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PubMed1979

Predictive probability early termination plans for phase II clinical trials.

A phase II clinical trial is designed to gather data to help decide whether an experimental treatment has sufficient effectiveness to justify further study. In a one-arm trial with dichotomous outcome, we wish to test a simple null hypothesis on the Bernoulli parameter against a one-sided alternative in a sample of N patients. It is advisable to have a rule to terminate the trial early when evidence accumulates that the treatment is ineffective. Predictive probabilities based on the binomial distribution and beta and uniform prior distributions for the binomial parameter are found to be useful as the basis of group sequential designs. Size, power and average sample size for these designs are discussed. A process for the specification of an early termination plan, advice on the quantification of prior beliefs, and illustrative examples are included.

Antineoplastic Agents↗

PubMedDate not supplied

[The determination of the upper limits of year-round morbidity].

The use of K. Pearson's criterion has made it possible to establish that the empirical rows presenting the annual data on dysentery morbidity for each month during the period of many years correspond to binomial distribution. For this reason, the calculation of the highest limit of annual morbidity for many years should be made with the use of the formulae of great radices of quadratic inequation [formula: see text] used in mathematical statistics for the determination of the highest limits in binomial distribution. For the number of observations (n) not the number of inhabitants (which contradicts to the notion of observation in the theory of probability), but the number of minimal values of monthly morbidity, used for the calculation of the minimal average morbidity value omega or theta*, should be taken. To obtain objective results, the minimal average value omega or theta* and the ratio t2/2n must be of the same order, where t is the critical value of Student's criterion equal to 1.96.

Bacterial Infections↗

PubMed1997

The latent class model for multiple binary screening tests.

Given multiple binary tests, such as repeated application of a blind screening test to each individual in a sample, we attempt to estimate the prevalence, sensitivity and specificity of the test without knowing the true disease status of those tested (gold standard). This problem is equivalent to finding the mixing distribution of a mixture of binomial distributions. We suggest a new method to determine the number of latent classes. Our simulations show that the coverage probabilities of the bootstrap confidence intervals of our estimates are correct. Our methods are illustrated by examples from published medical research.

Algorithms↗

PubMed1998

The subclass approach for mutational spectrum analysis: application of the SEM algorithm.

Analysis and comparison of mutational spectra represents an important problem in molecular biology. To analyse a mutational spectra we apply an algorithm based on the SEM subclass approach (Simulation, Expectation, Maximization). The algorithm tries to classify the mutational sites according to different mutation probabilities, and each site should belong to one class. Each class is approximated by binomial distribution and thus any real mutational spectrum is regarded as a mixture of binomial distributions. The separation process runs iteratively. Each iteration includes the simulation, maximization and estimation procedures. To evaluate the quality of the classification results, the X2 test is used. The algorithm has been checked on random spectra with preset parameters and on real mutational spectra. As has been shown, 17 out of 19 analysed real mutational spectra can be divided into two or more classes of sites, of which one contains hotspots of mutation. For the G:C-->A:T mutational spectra induced by Sn1 alkylating mutagenes (11 spectra) the classification accuracy was 0.95. To test different site volumes, each Sn1-induced spectrum was divided into the G-->A and C-->T spectra. The classification accuracy for these spectra was 0.96. From the analysis of classification errors it is possible to suggest that at least part of them cannot be ascribed to the faults of the algorithm but are caused by some special features of the mutagenesis itself. The results of the real data are in good relation with existing knowledge. The approach we present is an attempt to formalize the concept of a "mutational hotspot". The program implementing the SEM algorithm is available on the Web server (http:/(/)www.itba.mi.cnr.it/webmutation).

Algorithms↗

PubMed1976

On the regularities of distribution of Hypoderma bovis De Geer larvae parasitizing cattle herds in different parts of the range of this warble fly.

The type and parameters of the distribution of the second and third instar larvae of Hypoderma bovis in cattle herds in Czechoslovakia (54 herds, 7233 head), Mongolia (20 herds, 1809 head) and the USSR (48 herds, 4978 head) were studied. A statistical analysis showed a) that in the majority of cases negative binomial distribution serves as a model of the distribution of larvae with sufficient reliability; b) that the regularity of dependence of the distribution exponent k of the negative binomial distribution on the incidence of infestation remains constant in different parts of the range of this warble fly. The latter fact indicates that the regulatory systems limiting the population numbers of this warble fly are associated with host-parasite relationships and do not depend on a complex of conditions specific for various natural zones. In order to understand the regulatory processes in parasite populations it is necessary to study equally the regulatory mechanisms operating primarily on the level of specimens as well as the regulatory systems operating on the level of populations.

