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PubMed1999

Strength of evidence, judged probability, and choice under uncertainty.

This paper traces, within subjects, the relationship between assessed strength of evidence, judgments of probability, and decisions under uncertainty. The investigation relies on the theoretical framework provided by support theory (Tversky & Koehler, 1994; Rottenstreich & Tversky, 1997), a nonextensional model of judgment under uncertainty. Fans of professional basketball (N = 50) judged the probability that each of eight teams, four divisions, and two conferences would win the National Basketball Association championship. Additionally, participants rated the relative strength of each team, judged the probability that a given team would win the championship assuming a particular pairing in the finals, priced prospects contingent on the winner of the championship, and made choices between chance prospects. The data conformed to the major tenets of support theory, and the predicted relationships between assessed strength of evidence, hypothetical support, judged probabilities, and choices under uncertainty also held quite well.

Adult↗

PubMed1993

Estimation and use of protein backbone angle probabilities.

A procedure is described for estimating the probabilities for the backbone phi-psi angles of a protein molecule from the data base of known protein structures. The procedure is basically an adaptation of a published secondary structure prediction scheme, applied to the phi-psi angle bins rather than to the secondary types. The phi-psi angle probabilities estimated this way include all effects of local sequence and are "context sensitive" in that the probabilities for a given residue type depend on its position along the sequence. These probabilities can be used to predict the three-dimensional structure of short polypeptides that are stabilized mainly by local interactions only and to predict the protein folding initiation sites, with moderate to good success rates in each case. They are also potentially useful for efficient sampling in a Monte Carlo scheme of protein tertiary structure prediction methods.

Amino Acid Sequence↗

PubMed1995

Analytical solutions of the dinucleotide probability after and before random mutations.

The mutation process is a classical evolutionary genetic process mainly based on the (random) substitutions of one base (A = Adenine, C = Cytosine, G = Guanine, T = Thymine) for another. Two analytical solutions derived here allow us to analyse in genes the occurrence probabilities of motifs (e.g. dinucleotides) after substitutions (in the evolutionary sense: from the past to the present) and, unexpectedly, also before substitutions (after back substitutions, in the inverse evolutionary sense: from the present to the past). We generalize on the alphabet [A, C, G, T] of the analytical solutions and of the properties derived on the alphabet [R, Y] (R = purine = A or G, Y = pyrimidine = C or T). Application of the theory is based on the analytical solution giving the probabilities of the 16 dinucleotides AA, ..., TT in the protein (coding) genes of (nuclear) eukaryotes, viruses and prokaryotes and in (eukaryotic) introns after back substitutions (called primitive genes). After back substitutions, four of 16 dinucleotides--CG, TA, GT and AC--occur with low probabilities in each of these four primitive gene populations, except for CG in the primitive prokaryotic protein genes. In the primitive eukaryotic protein genes, the dinucleotide AT has also a significant low probability. We present the properties of the two analytical solutions, and the functions which may have these five dinucleotides in primitive genes are described in terms of biological signals.

Animals↗

PubMed2001

Improved detection of event-related functional MRI signals using probability functions.

Selecting an optimal event distribution for experimental use in event-related fMRI studies can require the generation of large numbers of event sequences with characteristics hard to control. The use of known probability distributions offers the possibility to control event timing and constrain the search space for finding optimal event sequences. We investigated different probability distributions in terms of response estimation (estimation efficiency), detectability (detection power, parameter estimation efficiency, sensitivity to true positives), and false-positive activation. Numerous simulated event sequences were generated selecting interevent intervals (IEI) from the uniform, uniform permuted, Latin square, exponential, binomial, Poisson, chi(2), geometric, and bimodal probability distributions and fixed IEI. Event sequences from the bimodal distribution, like block designs, had the best performance for detection and the poorest for estimation, while high estimation and detectability occurred for the long-decay exponential distribution. The uniform distribution also yielded high estimation efficiency, but probability functions with a long tail toward higher IEI, such as the geometric and the chi(2) distributions, had superior detectability. The distributions with the best detection performance also had a relatively high incidence of false positives, in contrast to the ordered distributions (Latin square and uniform permuted). The predictions of improved sensitivities for distributions with long tails were confirmed with empirical data. Moreover, the Latin square design yielded detection of activated voxels similar to the chi(2) distribution. These results indicate that high detection and suitable behavioral designs have compatibility for application of functional MRI methods to experiments requiring complex designs.

