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A formalism for the assignment of uncertainties to clinical probabilities of hypothyroidism, euthyroidism, and hyperthyroidism.

A formalism for the optimal estimation of the probabilities of hypothyroidism, euthyroidism, and hyperthyroidism is outlined. The scheme provides a means for assigning uncertainties to the estimates. These uncertainties can be used to determine whether or not the difference between two probabilities is statistically significant. Clinical data are utilized to illustrate the method.

Computers↗

A computer calculation of probability of monozygosity for twins.

A general algorithm is described to calculate the probability of monozygosity of concordant twins on the basis of blood type tests. Frequencies of all combinations of twins and parents are created with the aid of a translational matrix which facilitates conversion of genotypes to phenotypes automatically. The method of calculation is explained by taking Rh system in Germany as an example. The probability of monozygosity is calculated for all combinations of twin and/or father and/or mother. Effects of parental phenotypes on the efficiency in the diagnosis are analyzed quantitatively. Applicability of this method to other calculations concerning genetics is also discussed.

Blood Group Antigens↗

A SAS procedure for exact probability testing of difference between sample and population proportion.

Statistical testing of the hypothesis that the proportion of subjects in a defined population having a certain attribute (proportion of "positives" in a population, P) is equal to some specified value (P0) is frequently encountered in biomedical research. For example, a study might be carried out to statistically test whether the postoperative wound infection rate in patients having undergone an operation with a "new" surgical procedure is 20%, the same value that has been observed for the "established" surgical procedure. The significance test for this hypothesis (e.g., test H0: P = 0.20 against HA: P not equal to 0.20) is usually based on the normal theory approximation method. However, when the sample size is "small", especially if P0 is close to 0 or 1, the normal theory method can yield grossly unreliable results. In contrast, the significance test based on the exact binomial probability procedure always yields reliable results. A computer program coded in SAS is described herein to perform this exact probability test procedure.

Mathematical Computing↗

A disease-conscious method for sequential diagnosis by use of disease probabilities without assumption of symptom independence.

A method for automatic diagnosis of disease is formulated and applied to a data base of several hundred gastroenterological patients who were each known to have one of six diseases. Application of the method requires no assumptions regarding statistical independence of symptoms. Each disease is associated with its own disease-symptom function, and any order of dependence between the symptoms and each disease may be allowed for. A patient's symptoms are used to determine the value of any specified disease-symptom function. This value is then used to determine the probability that the patient has the corresponding disease. The method is applied to a sequential diagnosis of patients not contained in the initial data base. Additional symptoms are chosen according to their diagnostic value. The entire model is disease-conscious in that disease-symptom functions, disease probabilities and diagnostic values need be evaluated only for those diseases that are considered relevant to the diagnosis.

Bayes Theorem↗

An algorithm for approximating conditional probabilities.

When diagnostic programs are constructed within a probabilistic framework, it is often the case that computation of joint probabilities of exhaustive combinations of events is easy, but computation of the kind of conditional probabilities the user wishes to know, is hard. This paper describes a simple algorithm for computing the required values, and then suggests several heuristic optimizations that may enable suitable approximations to be obtained in a feasible time when the task is otherwise intractable. An account is given of a specific application of the method in the construction of a medical diagnostic program, which is described in more detail elsewhere.

Algorithms↗

Calculating the probability that microcracks initiate resorption spaces.

This paper explores the assumptions and limitations of the probability calculation that led to the conclusion by Burr et al. (1985) that microcracks initiate new remodeling events. It also corrects several minor errors in the calculation in the original manuscript. The results show that the probability that cracks and resorption spaces are associated depends heavily on a factor, F, that accounts for the possibility that some osteons that contain both a crack and a resorption space share a cement line with an adjacent osteon to which the crack more properly 'belongs.' F in turn depends on (1) the measurement criteria for cracks and resorption spaces, (2) the osteon population density in the bone, and (3) the mechanism by which cracks initiate remodeling. The theoretical maximum number of osteons that can contain both a crack and a resorption space (nmax) increases as the number of resorption spaces (r), the number of cracks (c), and F increase, but decreases as the osteon population density (d) increases. A larger nmax makes a direct association between cracks and resorption spaces more difficult to demonstrate experimentally.

