequentist methods, and that the full Bayesian analysis is preferable to an empirical Bayes approximation when the number of different smear takers is small and at least one individual smear taker has contributed only a few smears. Plots of Bayesian posterior distributions with 95 per cent confidence sets are suggested as a useful way of feeding back the results to individual clinicians.

Adult↗
PubMedDate not supplied

Goodness-of-fit issues in ROC curve estimation.

Zhou recently considered goodness-of-fit (GOF) testing for receiver operating characteristic (ROC) curves estimated by applying the binormal and other bidistributional models to rating method data. He interpreted significant GOF tests as evidence that different decision thresholds were applied to diseased and nondiseased subjects and concluded that, in such circumstances, an ROC curve does not exist. In this article the author demonstrates that the GOF test accommodates many alternative hypotheses and that a significant test result need not be equated with an interaction between disease status and decision criteria or with non-existence of an ROC curve. He develops a new family of ROC curves based on a fully parameterized bidistributional model. The family includes the binormal ROC curve, but generalizes its structure by signifying all identifiable deviations in parameters of the latent distributions that define the model. The family provides a unified framework of alternative models to the binormal assumption and of alternative hypotheses to the GOF test for that assumption.

Binomial Distribution↗
PubMed1994

Modeling methylation and IQ scores in fragile X females and mosaic males.

Both fragile X females and mosaic males carry a methylated FMR1 allele in some cells and an unmethylated allele in other cells. Due to FMR1 protein produced in cells with an unmethylated allele, these individuals are expected to display a less severe cognitive phenotype than non-mosaic affected males. A larger range in cognitive abilities is expected for these individuals due to individual variation in X-inactivation or mosaicism ratios. These cognitive effects are well documented for females and have been suggested for mosaic males. Data on fragile X females suggest an approximately linear decrease in mean IQ score as a function of the fraction of cells with the mutation carried on the active X chromosome. Analysis of these data suggests that threshold effects in the relationship between IQ score and X-inactivation ratios are negligible, and that X-inactivation occurs randomly (with no preferential inactivation of either X chromosome) at a stage when the embryo consists of approximately 5 cells. A similar analysis of future data on mosaic males could yield estimates of the probability that a given cell will carry a methylated FMR1 allele and of the number of embryonic cells at the time that mosaicism is established. Distributions of IQ scores among a population of heterozygotes or mosaic male are predicted for several values of these parameters. These distributions include random contributions to IQ scores due to non-fragile-X-related effects, as well as X-inactivation or mosaicism ratios that vary from one individual to another.

Alleles↗
PubMed1995

Bayesian approaches to random-effects meta-analysis: a comparative study.

Current methods for meta-analysis still leave a number of unresolved issues, such as the choice between fixed- and random-effects models, the choice of population distribution in a random-effects analysis, the treatment of small studies and extreme results, and incorporation of study-specific covariates. We describe how a full Bayesian analysis can deal with these and other issues in a natural way, illustrated by a recent published example that displays a number of problems. Such analyses are now generally available using the BUGS implementation of Markov chain Monte Carlo numerical integration techniques. Appropriate proper prior distributions are derived, and sensitivity analysis to a variety of prior assumptions carried out. Current methods are briefly summarized and compared to the full Bayes analysis.

Bayes Theorem↗
PubMed2000

Quantifying parasites in samples of hosts.

Whereas terminological recommendations require authors to use mean intensity or mean abundance to quantify parasites in a sample of hosts, awkward statistical limitations also force them to use either the median or the geometric mean of these measures when making comparisons across different samples. Here, we propose to reconsider this inconsistent practice by giving priority to biological realism in the interpretation of different statistical descriptors and choosing the statistical tools appropriate to our decisions. Prevalence, mean intensity, and indices of parasite distribution (such as median intensity) are suitable descriptors to quantify parasites in a sample of hosts. These measures have different biological interpretations and need different statistical methods to be compared between samples.

Animals↗
PubMed1996

Standard error and sample size determination for estimation of probabilities based on a test variable.

A method of sample size determination for estimation of probabilities based on a test variable is presented. Applications to estimation of sensitivity and specificity of medical tests are the focus of this research, although the methods can be applied to other areas of study such as engineering reliability. Examples are given for determining sample sizes required for the classification of patients with cutaneous lupus erythematosus based on the incidence of several markers. In this example, the test variable is the number of markers present. The methodology employs a weighted average of model-based and non-model-based estimates of the probability with the weights determined by the closeness to or the confidence in the given model. Formulas and charts required for determining sample size are provided for test variables that can be modeled by the binomial, Poisson, or normal distributions, i.e., for the most commonly encountered distributions for counting events (binomial and Poisson) and for measurements (normal). However, the methods given can be applied to any distribution, including multivariate. Especially when relatively small probabilities (the rare events) are being estimated, the techniques provided assistance in safeguarding against undersampling brought on by unwarranted confidence in a test variable distribution and against oversampling required for high accuracy in non-model-based probability estimators.

Epidemiologic Methods↗
PubMed2001

Saccadic choice with asynchronous targets: evidence for independent randomisation.