Adult↗

PubMed1985

["Advantages" of exclusion probability in blood group evaluation?].

There is no apparent advantage in using exclusion probability A (or WA) in cases where parentage is disputed in either normal or special cases. Furthermore, WA provides no more information than WEM. However, the converse is true: WA does not take the serotype of the putative father into account. Moreover, it is neither easier to understand nor easier to work with and, like WEM, it also requires a prior probability. WA is also not helpful in interpreting WEM; for this, one has to use mean WEM values for fathers and non-fathers. There is no reason to expect WA and WEM to converge at the upper end of the scale. WA is unsuitable for establishing the borderline where decisions may no longer be valid, as the error quota in individual cases can be greater than that allowed within the limits. 100-WEM % is the probability or error in categorical decisions in 100 cases with similar combinations. In contrast, 100-WA % cannot provide a reliable probability of error in individual cases because WA does not take full account of the phenotype of the putative father.

Blood Grouping and Crossmatching↗

PubMed1994

The probability of recovery and return to work from work disability as a function of time.

This paper describes a prospective longitudinal cohort study of musculoskeletal soft tissue pain impairment following a work related injury. It focuses on specific, univariate prognostic factors indicated in previous research studies that might affect the likelihood that injured workers will return to work or remain on work disability at any point in time. These factors include gender, age, return to work attempts and site of injury. Life table analysis was used to model the probability of work disability. The results showed that different disability and return to work patterns emerged for males and females. Males were more likely to return to work; however, females had a higher probability than males of remaining at work once they returned to work. Older workers had the highest probability of being off work any given number of days after injury; were less likely to return to work, and if they did, had a higher probability of becoming disabled again. Efforts to return early to work contributed to a decrease in overall work disability. Workers with low back injuries had a greater likelihood of recurrence compared to injuries at other body sites.

Adolescent↗

PubMedDate not supplied

Inter- and intra-individual probability maps in EEG cartography by use of nonparametric Fisher tests.

The three types of non-parametric permutation Fisher tests have been applied to inter-individual group studies and further to intra-individual multiple EEG recording sequences, providing computations of EEG probability maps testing two ordinal hypotheses. Two examples of previous group studies with "EEG local cerebral activation" are given: mental computation in a group of 20 controls and caffeine effects versus placebo in a group of 10 controls. For the intra-individual study, two successive recordings of 2.3 min eyes closed (EC1 and EC2), obtained at 50 min intervals, were compared by paired exact permutation Fisher tests (over 15 or 42 synchronous EEG sequences). These tests were applied to descriptive spectral parameters: RMS and % amplitudes, mean frequencies, resonance coefficient, for raw unfiltered EEG and delta, theta, alpha, alpha 1, alpha 2, beta 1, beta 2 frequency bands. Two hypotheses were tested for each of the computed 31 parameters, providing two probability maps indicating if the parameter was greater or lower in the first EEG recording or in the second. The second EEG sequence, EC2, was "EEG activated" compared to the first sequence EC1 if the following were present: decreased amplitudes mainly in raw EEG, low activity and alpha bands; increased frequencies mainly, in raw EEG, delta and beta 1 fast activities; increased fast activity percentages; decreased coefficient of resonance. The effect of choice of reference was also evaluated: probability maps for a frontal reference were different than other probability maps obtained after computation of average reference or source derivation.(ABSTRACT TRUNCATED AT 250 WORDS)

Brain Mapping↗

PubMed1995

Match probability calculations for multi-locus DNA profiles.

