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PubMed2000

Tumour control probability: a formulation applicable to any temporal protocol of dose delivery.

An analytic expression for the tumour control probability (TCP), valid for any temporal distribution of dose, is discussed. The TCP model, derived using the theory of birth-and-death stochastic processes, generalizes several results previously obtained. The TCP equation is [equation: see text] where S(t) is the survival probability at time t of the n clonogenic tumour cells initially present (at t = 0), and b and d are, respectively, the birth and death rates of these cells. Equivalently, b = 0.693/Tpot and d/b is the cell loss factor of the tumour. In this expression t refers to any time during or after the treatment; typically, one would take for t the end of the treatment period or the expected remaining life span of the patient. This model, which provides a comprehensive framework for predicting TCP, can be used predictively, or--when clinical data are available for one particular treatment modality (e.g. fractionated radiotherapy)--to obtain TCP-equivalent regimens for other modalities (e.g. low dose-rate treatments).

Brachytherapy↗

PubMed2004

Prostate implant evaluation using tumour control probability--the effect of input parameters.

In this paper, we examine the effect of treatment parameters in a model used to evaluate permanent prostate implants. The model considers the prostate to be composed of 12 sub-sections, each sub-section is assigned a cell density based on the probability of finding cancer foci in that sub-section. Wasted dose as a result of the dose rate from the implant falling below a level adequate to counteract repopulation was found to vary by 2-16% over the range of radiosensitivity and repopulation rates considered. Within the model, applied to five dose distributions, the uncertainty in the tumour control probability (TCP) values calculated for each sub-section as a result of differences in the model parameters, was found to be less than 12% in most cases for the good quality implants. The difference in TCP values was much larger for the poor quality implant. Substituting a heterogeneous distribution of alpha for a single mean value resulted in generally lower TCP values though introducing a cutoff value with a Gaussian distribution had a profound effect on the calculated values. Despite uncertainties in the parameters, the model was able to identify sub-sections at risk of local recurrence but as a result of these uncertainties, the TCP values can only be considered in the relative rather than absolute sense.

Brachytherapy↗

PubMed2004

Inclusion of organ movements in IMRT treatment planning via inverse planning based on probability distributions.

In this paper, we investigate an off-line strategy to incorporate inter-fraction organ motion in IMRT treatment planning. It was suggested that inverse planning could be based on a probability distribution of patient geometries instead of a single snap shot. However, this concept is connected to two intrinsic problems: first, this probability distribution has to be estimated from only a few images; and second, the distribution is only sparsely sampled over the treatment course due to a finite number of fractions. In the current work, we develop new concepts of inverse planning which account for these two problems.

Humans↗

PubMed2003

A transition probability model for amino acid substitutions from blocks.

Substitution matrices have been useful for sequence alignment and protein sequence comparisons. The BLOSUM series of matrices, which had been derived from a database of alignments of protein blocks, improved the accuracy of alignments previously obtained from the PAM-type matrices estimated from only closely related sequences. Although BLOSUM matrices are scoring matrices now widely used for protein sequence alignments, they do not describe an evolutionary model. BLOSUM matrices do not permit the estimation of the actual number of amino acid substitutions between sequences by correcting for multiple hits. The method presented here uses the Blocks database of protein alignments, along with the additivity of evolutionary distances, to approximate the amino acid substitution probabilities as a function of actual evolutionary distance. The PMB (Probability Matrix from Blocks) defines a new evolutionary model for protein evolution that can be used for evolutionary analyses of protein sequences. Our model is directly derived from, and thus compatible with, the BLOSUM matrices. The model has the additional advantage of being easily implemented.

Amino Acid Substitution↗

PubMed1995

Method for calculation of probability of matching a bounded regular expression in a random data string.

A method is presented for determining within strict bounds the probability of matching a regular expression with a match start point in a given section of a random data string. The method in general requires time and space exponential in the number of optional characters in the regular expression, but in practice was used to determine bounds for probabilities of matching all the ProSite patterns without difficulty.

Algorithms↗

PubMed2006

Probalign: multiple sequence alignment using partition function posterior probabilities.