Animals↗

PubMed1976

On the regularities of distribution of Hypoderma bovis De Geer larvae parasitizine cattle herds in different parts of the range of this warble fly.

The type and parameters of the distribution of the second and third instar larvae of Hypoderma bovis in cattle herds in Czechoslovakia (54 herds, 7233 head), Mongolia (20 herds, 1809 head) and the USSR (48 herds, 4978 head) were studied. A statistical analysis showed a) that in the majority of cases negative binomial distribution serves as a model of the distribution of larvae with sufficient reliability; b) that the regularity of dependence of the distribution exponent k of the negative binomial distribution on the incidence of infestation remains constant in different parts of the range of thes warble fly. The latter fact indicates that the regulatory systems limiting the population numbers of this warble fly are associated with host-parasite relationships and do not depend on a complex of conditions specific for various natural zones. In order to understand the regulatory processes in parasite populations it is necessary to study equally the regulatory mechanisms operating primarily on the level of specimens as well as the regulatory systems operating on the level of populations.

Animals↗

PubMed1988

Doxapram dosage regimen in apnea of prematurity based on pharmacokinetic data.

To 18 premature apneic patients refractory to theophylline, doxapram (0.5-2.5 mg/kg/h) was administered in combination with therapeutic doses of theophylline. Doxapram concentrations in serum were measured 48 h after commencement of the infusion and then in 2-hour intervals during a 6-8 h withdrawal. Total body clearance (dose/Css) of the drug ranged from 0.20 to 0.56 liter/h in 13 patients and 1.14 to 1.75 liter/h in 4 patients suggesting a binomial distribution in the disposition kinetics of the drug. Other pharmacokinetic indices, although variable, did not exhibit binomial distribution. The mean volume of distribution and half-life of doxapram were 7.33 +/- 4.55 liter/kg and 8.17 +/- 4.13 h, respectively. Based on our calculations to accelerate the attainment of a steady-state plasma concentration (Css) of approximately 1.5 mg/l, a loading dose of 5.5 mg/kg and a maintenance dose of 1 mg/kg/h along with serum concentration monitoring are recommended.

Apnea↗

PubMed1986

Estimation and analysis of the concentration-response surfaces associated with multiple-agent combinations.

Chinese hamster cells (V79) were treated with ethylnitrosourea (ENU) and cis-diamminedichloroplatinum(II) (DDP) alone and in combination. Sister chromatid exchanges (SCEs) were quantified as measures of genotoxicity of the two agents. The combination experiment employed a factorial design in which cells were treated, in various concentration combinations, with both agents simultaneously. Response surface methodology, using a polynomial model based on a negative binomial distribution of SCE events, was employed for analysis of the interactions of the two genotoxic agents. The negative binomial distribution, a generalization of the Poisson distribution, is required since SCEs are discrete variables which, under the conditions of these experiments, have a distribution which exhibits extra-Poisson variability. The model of the ENU/DDP combinations indicated an increasingly less-than-additive effect resulting from increasing concentrations of each agent in the combination. The analysis of these experiments demonstrates the usefulness of a powerful statistical procedure for evaluating the biological effects resulting from exposure to multiple cytotoxic agents. The methodology can be used with many other types of endpoints and is not limited by the number of treatment agents.

Cells, Cultured↗

PubMed1976

The distribution of fetal death in control mice and its implications on statistical tests for dominant lethal effects.

In dominant lethal testing fetal death is generally assumed to follow either a Poisson or binomial distribution. However, both of these models were found to be inappropriate when three large sets of mouse control data and other data sets from the literature were examined. The validity of statistical test procedures based on these inappropriate models was then studied in detail. It was found that chi-square tests (which assume an underlying binomial distribution) may seriously exaggerate the level of significance and hence should not be used. In contrast, the inappropriateness of the underlying Poisson or binomial model appeared to have little effect on the validity of pairwise comparisons by analysis of variance procedures. Unlike chi-square, these procedures regard the pregnant female rather than the individual implant as the experimental unit. However, a statistical analysis of dominant lethal data generally involves more than a series of pairwise comparisons, and it is unclear how an invalid underlying model may affect statistical test procedures in this more complex situation. Moreover, it is difficult to justify the use of statistical models that are demonstrably invalid when a reasonable alternative exists. Thus, until a satisfactory parametric model can be found and appropriate test procedures derived, we prefer to analyze dominant lethal data by non-parametric (distribution-free) methods. Proportion of dead implants per female appears to be a more meaningful measure of fetal death than number of dead implants per female for several seasons which include (1) analyses based on proportions take the total number of implants per female into account and (2) analyses based on proportions make more reasonable assumptions concerning pre-implantation losses and are more powerful when such losses occur. Despite our concern with the appropriateness of the underlying model, in practice we have found few instances in which non-parametric and analysis of variance procedures have led to markedly different conclusions.