The paper considers aspects of the match probability calculation for multi-locus DNA profiles and a related calculation which aims to assess the probability that a pair of profiles is concordant for the presence and absence of bands. It is suggested that levels of allelism and linkage for multi-locus profiles may be higher than reported in previous studies, and that comparison of bandsharing values between different studies is problematic. Our view is that the independence assumptions which underpin the calculations have not been established. The effect of ignoring (local) heterogeneities in band frequencies may be non-conservative. Concerns thus raised about the match probability calculation could be important in practical casework. The speculative nature of some aspects of the concordance probability calculation would seem to render it inappropriate for use in court.

Alleles↗

PubMed2006

A diffusion approach to approximating preservation probabilities for gene duplicates.

Consider a haploid population and, within its genome, a gene whose presence is vital for the survival of any individual. Each copy of this gene is subject to mutations which destroy its function. Suppose one member of the population somehow acquires a duplicate copy of the gene, where the duplicate is fully linked to the original gene's locus. Preservation is said to occur if eventually the entire population consists of individuals descended from this one which initially carried the duplicate. The system is modelled by a finite state-space Markov process which in turn is approximated by a diffusion process, whence an explicit expression for the probability of preservation is derived. The event of preservation can be compared to the fixation of a selectively neutral gene variant initially present in a single individual, the probability of which is the reciprocal of the population size. For very weak mutation, this and the probability of preservation are equal, while as mutation becomes stronger, the preservation probability tends to double this reciprocal. This is in excellent agreement with simulation studies.

Algorithms↗

PubMed2006

Lesion probability maps of white matter hyperintensities in elderly individuals: results of the Austrian stroke prevention study.

OBJECTIVE: White matter hyperintensities (WMH) are common on brain MRI of the elderly. Their size ranges from punctate to early confluent to confluent lesions. While this increase in extension is frequently seen as evidence for a continuum of changes, histological data and clinical follow-up suggest differences in underlying pathology and their progression. METHODS: We tested this hypothesis by exploring the distributions of punctuate and confluent lesions using lesion probability maps (LPM) generated from MRI scans of 189 participants (mean age 60.8+/-6.2 years) in the Austrian Stroke Prevention Study. We dichotomised WMH according to the classification by Fazekas et al. [punctate (n=143) vs. early confluent and confluent (n=33)] to run voxel-based t-tests using permutation-based nonparametric inference. To test alternative hypotheses, we created similar LPM for age and arterial hypertension. RESULTS: We observed significant differences in the spatial distribution of lesions for the two WMH groups (p<0.01). Punctate lesions were more diffusely distributed throughout the cerebral white matter (peak probability approximately 5%) relative to confluent lesions (peak probability 45%). Confluent lesions had greatest likelihood of being found in perfusion "watershed" regions. These differences in distribution could not be explained by differences in age or hypertension only, as both greater age and the diagnosis of hypertension were associated with WMH abutting the occipital horns. CONCLUSIONS: Punctate and early confluent to confluent WMH show distinguishable differences in their spatial distribution within a normal elderly population. The pattern of punctate WMH is probably a consequence of mixed etiologies. Preferential localization of the more confluent WMH with arterial watershed areas implies a stronger ischemic component in their development.

Age Factors↗

PubMed2006

The probability of treatment induced drug resistance.

We propose a discrete time branching process to model the appearance of drug resistance under treatment. Under our assumptions at every discrete time a pathogen may die with probability 1-p or divide in two with probability p. Each newborn pathogen is drug resistant with probability mu. We start with N drug sensitive pathogens and with no drug resistant pathogens. We declare the treatment successful if all pathogens are eradicated before drug resistance appears. The model predicts that success is possible only if p<1/2. Even in this case the probability of success decreases exponentially with the parameter m=muN. In particular, even with a very potent drug (i.e. p very small) drug resistance is likely if m is large.