MOTIVATION: The maximum expected accuracy optimization criterion for multiple sequence alignment uses pairwise posterior probabilities of residues to align sequences. The partition function methodology is one way of estimating these probabilities. Here, we combine these two ideas for the first time to construct maximal expected accuracy sequence alignments. RESULTS: We bridge the two techniques within the program Probalign. Our results indicate that Probalign alignments are generally more accurate than other leading multiple sequence alignment methods (i.e. Probcons, MAFFT and MUSCLE) on the BAliBASE 3.0 protein alignment benchmark. Similarly, Probalign also outperforms these methods on the HOMSTRAD and OXBENCH benchmarks. Probalign ranks statistically highest (P-value < 0.005) on all three benchmarks. Deeper scrutiny of the technique indicates that the improvements are largest on datasets containing N/C-terminal extensions and on datasets containing long and heterogeneous length proteins. These points are demonstrated on both real and simulated data. Finally, our method also produces accurate alignments on long and heterogeneous length datasets containing protein repeats. Here, alignment accuracy scores are at least 10% and 15% higher than the other three methods when standard deviation of length is >300 and 400, respectively. AVAILABILITY: Open source code implementing Probalign as well as for producing the simulated data, and all real and simulated data are freely available from http://www.cs.njit.edu/usman/probalign

Algorithms↗

PubMed1999

Quantifying variability in the planum temporale: a probability map.

The acquisition of definitive evidence for systematic hemispheric asymmetries in the size of the planum temporale (PT) has been restricted by difficulties in identifying, standardizing and measuring the region of interest. In this paper an operational definition for identifying the problematic posterior border of the PT on magnetic resonance imaging (MRI) scans is proposed. An interactive voxel-painting program was used to identify and label the PT simultaneously in horizontal, sagittal and coronal planes in MRI scans, transformed into the standardized Talairach-Tournoux stereo-taxic space, from 50 normal right-handed volunteers. Both grey matter volume and cortical surface area of the PT were measured, while controlling for individual variation in overall brain shape and volume. The labeled tissue was averaged together to produce a probability map in standardized space of the region of interest. The PT region is highly variable, with no single voxel being labeled with a probability of >65%. In this study there were no significant hemispheric differences in volume or area of the PT. An asymmetry in area and volume was introduced by using an alternative method - the 'knife-cut' method - for identifying the posterior border. Implications for functional neuroimaging of the PT are discussed.

Adult↗

PubMed1989

Gene genealogy in three related populations: consistency probability between gene and population trees.

A genealogical relationship among genes at a locus (gene tree) sampled from three related populations was examined with special reference to population relatedness (population tree). A phylogenetically informative event in a gene tree constructed from nucleotide differences consists of interspecific coalescences of genes in each of which two genes sampled from different populations are descended from a common ancestor. The consistency probability between gene and population trees in which they are topologically identical was formulated in terms of interspecific coalescences. It was found that the consistency probability thus derived substantially increases as the sample size of genes increases, unless the divergence time of populations is very long compared to population sizes. Hence, there are cases where large samples at a locus are very useful in inferring a population tree.

Diploidy↗

PubMed1993

Estimation of genotype distributions and posterior genotype probabilities for beta-mannosidosis in Salers cattle.

beta-Mannosidosis is a lethal lysosomal storage disease inherited as an autosomal recessive in man, cattle and goats. Laboratory assay data of plasma beta-mannosidase activity represent a mixture of homozygous normal and carrier genotype distributions in a proportion determined by genotype frequency. A maximum likelihood approach employing data transformations for each genotype distribution and assuming a diallelic model of inheritance is described. Estimates of the transformation and genotype distribution parameters, gene frequency, genotype fitness and carrier probability were obtained simultaneously from a sample of 2,812 observations on U.S. purebred Salers cattle with enzyme activity, age, gender, month of pregnancy, month of testing, and parents identified. Transformations to normality were not required, estimated gene and carrier genotype frequencies of 0.074 and 0.148 were high, and the estimated relative fitness of heterozygotes was 1.36. The apparent overdominance in fitness may be due to a nonrandom sampling of progeny genotypes within families. The mean of plasma enzyme activity was higher for males than females, higher in winter months, lower in summer months and decreased with increased age. Estimates of carrier probabilities indicate that the test is most effective when animals are sampled as calves, although effectiveness of the plasma assay was less for males than females. Test effectiveness was enhanced through averaging repeated assays of enzyme activity on each animal. Our approach contributes to medical diagnostics in several ways. Rather than assume underlying normality for the distributions comprising the mixture, we estimate transformations to normality for each genotype distribution simultaneously with all other model parameters. This process also excludes potential biases due to data preadjustment for systematic effects. We also provide a method for partitioning phenotypic variation within each genotypic distribution which allows an assessment of the value of repeat measurements of the predictive variable for genotype assignment.

Animals↗

PubMed1999

Probability of identity by descent in metapopulations.