In the LATER model, randomness of saccadic latency arises through random variation in the rate of rise of the decision signal. But does it vary independently at different locations? If so, when pairs of targets are presented asynchronously, and the participant makes a saccade to the more salient one, the choice of target should be stochastic. Further, it should be possible to predict the probabilities at different asynchronies from the latency distributions for each target on its own. This study verifies the prediction in human subjects. In the real world, independent random variation of latency at different locations will give rise to randomness of choice of target.

Adult↗
PubMed1994

Seroepidemiologic survey of Borrelia burgdorferi exposure of dairy cattle in Wisconsin.

An ELISA, using purified flagellin of Borrelia burgdorferi as the solid-phase antigen, was used to measure antibody concentrations to B burgdorferi in dairy cattle in Wisconsin. Serum obtained from 5,060 cows in 160 randomly selected herds in the state were tested. Serum from an additional 2,600 cattle in Barron County, Wis, a county with a high annual incidence of B burgdorferi infections in human beings, was also tested. Only 7% of the cows that were tested, but 66% of the herds that were tested, were seropositive for B burgdorferi. Sixteen percent of the herds had a prevalence of > or = 15% seropositive cows, whereas 50% of the herds had a prevalence of 1 to 14% seropositive cows. Seropositive herds were concentrated in the west-central part of Wisconsin. An association existed between the geographic location of seropositive herds and counties in which B burgdorferi infection of human beings was acquired (P < 0.05) as well as the geographic location of seropositive herds and the geographic distribution of Ixodes scapularis (P < 0.05). Barron County, in which B burgdorferi infection is endemic, had a significantly (P < 0.05) higher percentage of seropositive cows (17%) than did the state of Wisconsin (7%).

Analysis of Variance↗
PubMed2006

Limited-information goodness-of-fit testing of item response theory models for sparse 2 tables.

Bartholomew and Leung proposed a limited-information goodness-of-fit test statistic (Y) for models fitted to sparse 2(P ) contingency tables. The null distribution of Y was approximated using a chi-squared distribution by matching moments. The moments were derived under the assumption that the model parameters were known in advance and it was conjectured that the approximation would also be appropriate when the parameters were to be estimated. Using maximum likelihood estimation of the two-parameter logistic item response theory model, we show that the effect of parameter estimation on the distribution of Y is too large to be ignored. Consequently, we derive the asymptotic moments of Y for maximum likelihood estimation. We show using a simulation study that when the null distribution of Y is approximated using moments that take into account the effect of estimation, Y becomes a very useful statistic to assess the overall goodness of fit of models fitted to sparse 2(P) tables.

Binomial Distribution↗
PubMed2003

Population-level right-paw preference in rats assessed by a new computerized food-reaching test.

We re-studied the distribution of paw preference in rats using a new computerized food-reaching test, which recorded the times and time intervals between the single right- and left-paw entries. Using the traditional food-reaching test, we found that of 144 rats, 72.7% were right-handed, 19.7% left-handed, and 7.6% mixed-handed. This population-level J-shaped right-hand preference did not fit a binomial chance distribution (25:25:50). Of right -handers, 99.5% first used their right paw and 0.5% left paw; of left-handers, 98.6% first used their left paw and 1.4% right paw. Of mixed-handers, 59% first used the right paw and 41% left paw for food reaching. The time interval between putting the rat into the test cage and the first right-paw entry was significantly shorter than the first left-paw entry in total sample. Males were faster than females (shorter time intervals between right- or left-paw entries). The distribution of the time intervals between right- or left-paw entries was inverse J-shaped, which exhibited a normal distribution after taking the logarithms of the time intervals. There was no significant difference between time intervals for the left-paw entries; time intervals for the right-paw entries were significantly shorter in males than females, accentuating the role of the left brain for sex differences in motor control. The results suggested that humans are not unique in population-level right-hand preference; our new method would be suitable for new developments in handedness research.

Animals↗
PubMed2000

Molecular genetic maps in wild emmer wheat, Triticum dicoccoides: genome-wide coverage, massive negative interference, and putative quasi-linkage.

The main objectives of the study reported here were to construct a molecular map of wild emmer wheat, Triticum dicoccoides, to characterize the marker-related anatomy of the genome, and to evaluate segregation and recombination patterns upon crossing T. dicoccoides with its domesticated descendant Triticum durum (cultivar Langdon). The total map length exceeded 3000 cM and possibly covered the entire tetraploid genome (AABB). Clusters of molecular markers were observed on most of the 14 chromosomes. AFLP (amplified fragment length polymorphism) markers manifested a random distribution among homologous groups, but not among genomes and chromosomes. Genetic differentiation between T. dicoccoides and T. durum was attributed mainly to the B genome as revealed by AFLP markers. The segregation-distorted markers were mainly clustered on 4A, 5A, and 5B chromosomes. Homeoalleles, differentially conferring the vigor of gametes, might be responsible for the distortion on 5A and 5B chromosomes. Quasilinkage, deviation from free recombination between markers of nonhomologous chromosomes, was discovered. Massive negative interference was observed in most of the chromosomes (an excess of double crossovers in adjacent intervals relative to the expected rates on the assumption of no interference). The general pattern of distribution of islands of negative interference included near-centromeric location, spanning the centromere, and median/subterminal location. [An appendix describing the molecular marker loci is available as an online supplement at http://www.genome.org.]