Drug Resistance, Microbial↗

PubMed1990

Using the patient's history to estimate the probability of coronary artery disease: a comparison of primary care and referral practices.

PURPOSE: According to probability theory, the interpretation of new information should depend on the prior probability of disease. We asked if this principle applies to interpreting the history in patients with chest pain. We compared the prevalence of coronary artery disease (CAD) in patients who had similar histories but who came from populations with different disease prevalence. PATIENTS AND METHODS: We studied two high-disease-prevalence populations (patients referred for coronary arteriography) and two low-disease-prevalence populations (patients from primary care practices). We used clinical characteristics of one arteriography population to develop a logistic rule for estimating the probability of coronary artery narrowing. The number of clinical findings determined the logistic score, which was proportional to the prevalence of CAD. RESULTS: The prevalence of CAD was much lower in the primary care population than in the arteriography population, even when patients with similar logistic scores, and thus similar clinical histories, were compared. CONCLUSION: A clinician must take account of the overall prevalence of disease in the clinical setting when using the patient's history to estimate the probability of disease. Failure to observe this caution may lead to errors in test selection and interpretation.

Adult↗

PubMed1979

Probability of menopause with increasing duration of amenorrhea in middle-aged women.

The empirical percent probability that natural menopause has occurred after first presentation of amenorrhea of various durations in women greater than or equal to 45 years of age has been calculated using data from a cohort of subjects who prospectively recorded menstrual flow and related gynecologic events. The probability that menopause has occurred increases with the amenorrheal interval (duration), and for a given interval, the probability increases with age. After 180 days of amenorrhea, 45% to 72% of subjects were menopausal; after 360 days, 90%. These data may offer assistance in advising patients on the probability of menopause and the continuance of contraceptive practices, and in considering whether late genital bleeding after amenorrhea represents a physiologic or pathologic process.

Age Factors↗

PubMedDate not supplied

Similarity, plausibility, and judgments of probability.

Judging the strength of an argument may underlie many reasoning and decision-making tasks. In this article, we focus on "category-based" arguments, in which the premises and conclusion are of the form All members of C have property P, where C is a natural category. An example is "Dobermans have sesamoid bones. Therefore, German shepherds have sesamoid bones." The strength of such an argument is reflected in the judged probability that the conclusion is true given that the premises are true. The processes that mediate such probability judgments depend on whether the predicate is "blank"--an unfamiliar property that does not enter the reasoning process (e.g., "have sesamoid bones")--or "non-blank"--a relatively familiar property that is easier to reason from (e.g., "can bite through wire"). With blank predicates, probability judgments are based on similarity relations between the premise and conclusion categories. With non-blank predicates, probability judgements are based on both similarity relations and the plausibility of premises and conclusion.

Decision Making↗

PubMed1987

Impact of endoscopy on mortality from occult cancer in radiographically benign gastric ulcers. A probability analysis model.

Endoscopy is commonly used in the management of patients with radiographically benign gastric ulcers to detect occult malignancy. Clinical studies examining the cost-effectiveness of using endoscopy in such patients, however, have not been done. To address this issue using probability analysis, a probability tree was designed incorporating the possible clinical courses of patients with radiographically benign gastric ulcers managed with and without endoscopy, and probability estimates for each course were derived by compiling data from the literature. Probability and sensitivity analysis was used to compare the impact on overall mortality rate and cost-effectiveness of six commonly practiced methods of using endoscopy to manage patients with radiographically benign gastric ulcers: (1) all follow-up by upper gastrointestinal x-ray only; (2) endoscopy for nonhealing ulcers only; (3) endoscopy for all ulcers before medical therapy with all follow-up by upper gastrointestinal x-ray; (4) endoscopy for all ulcers after an initial trial of medical therapy; (5) endoscopy for all ulcers before therapy and for nonhealers; (6) endoscopy before therapy, and all follow-up by endoscopy. This analysis predicts that the greatest decrease in mortality rate occurs when endoscopy is used before medical therapy and for all follow-up, reducing the estimated number of deaths per 1000 patients with radiographically benign gastric ulcers from 36.7 with follow-up by upper gastrointestinal x-ray only to 27.2. However, initial endoscopy with all subsequent follow-up by upper gastrointestinal x-ray increased the overall death rate by only a small amount, to 28.0, and was consistently the most cost-effective method, requiring 116 endoscopies and approximately 60,000 diagnostic dollars per additional 5-yr survivor.