Animals↗

PubMedDate not supplied

[Radiation damages in human lymphocytes studied by micronucleus and chromosomal analysis].

It was shown that the dependence of the micronucleus number and chromosome aberration on irradiation dose is linear quadratic, the values of linear coefficient being different. The distribution of ameliorators and children from the areas with higher irradiation level by micronucleus test conforms to Poisson distribution, while the distribution by chromosomal analysis approaches to binomial distribution.

Adult↗

PubMed1996

Description of interacting channel gating using a stochastic Markovian model.

Single-channel recordings from membrane patches frequently exhibit multiple conductance levels. In some preparations, the steady-state probabilities of observing these levels do not follow a binomial distribution. This behavior has been reported in sodium channels, potassium channels, acetylcholine receptor channels and gap junction channels. A non-binomial distribution suggests interaction of the channels or the presence of channels or the presence of channels with different open probabilities. However, the current trace sometimes exhibits single transitions spanning several levels. Since the probability of simultaneous transitions of independent channels is infinitesimally small, such observations strongly suggest a cooperative gating behavior. We present a Markov model to describe the cooperative gating of channels using only the all-points current amplitude histograms for the probability of observing the various conductance levels. We investigate the steady-state (or equilibrium) properties of a system of N channels and provide a scheme to express all the probabilities in terms of just two parameters. The main feature of our model is that lateral interaction of channels gives rise to cooperative gating. Another useful feature is the introduction of the language of graph theory which can potentially provide a different avenue to study ion channel kinetics. We write down explicit expressions for systems of two, three and four channels and provide a procedure to describe the system of N channels.

Animals↗

PubMed1981

Quantitative analysis of intercellular adhesive specificity in freshly explanted and cultured cells.

A new method is presented for the quantitative analysis of intercellular adhesive specificity. In this assay, two cell types are mixed, one unlabeled and the other labeled with the fluorescent dye, fluorescamine [4-phenylspiro(feran-2[3H],1'-phthalan)-3,3'-dione]. The resulting aggregates are analyzed by fluorescence microscopy to determine the number of labeled and unlabeled cells per aggregate. Random (nonspecific) aggregation was characterized by a binomial distribution, and adhesive specificity was accordingly quantified by the deviation (as determined by a chi-square test) from the calculated binomial distribution. The labeling procedure was simple and rapid, and experiments with 18 different cell types showed that it did not affect cell viability, morphology, rate and extent of adhesion, plating efficiency, and the capability of myogenic cells to undergo terminal differentiation. Most important, assays with morphologically identifiable cell pairs indicated that the fluorescent label neither induced apparent nor destroyed existing adhesive specificity. The most pronounced adhesive specificities were observed with freshly explanted cells from adult tissues and also with mixtures of simian virus 40-transformed and nontransformed BALB/c 3T3 cells. A glucosamine-6-phosphate N-acetylase-deficient mutant 3T3 line (AD6), however, aggregated randomly with parental 3T3 cells. Lectin-resistant mutant Chinese hamster ovary (CHO) cells displayed marginal adhesive specificity when mixed with normal CHO cells.

Adipose Tissue↗

PubMed1983

Non-random chromosome loss in PHA-stimulated lymphocytes from normal individuals.

31773 lymphocyte metaphase cells from 280 karyotypically normal men aged 18-46 were examined for chromosome gain or loss. Chromosome loss was much more common than chromosome gain. Frequency of chromosome loss did not conform to a binomial distribution. There is a striking non-linear, inverse relationship between likelihood of loss and chromosome length. Chromosome gain shows a near binomial distribution between cells and no clear relationship to chromosome length. These facts indicate that the hypodiploid cells mostly arose as technical artefacts during slide preparation but that hyperdiploid cells were mainly due to non-disjunctional gain.

Adolescent↗

PubMed1988

The statistical analysis of graft patency data in a clinical trial of antiplatelet agents following coronary artery bypass grafting.