Binomial Distribution↗
PubMed1996

High-resolution 29Si solid-state NMR study of silicon functionality distribution on the surface of silicas.

29Si solid-state NMR allows us to distinguish silicon atoms involved in siloxane bridges (Q4), single silanol (Q3) and geminal silanol groups (Q2) on the surface of silica. The relative proportions of each species can be obtained by Magic Angle Spinning (MAS) associated with 1H-->29Si crosspolarization (CP/MAS). This preliminary study deals with the silicon functionality of MCM-41, a purely siliceous, amorphous and mesoporous silica. From the 29Si spectra the relative proportions are estimated to be 3.7% Q2 27.3% Q3 and 69.0% Q4, while the ratio Q2/Q2 + Q3) is 0.12. These results are found to be in perfect agreement with a binomial probability distribution of sites.

Isotopes↗
PubMed1993

A quantitative framework for evaluating the effect of community treatment on the morbidity due to ascariasis.

There is growing emphasis on the use of community treatment to reduce the level of morbidity caused by helminth infection. The design of chemotherapy programmes, in terms of frequency of treatment and proportion of the community treated, would be assisted by a quantitative framework which enabled the morbidity reduction achieved by different approaches to be compared. The present study describes a model developed for this purpose which embodies two innovative features. First, a quantitative score of morbidity (the proportion of individuals harbouring an intense infection) is used to rate the success of a programme and, second, the distribution of helminths in the host population is generated by a mechanism that allows the distribution to change dynamically as a function of both treatment and reinfection. The model behaviour, using values typical of Ascaris lumbricoides, indicates that the benefit derived from community chemotherapy increases non-linearly with the coverage and efficacy of treatment.

Animals↗
PubMed2001

Stochastic radial basis functions.

Stochastic signal processing can implement gaussian activation functions for radial basis function networks, using stochastic counters. The statistics of neural inputs which control the increment and decrement operations of the counter are governed by Bernoulli distributions. The transfer functions relating the input and output pulse probabilities can closely approximate gaussian activation functions which improve with the number of states in the counter. The means and variances of these gaussian approximations can be controlled by varying the output combinational logic function of the binary counter variables.

Binomial Distribution↗
PubMed2001

Nonoverlapping clusters: approximate distribution and application to molecular biology.

An approach is developed for the screening of genomic sequence data to identify gene regulatory regions. This approach is based on deciding if putative transcription factor binding sites are clustered together to a greater extent than one would expect by chance. Given n events occurring on an interval of width L (L base pairs), an r:w cluster is defined as r + 1 consecutive events all contained within a window of length wL. Accurate and easily computable approximations are derived for the distribution of the number of nonoverlapping r:w clusters under the model that the positions of the n events have a uniform distribution. Simulations demonstrate that these approximations have greater accuracy than existing methods. The approximation is applied to detect erythroid-specific regulatory regions in genomic DNA sequences, first in an artificial case where r is specified a priori and then as part of an exploratory approach.

Binding Sites↗
PubMed1989

Sampling stratospheric aerosols with impactors.

Derivation of statistically significant size distributions from impactor samples of rarefied stratospheric aerosols imposes difficult sampling constraints on collector design. It is shown that is is necessary to design impactors of different size for each range of aerosol size collected as as to obtain acceptable levels of uncertainty with a reasonable amount of data reduction.

Aerosols↗
PubMed1995

A 21 year retrospective study of reports of paresthesia following local anesthetic administration.

A retrospective study of paresthesia following the injection of local anesthetic in dentistry was conducted by examining every report of paresthesia recorded by Ontario's Professional Liability Program from 1973 to 1993, inclusive. Only those cases where surgery was not conducted were considered in this study. The parameters examined included patient age and gender, needle gauge, site of injection, area affected, report of pain or any additional symptoms, and the type of local anesthetic used. From 1973 to 1993, there were 143 reports of paresthesia not associated with surgery. There were no significant differences found with respect to patient age, patient gender, or needle gauge. All reports involved anesthesia of the mandibular arch, with the tongue most frequently reported to be symptomatic, followed by the lip. Pain was reported in 22 per cent of the cases. Paresthesia was reported most often following the injection of articaine and prilocaine. In 1993 alone, there were 14 reports of paresthesia not associated with surgery. This can be projected to an incidence of 1:785,000 injections. Articaine was administered in 10 of these cases or prilocaine in the other four. The observed frequencies of paresthesia following the administration of articaine (p < 0.002) or prilocaine (p < 0.025) were significantly greater than the expected frequencies for these agents, based on the distribution of local anesthetic use in Ontario in 1993. These results are consistent with the suggestion that local anesthetic formulations may have the potential for mild neurotoxicity. Further studies are needed to investigate the mechanisms for this, and to determine whether similar findings would be found elsewhere.

Adult↗