Cost-Benefit Analysis↗

PubMed1989

Assessment of probability of survival in penetrating injuries using the TRISS methodology.

By the TRISS methodology, probability of survival in injury can be estimated. It is based on a statistical analysis of outcome which is influenced by the severity of the injuries as expressed in the Injury Severity Score (ISS), the physiological function as expressed in the Trauma Score (TS) and the patient's age. We have used the TRISS formula in 206 patients with penetrating injury. Of these patients, 149 sustained stab wounds, 32 gunshot wounds and 25 others. ISS ranged from 2 to 38, the mean ISS being 9. The function was good (TS greater than 14) in 85 per cent. Estimated probability of survival ranged from 1.00 to 0.42. Three patients (1.5 per cent) died. The probability of their survival was 0.92, 0.96 and 0.98, respectively. All the fatal cases had serious predisposing conditions: chronic pulmonary disease, alcoholism, and psychiatric illness. In penetrating injury, the patient's functional status at the start of treatment is of greater importance for the outcome than the anatomical severity. The concept of the methodology of TRISS for assessment of probability of survival seems useful for review and comparison in injury care.

Abbreviated Injury Scale↗

PubMed1995

Formulas expressing life expectancy, survival probability and death rate in life table at various ages in US adults.

The National Center for Health Statistics (Monthly Vital Statistics Report, 41 (1993) 1-36; Pediatrics, 92 (1993) 743-754) reported the life table for the total population of the United States, 1992, on the basis of vital statistics. The life table shows life expectancy, survival and death rate at various ages. Formulas expressing death rate, survival probability and life expectancy at various ages in US adults are constructed from the data of the National Center for Health Statistics (NCHS). A mathematical model of the 'probacent'-probability equation previously published by the author is employed in this study. Analysis of the computer-assisted predicted values and the data reported by the NCHS indicates that the formulas are accurate and reliable with a close agreement in expressing death rate, survival probability and life expectancy at various ages in US adults of 25 years of age and older. The formulas can determine the relationship between the age and the death rate, the survival probability or the life expectancy and may be of value for epidemiologic evaluation of US adults.

Adult↗

PubMed1994

Fetal heart rate variation described using a probability distribution matrix.

We devised a new method using a probability distribution matrix to simultaneously describe variation in the characteristics of fetal heart rate (FHR) and beat-to-beat difference (DFHR) between the present and the immediately following FHR. The FHRs were plotted in columns, DFHRs in rows and probabilities in the corresponding elements of the matrix. The age-related changes of FHR data obtained from 743 fetuses at 23-40 weeks gestation were analysed using a pulsed Doppler cardiotocograph with an autocorrelation system. While keeping an almost symmetrical spread around 0 beats/min of DFHR, three particular probability distribution patterns of FHR versus DFHR emerged with advance in gestation: (i) oval with a monomodal peak from 23/24 to 29/30 weeks, (ii) ellipsoid with a monomodal peak and plateau from 31/32 to 33/34 weeks and (iii) elongated ellipsoid with bimodal peaks from 35/36 weeks of gestation onwards. The probability distribution matrix presented enables one to condense any amount of FHR data into one uniform description. This allows analysis of data, en bloc, achieving a quantitative inter-group comparison, on an equivalent scale.

Age Factors↗