Animals↗

Calculation of probabilities of random occurrence of different types of palindromes.

Formulas for the calculation of probabilities of the random occurrence of different types of true and complementary palindromes in DNA of arbitrary nucleotide composition were proposed. Calculations using the formulas developed show that the probabilities of random occurrence depend significantly, as expected, on the combinatorial restrictions, imposed on the palindromes, and in some cases also on the nucleotide composition of the DNA. Calculations performed demonstrated that even comparatively short (6/8 etc.) palindromes of certain types could ensure the required specificity of the protein-DNA interaction in transcription, replication etc.

Base Composition↗

Cell survival probability under ionizing radiation.

The survival probability of a living cell exposed to ionizing radiation in an experimental setup is derived. The survival of a cell depends on the severity of the radiation damage and efficiency of the cellular repair. The formula of the survival probability is expressed as a function of dose, nonlinear rate of lesion induction, nonlinear rate of cellular repair, and a key experimental parameter--the holding time. The result is an extension of the Markovian dose-response model developed by Yang and Swenberg.

Animals↗

The probability of permanence.

Numerical experiments suggest that cooperation is a very rare phenomenon in autocatalytic networks with more than about five interacting species. There is strong evidence that the probability for cooperative behavior in random networks decreases at least exponentially and at most as an2 with the number n of interacting species. The evolution of larger persistent networks by subsequent incorporation of additional species into a cooperative network is shown to be even less probable. This leads to the conclusion that hypercycle-type interactions alone are not sufficient to maintain the genetic information of more than a few interacting species in a pure RNA world.

Ecology↗

A path probability model for sister-chromatid exchanges induced by alkylating agents.

A path probability model is described for evaluation of sister-chromatid exchanges (SCEs) induced by alkylating agents following treatment of G1 cells at the beginning of the first or second cycles of BrdUrd incorporation, or during G1 corresponding to an exact cell-cycle interval preceding BrdUrd incorporation. Algebraic expressions are derived for calculations of expected induced SCE frequencies (over baseline levels) in second and third (reciprocal and nonreciprocal SCEs) division cells for the described treatment protocols. The derivations take into consideration: p, the probability of a specific lesion inducing an SCE; rn, the extent of repair within the nth post-treatment cycle; and X, the number of lesions induced. Expressions are also derived for expected ratios of single: twin exchanges in endoreduplicated or tetraploid cells.

Alkylating Agents↗

Survival probabilities of infants delivered prior to the 34th week of pregnancy as estimated by means of a logistic model.

Survival of 188 infants born alive before the 34th wk of pregnancy is assessed in relation both to birthweight and duration of pregnancy. A logistic model is used which describes, based on these parameters, probabilities of 1-yr survival of relatively small populations in a continuous way. Although there may be differences between measured and estimated birthweight, this method might enable the perinatologist to estimate before birth the survival probabilities if he knows the duration of pregnancy and estimated birthweight.

Birth Weight↗

Statistical approach for the estimation of daily physical activity levels using the probability density function of heart rate.

An investigation was undertaken into the statistical properties of heart rate during daily physical activity. The probability density function of the heart rate was estimated using the Gram-Charlier series. In addition, the probability density was separated into two Gaussian distributions: relatively low and relatively high heart rates. The former appeared to correspond to the metabolic rate associated with basic daily living and the latter appeared to be associated with more active physical activity of the type necessary to sustain or elevate the level of physical fitness. The higher heart rate distribution of five subjects occupied 8.72 +/- 2.15% of a period of waking. The validity of the statistical approach was confirmed with fractional estimation error of 1.22 +/- 0.62%.

Heart Rate↗

The probability with which EMS-initiated mutagenic lesions generate mutations in CHO cells.