Because most coronary artery bypass patients receive more than one graft at surgery, it is most important to determine whether statistical analysis of graft patency should be performed on the premise that the multiple grafts within patients are dependent or independent experimental units. Veterans Administration Cooperative Study No. 207 was a multicenter clinical trial comparing four different antiplatelet regimens to placebo in the prevention of graft occlusion following coronary artery bypass grafting. Using the results from the 1-week postoperative angiograms from the Veterans Administration Cooperative Study No. 207, in which there were 3.2 distal anastomoses per patient, we have tested the hypothesis that grafts within patients tend to act dependently with respect to patency or occlusion by comparing the graft patency data to a binomial distribution (i.e., that distribution that would have been manifest if grafts were independent). Because the graft patency results in Study No. 207 significantly deviated from the binomial distribution (p = 0.0003), a more appropriate analysis for graft patency data was applied using a ratio estimate as applied to cluster sampling. The statistical methods used in 11 previous clinical trials of antithrombotic therapy after coronary artery bypass grafting were examined. Only one of the previous studies used such an analysis, and three additional reports attempted to correct for dependency of grafts within patients in their analyses using other statistical methods. In seven of the studies the investigators did not address the potential problem of a dependent relationship between multiple grafts within patients. We conclude that grafts within patients act as dependent experimental units and that the ratio estimate as applied to cluster sampling may be appropriately applied to these data.

Clinical Trials as Topic↗

PubMed1979

[Falsely positive values in multi-channel analysis: An iniquiry into reference and patient groups (author's transl)].

The number of falsely positive values occurring in 12-channel analysis was determined in two groups of patients and reference individuals. It revealed that the portion of falsely positive values actually found was statistically significant beyond that calculated on the assumption of a binomial distribution. Partly distinct correlations of the parameters combined to a profile as well as clear deviations from the normal distribution have to be taken into consideration as reasons for this discrepancy between theory and reality. The results show that the application of the binomial distribution leads to statements which significantly differ from the conditions actually present.

Autoanalysis↗

PubMed1993

A reappraisal of the use of multiple choice questions.

The terms Multiple True/False and Best Answer deserve wider applicability than at present when discussing multiple choice questions (MCQs). They describe the truthfulness of the choices and distinguish between the question types. The choice which matches the key in a MCQ is best called the correct answer. Multiple True/False questions contain either true (accepted) or false (unaccepted) ideas in the correct answers while in the Best Answer type, all choices are true. Using a complex recording procedure to indicate the selections already made, as in the K-type MCQ, does not assess any additional abilities. Candidates answering Multiple True/False MCQs should be asked to respond to each choice as either true or false. This helps to discriminate between those who can detect the falsity of a false choice from those who cannot. When dealing with guessing, examiners need to be cognizant of issues such as blind guessing and informed guessing, proclivity for risk-taking, extension of the marking range and probabilities according to the binomial distribution.

Binomial Distribution↗

PubMed1997

[Confidence of 100 per cent sensitivity and specificity].

A new strategy and four new methods are presented to calculate the limits of the confident interval for an estimate of a proportion equal to 1.0 or 0.0. A current formula which includes 1/(2n) for continuity correction leads to a confident interval which does not include the parameter estimate. Thus, it is proposed: 1) The exclusion of the factor 1/(2n) in that formula leads to correct most of its inconsistencies. The new strategy assumes that the upper limit of a confident interval when the estimates is 100%. The lower limit is calculated by assuming that there is a proportion in the population, from where the sample was taken, such as the probability of getting 100% in the sample is equal to the probability of falling into type I error of current statistics (0.05, 0.01, etc). Three methods are proposed with this strategy. 2) A combinatorial solution based in the knowledge of the number of individuals at whom the test can be applied. 3) A solution based on the binomial distribution. 4) A solution based on the Poisson distribution.

Binomial Distribution↗

PubMed1993

Substitution rate variation among sites in hypervariable region 1 of human mitochondrial DNA.

More than an order of magnitude difference in substitution rate exists among sites within hypervariable region 1 of the control region of human mitochondrial DNA. A two-rate Poisson mixture and a negative binomial distribution are used to describe the distribution of the inferred number of changes per nucleotide site in this region. When three data sets are pooled, however, the two-rate model cannot explain the data. The negative binomial distribution always fits, suggesting that substitution rates are approximately gamma distributed among sites. Simulations presented here provide support for the use of a biased, yet commonly employed, method of examining rate variation. The use of parsimony in the method to infer the number of changes at each site introduces systematic errors into the analysis. These errors preclude an unbiased quantification of variation in substitution rate but make the method conservative overall. The method can be used to distinguish sites with highly elevated rates, and 29 such sites are identified in hypervariable region 1. Variation does not appear to be clustered within this region. Simulations show that biases in rates of substitution among nucleotides and non-uniform base composition can mimic the effects of variation in rate among sites. However, these factors contribute little to the levels of rate variation observed in hypervariable region 1.

Biological Evolution↗