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PubMed1983

Cell elongation and division probability during the Escherichia coli growth cycle.

A new method is presented for determining the growth rate and the probability of cell division (separation) during the cell cycle, using size distributions of cell populations grown under steady-state conditions. The method utilizes the cell life-length distribution, i.e., the probability that a cell will have any specific size during its life history. This method was used to analyze cell length distributions of six cultures of Escherichia coli, for which doubling times varied from 19 to 125 min. The results for each culture are in good agreement with a single model of growth and division kinetics: exponential elongation of cells during growth phase of the cycle, and normal distributions of length at birth and at division. The average value of the coefficient of variation was 13.5% for all strains and growth rates. These results, based upon 5,955 observations, support and extend earlier proposals that growth and division patterns of E. coli are similar at all growth rates and, in addition, identify the general growth pattern of these cells to be exponential.

Cell Cycle↗

PubMed1984

Diagnostic probability matrix for identification of slowly growing mycobacteria in clinical laboratories.

A probability matrix is presented for identification of slowly growing mycobacteria that are likely to be encountered in clinical laboratories. The matrix includes 23 features that are useful for identifying members of 14 species or species complexes. The computer program identifies strains as a function of the ID (identification) score, which measures the discrimination among possible alternative identifications, and the R (ratio) score, which measures the degree of fit to the most likely taxa. It is not necessary to employ all 23 tests when initiating an identification; the program will suggest additional tests to perform when a partial data set fails to yield a definitive identification. Two independent sets of cultures comprising a total of 1,212 strains were used to test the matrix. Correct diagnoses were based on clustering behavior in numerical taxonomic analysis with larger numbers of features. The probable efficiencies with the two sets were 94.2 and 83.4%, respectively, and the accuracy of the definitive identifications for both sets exceeded 95%. A discussion is presented of situations when it may be appropriate to override an R score that has caused the rejection of an identification and to thereby enhance the efficiency.

Catalase↗

PubMed1990

How do parents of babies interpret qualitative expressions of probability?

One hundred mothers and 50 medical students and doctors were interviewed to examine their understanding of eight common probability expressions as they are used in statements of the kind that doctors regularly make to mothers of babies. Respondents were asked to translate each term into a number on a scale from 0 to 10. There was a wide range of interpretation of the expressions, and significant differences were found between the mothers and medical group for seven of the expressions. Most mothers expressed a preference for receiving information in numerical terms. We advise that verbal probability expressions should be restricted, and more information presented in numerical terms.

Communication↗

PubMed1986

Mortality probability in victims of fire trauma: revised equation to include inhalation injury.

There are no clear guidelines on the early diagnosis of injury due to inhalation of smoke. A clinical scoring system in the form of a previously prepared questionnaire may be used in the accident and emergency department by staff who are inexperienced in the management of inhalation injury. By quantifying injury due to smoke inhalation, its contribution to mortality in a large group of fire victims was established and a revised mortality probability equation derived using age, percentage surface area of the burn, and extent of inhalation injury. This mortality probability equation may be used to divide patients into risk categories for early intensive care management and allows the comparison of mortality data between accident and emergency units receiving varying numbers of patients with injuries due to burns and smoke inhalation.

Adolescent↗

PubMed1995

Probability of adverse events that have not yet occurred: a statistical reminder.

The probability of adverse and undesirable events during and after operations that have not yet occurred in a finite number of patients (n) can be estimated with Hanley's simple formula, which gives the upper limit of the 95% confidence interval of the probability of such an event: upper limit of 95% confidence interval = maximum risk = 3/n (for n > 30). Doctors and surgeons should keep this simple rule in mind when complication rates of zero are reported in the literature and when they have not (yet) experienced a disastrous complication in a procedure.

Confidence Intervals↗

PubMed1998

Probabilities associated with counting average motor unit firing rates in active human muscle.