Equilibrium probabilities of identity by descent (IBD), for pairs of genes within individuals, for genes between individuals within subpopulations, and for genes between subpopulations are calculated in metapopulation models with fixed or varying colony sizes. A continuous-time analog to the Moran model was used in either case. For fixed-colony size both propagule and migrant pool models were considered. The varying population size model is based on a birth-death-immigration (BDI) process, to which migration between colonies is added. Wright's F statistics are calculated and compared to previous results. Adding between-island migration to the BDI model can have an important effect on the equilibrium probabilities of IBD and on Wright's index.

Animals↗

PubMed1998

Modelling of the probability of success of the stages of in-vitro fertilization and embryo transfer: stimulation, fertilization and implantation.

The aim of this study was to find the factors explaining the probability of success of in-vitro fertilization (IVF)-embryo transfer and its different stages: stimulation, fertilization and implantation. The sample came from a retrospective cohort followed in the IVF-embryo transfer centre of the Centre Hospitalier Universitaire of Pellegrin, Bordeaux, France; the data from 471 couples giving rise to 923 IVF-embryo transfer cycles were recorded. Four logistic regression models were specified for global process, stimulation, fertilization and implantation stages. Random effect models were used for taking into account the correlations of the different cycles for the same woman. The main outcome measures were: ongoing pregnancy, number of oocytes, number of embryos. A total of 135 ongoing pregnancies was observed. The significant explanatory variables were for global process: age [> or = 38 years: odds ratio (OR) = 0.28], donor sperm IVF-embryo transfer (OR = 2.1), number of ampoules (OR = 0.98), previous IVF-embryo transfer livebirth (OR = 2.36); for stimulation: age (> or = 35 years: OR = 0.38) and number of days of treatment > 13 days (OR = 0.20); for fertilization: accident during previous IVF-embryo transfer gestation (OR = 0.39), absolute tubal infertility (OR = 1.38) and the number of ampoules of human menopausal gonadotrophin (HMG) per day (OR = 0.85); for implantation: age (age > or = 38 years: OR = 0.34), donor sperm IVF-embryo transfer (OR = 4.58), number of ampoules (OR = 0.98), number and quality of the embryos. Estimates of the probabilities of success are also given for the global process.

Adult↗

PubMed1990

'Clustering'--real or apparent? Probability maps of childhood cancer in the West Midlands Health Authority region.

The West Midlands Regional Children's Tumour Registry collects detailed information on all cases of childhood cancer in the West Midlands Health Authority Region (WMHAR). The distribution by electoral ward of all cases diagnosed in the WMHAR between 1980 and 1984 has been determined. Analysis has also been performed for leukaemias/non-Hodgkin's lymphomas alone. We suggest that this latter grouping should be universally employed, owing to the difficulty of accurately separating out cases of leukaemia. Both spatial analyses showed several wards with significantly excessive rates on the basis of their cumulative Poison probability. Observed/expected ratios of 3-35 were seen for cases in significant wards, which are similar to the ratios seen in analysis of incidence around nuclear installations. However, further detailed consideration of these individual significance levels in the light of the number of statistically significant wards which would occur by chance alone, due to the multiple use of the test, accounted completely for the number of wards obtained in each of the groups considered. Thus, apparent 'clustering' of cases could be mere statistical artefact. In the WMHAR, therefore, using the technique of probability mapping, no true spatial pattern of incidence was found, other than that which would occur by chance alone. This, in a large area without nuclear installations and an even mix of rural and industrialised regions, could be seen as control data for those studies which have considered cases of childhood leukaemia around nuclear facilities, where the observation of single point clusters associated with suspected sites restricts assessments of spatial pattern in the rest of the area.(ABSTRACT TRUNCATED AT 250 WORDS)

Adolescent↗

PubMed1992

The probability of progression to AIDS in a cohort of male sexual contacts of men with HIV disease.

In a cohort of 249 male sexual contacts of men with AIDS or an AIDS-related condition (ARC), 143 cohort members were seropositive on enrollment and 16 seroconverted during follow-up. A logistic Weibull mixture model was used to estimate the probability of progression to AIDS after HIV infection when infection was assumed to occur during the period of sexual contact with the primary case. Forty cohort members developed AIDS while under study. It appears that at least 50% of men with HIV disease will progress to AIDS and that the best estimate of this probability lies anywhere in the interval 70% to 100%.

Acquired Immunodeficiency Syndrome↗

PubMed1986

Approximate computation of probability functions for pedigree analysis.