Motor unit firing rates in human muscle can be determined from recordings made with small-diameter microelectrodes inserted directly into the muscle during voluntary contraction. Frequently, these counts are pooled to give an average motor unit firing rate under a given set of conditions. Since the fibers of one motor unit are dispersed among the cells of several others, it is conceivable that discharge rates can be measured in more than one cell from the same unit. If this occurred frequently, the distribution of firing rates could be influenced by those from units counted more than once. Based on literature values, we made the following assumptions: vastus lateralis contains approximately 300 motor units, with an average innervation ratio of 1500. Muscle cell diameter is about 50 to 100 microns and cells are randomly distributed over a motor unit territory of 10 microns diameter. The recording range of a microelectrode is about 600 microns. Given the distribution of cells normally found in whole human muscle, the probability of recording from two or more cells of the same motor unit at 50% MVC follows a Poisson distribution with a mean of 0.44. This model suggests that although there is a low probability of some duplication in this technique, the extent to which it influences the distribution of average motor unit firing rates is minimal over the entire range of forces produced by vastus lateralis.

Adult↗

PubMed1981

Probability models in the analysis of radiation-related complications: utility and limitations.

In order to predict radiation-related enteric damage, 92 women were studied who had received identical radiation doses for cancer of the ovary from 1970 through 1977. A logistic model was used to predict the probability of complication as a function of number of laparotomies, hypertension, and thin physique. The utility and limitations of such probability models are presented.

Body Composition↗

PubMed1986

Probability of causation tables and their possible implications for the practice of diagnostic radiology.

In compliance with requirements in the Orphan Drug Act (97-414) of 1983, tables were recently constructed by an ad hoc committee of the National Institutes of Health (NIH) in which the probabilities that certain specific cancers are caused by previous radiation exposure are estimated. The reports of the NIH committee and a National Academy of Science oversight committee may have broad implications for the future practice of diagnostic radiology. The basis on which the probability of causation tables were established and some of the possible implications for diagnostic radiology are discussed.

Dose-Response Relationship, Radiation↗

PubMed1987

Clinical outcomes of patients with suspected pulmonary embolism and low-probability aerosol-perfusion scintigrams.

The clinical outcomes of 183 patients with suspected pulmonary embolism (PE) and a "low probability of PE" interpretation of aerosol-perfusion scintigrams were reviewed. Based in part on the scintigraphic findings, 173 of the patients (94.5%) were not treated with anticoagulants. Over a mean follow-up period of 8.4 months, only one patient (who was from the untreated group) had clinical evidence of PE. These results suggest that a low-probability interpretation of the aerosol-perfusion scintigram is generally reliable and a suitable indicator for clinical decision making in patients suspected of having PE.

Aerosols↗

PubMed1996

Application of probability-generating functions in evaluation of some isotopomer distributions.

A method for calculating probability functions and moments of a distribution of isotopomers, constructed by Kelleher and Masterson (2), is described. The method involves the use of the so-called probability-generating functions, a mathematical device especially convenient for the purpose of calculation of probabilistic quantities in discrete models of the Kelleher-Masterson type.

Models, Biological↗

PubMed2002

Decoding neural spike trains: calculating the probability that a spike train and an external signal are related.

Experimental and clinical applications of extracellular recordings of spiking cell activity frequently are used to relate the activity of a cell to externally measurable signals such as surface potentials, sensory stimuli, or movement measurements. When the external signal is time-varying, correlation methods have traditionally been used to quantify the degree of relation with the neural firing. However, in some circumstances correlation methods can give misleading results. A new algorithm is described that estimates the extent to which a spike train is related to a continuous time-varying signal. The technique calculates the probability of generating a spike train with Poisson statistics if the time-varying signal determines the Poisson rate. This is accomplished by successive division of the signal and the spike train into halves and recursive calculation of the probability of each half-signal. The performance of the new algorithm is compared with the performance of correlation methods on simulated data.

Action Potentials↗

PubMedDate not supplied

Estimation of transmission probabilities in families ascertained through a proband with variable age-at-onset disease: application to the HLA A, B and DR loci in Finnish families with type 1 diabetes. The DiMe Study Group.