Approximation by factorization of R functions is considered as a way of making the peeling method for calculation of probability functions more efficient and applicable to larger and more complex pedigrees. We show that, in some situations, the method is not approximate but a simplified way of calculating the true probability functions. The entropy function is used for a measure of the quality of factorization. The method is illustrated by an analysis of the origin of the B allele in the ABO blood type system on Tristan da Cunha.

ABO Blood-Group System↗

PubMed2003

Risk-adjusted sequential probability ratio tests: applications to Bristol, Shipman and adult cardiac surgery.

OBJECTIVE: To investigate the use of the risk-adjusted sequential probability ratio test in monitoring the cumulative occurrence of adverse clinical outcomes. DESIGN: Retrospective analysis of three longitudinal datasets. SUBJECTS: Patients aged 65 years and over under the care of Harold Shipman between 1979 and 1997, patients under 1 year of age undergoing paediatric heart surgery in Bristol Royal Infirmary between 1984 and 1995, adult patients receiving cardiac surgery from a team of cardiac surgeons in London,UK. MAIN OUTCOME MEASURE: Annual and 30-day mortality rates. RESULTS: Using reasonable boundaries, the procedure could have indicated an 'alarm' in Bristol after publication of the 1991 Cardiac Surgical Register, and in 1985 or 1997 for Harold Shipman depending on the data source and the comparator. The cardiac surgeons showed no significant deviation from expected performance. CONCLUSIONS: The risk-adjusted sequential probability test is simple to implement, can be applied in a variety of contexts, and might have been useful to detect specific instances of past divergent performance. The use of this and related techniques deserves further attention in the context of prospectively monitoring adverse clinical outcomes.

Adult↗

PubMed1989

Projecting individualized probabilities of developing breast cancer for white females who are being examined annually.

To assist in medical counseling, we present a method to estimate the chance that a woman with given age and risk factors will develop breast cancer over a specified interval. The risk factors used were age at menarche, age at first live birth, number of previous biopsies, and number of first-degree relatives with breast cancer. A model of relative risks for various combinations of these factors was developed from case-control data from the Breast Cancer Detection Demonstration Project (BCDDP). The model allowed for the fact that relative risks associated with previous breast biopsies were smaller for women aged 50 or more than for younger women. Thus, the proportional hazards models for those under age 50 and for those of age 50 or more. The baseline age-specific hazard rate, which is the rate for a patient without identified risk factors, is computed as the product of the observed age-specific composite hazard rate times the quantity 1 minus the attributable risk. We calculated individualized breast cancer probabilities from information on relative risks and the baseline hazard rate. These calculations take competing risks and the interval of risk into account. Our data were derived from women who participated in the BCDDP and who tended to return for periodic examinations. For this reason, the risk projections given are probably most reliable for counseling women who plan to be examined about once a year.

Adult↗

PubMed2006

DNA looping by two-site restriction endonucleases: heterogeneous probability distributions for loop size and unbinding force.

Proteins interacting at multiple sites on DNA via looping play an important role in many fundamental biochemical processes. Restriction endonucleases that must bind at two recognition sites for efficient activity are a useful model system for studying such interactions. Here we used single DNA manipulation to study sixteen known or suspected two-site endonucleases. In eleven cases (BpmI, BsgI, BspMI, Cfr10I, Eco57I, EcoRII, FokI, HpaII, NarI, Sau3AI and SgrAI) we found that substitution of Ca2+ for Mg2+ blocked cleavage and enabled us to observe stable DNA looping. Forced disruption of these loops allowed us to measure the frequency of looping and probability distributions for loop size and unbinding force for each enzyme. In four cases we observed bimodal unbinding force distributions, indicating conformational heterogeneity and/or complex binding energy landscapes. Measured unlooping events ranged in size from 7 to 7500 bp and the most probable size ranged from less than 75 bp to nearly 500 bp, depending on the enzyme. In most cases the size distributions were in much closer agreement with theoretical models that postulate sharp DNA kinking than with classical models of DNA elasticity. Our findings indicate that DNA looping is highly variable depending on the specific protein and does not depend solely on the mechanical properties of DNA.

Binding Sites↗

PubMed1989

Probability of introducing diseases because of false negative test results.

The use of diagnostic tests for the selection of healthy individual persons or animals for inclusion in certain groups carries with it an inherent risk of including those with infections because they falsely reacted negatively. The factors of sensitivity of the test, prevalence of the disease, and the size of the group all influence the degree of such risk. The probability of including an infected individual person or animal can be calculated combining conditional probability and the binomial distribution.

Animals↗