An open problem of some interest in the study of HLA has been the possible existence of transmission distortion in the human HLA complex. In this paper, transmission probabilities are estimated and tested using data on HLA A, B and DR loci genotypes of parents and offspring ascertained from the entire population of Finland (Childhood Diabetes in Finland Study) through one or more offspring diagnosed with insulin-dependent diabetes mellitus (IDDM) during the recruitment period from September 1986 to July 1989. First, we show how to get unbiased estimates of transmission probabilities from the family data collected in the disease registry of incident cases. This is accomplished by assuming that transmission of HLA genes to children in the general population is conditionally independent given the parents' genotypes, and the birth dates of all offspring. Based on the sampling (ascertainment) process in the study on Childhood Diabetes in Finland, younger siblings of the index child (the oldest proband) are independent of the ascertainment and therefore give rise to unbiased inference regarding allele transmission. The hypothesis of Mendelian transmission of alleles at each locus was tested using the standard chi(2) test. Goodness-of-fit of the Mendelian inheritance model to the individual locus data is calculated by maximizing the likelihood function over allele transmission intensities at each locus. The existence of a strong transmission distortion is not supported by this study at the loci considered.

Adolescent↗

PubMed2004

A new method for computing the multipoint posterior probability of linkage.

The posterior probability of linkage (PPL) is a Bayesian statistic which directly measures the probability of linkage between a trait locus and a marker (in the 2-point case) or a genomic region (in the multipoint case). It has several benefits, including ease of interpretation, the ability to incorporate prior genomic information, and a mathematically rigorous and robust procedure for accumulating linkage information across multiple heterogeneous datasets. To date, the majority of work on the PPL has focused on the development of the 2-point statistic, with only preliminary attempts at the development of an equivalent multipoint version. In this paper we present a new way of computing of the multipoint PPL. This new version imputes to each genomic point an estimate of the 2-point PPL we would have obtained from a fully informative marker giving similar evidence for linkage. This version, which we call the imputed PPL, is shown to be superior to previously developed versions.

Bayes Theorem↗

PubMed2005

The posterior probability of linkage allowing for linkage disequilibrium and a new estimate of disequilibrium between a trait and a marker.

The posterior probability of linkage (PPL) statistic has been developed as a method for the rigorous accumulation of evidence for or against linkage allowing for both intra- and inter-sample heterogeneity. To date, the method has assumed linkage equilibrium between alleles at the trait locus and the marker locus. We now generalize the PPL to allow for linkage disequilibrium (LD), by incorporating variable phase probabilities into the underlying linkage likelihood. This enables us to recover the marginal posterior density of the recombination fraction, integrating out nuisance parameters of the trait model, including the locus heterogeneity (admixture) parameter, as well as a vector of LD parameters. The marginal posterior density can then be updated across data subsets or new data as they become available, while allowing parameters of the trait model to vary between data sets. The method applies immediately to general pedigree structures and to markers with multiple alleles. In the case of SNPs, the likelihood is parameterized in terms of the standard single LD parameter D'; and it therefore affords a mechanism for estimation of D' between the marker and the trait, again, without fixing the parameters of the trait model and allowing for updating across data sets. It is even possible to allow for a different associated allele in different populations, while accumulating information regarding the strength of LD. While a computationally efficient implementation for multi-allelic markers is still in progress, we have implemented a version of this new LD-PPL for SNPs and evaluated its performance in nuclear families. Our simulations show that LD-PPLs tend to be larger than PPLs (stronger evidence in favor of linkage/LD) with increased LD level, under a variety of generating models; while in the absence of linkage and LD, LD-PPLs tend to be smaller than PPLs (stronger evidence against linkage). The estimate of D' also behaves well even in relatively small, heterogeneous samples.

Genes, Dominant↗

PubMed2006

A posterior probability of linkage-based re-analysis of schizophrenia data yields evidence of linkage to chromosomes 1 and 17.

OBJECTIVE: Linkage analysis using 22 Canadian pedigrees identified a promising schizophrenia candidate region on 1q23 with a maximum 2-point HLOD under a recessive model of 5.8 [Brzustowicz et al. 2000]. In the current study, we revisited this data set using a Bayesian linkage analysis technique, namely the posterior probability of linkage (PPL). METHODS: The PPL has been developed as an alternative to traditional linkage analysis. It differs from both LOD scores and 'non-parametric' methods in that it directly measures the probability of linkage given the data, and incorporates prior genomic information. RESULTS: As expected, PPL results for 1q23 supported the previously observed linkage, with an estimated multipoint PPL of 99.7%. However, the PPL supported two further results: a second peak on chromosome 1 at 1p13 with a multipoint with PPL of 70% and a chromosome 17 marker (D17S784 at 17q25) with a multipoint PPL of 44%. CONCLUSIONS: The PPL-based analysis presented has the advantage over other likelihood-based linkage methods in that it avoids maximization and produces a less complex view of the strength of evidence for linkage.

Chromosomes, Human, Pair 1↗

PubMed1980

Probability calculations in pedigrees under complex modes of inheritance.

It is shown that the method of Heuch and Li for recursive calculation of conditional genotype probabilities in pedigrees also applies to joint phenotype probability calculations. This procedure was applied to complex modes of inheritance, with possible applications to both genetic analysis and genetic counseling.

Genetic Counseling↗

PubMed1981

A general transmission probability model for pedigree data.

The three basic transmission probabilities of the two-allele autosomal genetic model proposed by Elston and Stewart in 1971 are made dependent on sex. It is shown that this more general model, comprising twelve transmission probabilities, subsumes the most important simple modes of genetically or environmentally determined transmission that may be responsible for the familial aggregation of traits. Although this does not necessarily solve the problem of testing alternative hypotheses, it provides a holistic parametrization of familial transmission.

Alleles↗

PubMed1995

Comparison of upper limit of vulnerability and defibrillation probability of success curves using a nonthoracotomy lead system.

BACKGROUND: An upper limit to the strength of shocks that induce fibrillation during the vulnerable period, the upper limit of vulnerability (ULV), has been shown to exist in both humans and animals. The purpose of this study was to compare ULV and defibrillation (DF) probability of success curves for a clinically useful nonthoracotomy lead system. METHODS AND RESULTS: Sixteen pentobarbital-anesthetized pigs were studied. Single-capacitor biphasic waveforms with both phases 5.5 ms in duration were used for ULV and DF testing. A right ventricular catheter electrode served as first-phase cathode and a superior vena cava catheter electrode coupled with a cutaneous R2 patch electrode served as common first-phase anodes. A pacing catheter was placed in the right ventricle to deliver a train of 15 S1 stimuli at a pacing interval of 250 to 300 ms. A ULV shock was delivered on the peak of the T wave as measured from the surface ECG; if ventricular fibrillation was induced, a DF shock was delivered after 10 seconds of fibrillation. Shock voltages were determined by an up-down protocol. Ventricular fibrillation was induced an average of 53 times in each animal. The composite data indicate that below V97, that is, the voltage that leaves the animal in normal sinus rhythm 97% of the time when delivered on the peak of the T wave or the voltage that defibrillates 97% of the time, ULV is lower than DF. ULV and DF became significantly correlated at V80 and maximally correlated at V97. Even at V97, however, ULV and DF differed by more than 100 V in 2 of the 16 animals. CONCLUSIONS: ULV approximately equaled DF at V97. This is fortunate because it is clinically important to set the device voltage at the uppermost portion of the probability of success curve. Estimating DF V97 from ULV V97 would reduce the number of fibrillation inductions needed to establish defibrillation shock strength requirements. However, the large difference between ULV V97 and DF in a few animals indicates that further improvement and testing of algorithms for determining ULV V97 must be developed before the technique is used clinically.

Animals↗