In this note we distinguish between multiple mutations affecting a given locus which are generated at separate error-prone lesions and multiple independent mutations generated at a single error-prone lesion. We describe a basis for determining the probability with which the latter class of mutations occurs based on the mutant fraction in the progeny and determine an average probability of 0.6 mutations/replication/mutagenic site for those EMS-modified sites which are mutagenic for G6PDH activity in CHO cells.

Animals↗

Comparison of treatment techniques for conformal radiotherapy of the prostate using dose-volume histograms and normal tissue complication probabilities.

The aim of this study was to evaluate the relative merits of the coplanar field arrangements most frequently used for conformal radiotherapy of the prostate using dose-volume histograms and normal tissue complication probabilities (NTCPs). Twelve patients with early prostate cancer underwent a planning CT scan of the pelvis. Isocentric plans for each patient were devised using three, four, six and eight conformal fields and beam-weights optimised using fast simulated annealing to give a dose homogeneity across the planning target volume of +/- 5% or better while minimising irradiation of the relevant organs at risk. The plans were then evaluated using dose-volume histograms of the organs at risk (bladder, rectum and both femoral heads) and the Lyman model of normal tissue complication probability for the rectum. Analysis of dose-volume histogram data averaged over the 12 patients indicates an advantage for six (p = 0.002) and eight (p = 0.0001) fields with respect to the percentage volume of the femoral heads receiving > 50% of the prescribed dose compared with three fields. There was a similar advantage for six (p = 0.0007) and eight (p = 0.0001) fields compared with four fields. Ranking of the treatment techniques indicates that the four-field technique is the worst with respect to femoral head irradiation but the best with respect to reducing rectal irradiation. A higher dose can be prescribed to the isocentre with the four-field technique for a 5% rectal NTCP. The six-field technique led to sparing of the bladder when the different treatment techniques were ranked using bladder dose-volume histogram data. We conclude that none of the techniques studied consistently proved to be superior when applied to this sample of patients with prostate cancer with respect to sparing all the organs at risk. The absolute differences between techniques are small and would be very difficult to detect with respect to clinically relevant endpoints.

Algorithms↗

Optimal determination of most probable numbers.

Choosing the design of a dilution series experiment on the basis of availability of most probable number tables can result in a non-optimal design. Similarly, certain tables and/or rules for declaring dilution series results 'improbable' do not always give optimal decisions. Further, tables of most probable number confidence intervals are not all based on the same assumptions and give different intervals--which should be used? The aim of this article is to draw microbiologists' attention to these issues and to suggest practical solutions.

Bias↗

APL programs for outcome probabilities and confidence limits in sequential binomial trials.

For closed sequential binomial sampling plans (including plans for multistage sampling), the probability of reaching each terminal point is calculated. These probabilities are cumulated from "each side" of the plan. Thus, the power function obtainable by defining any (reasonable) acceptance region can be studied. Corresponding to a given outcome of the trial confidence limits can be calculated by an auxiliary program.

Clinical Trials as Topic↗

Strength-probability-time (SPT) diagram--an adjunct to the assessment of dental materials?

This investigation sought to construct and compare strength-probability-time (S-P-T) diagrams for four dental materials. Three of these were resin composites and one was dental plaster. In the case of dental plaster a total of 90 compressive specimens as fabricated whereas for each of the other materials a total of 75 specimens was prepared. The compressive strength of equal sized groups of each material was then determined at the crosshead (XHD) speeds of 1, 5 and 10 mm min-1 respectively. The data was subjected to Weibull analysis to relate the probability of failure to the applied stress. Where strong correlations were found between the (i) mean compressive strength and crosshead speed, (ii) individual compressive strengths and failure times, the data was used to determine the crack velocity exponent (n) and produce a S-P-T diagram. Although only one of the materials (P-50) evaluated fulfilled all the necessary criteria and yielded a value of n = 16.13 (7.22), it is suggested that this method may enable comparisons to be made amongst other materials satisfying the required conditions. As such diagrams are based upon a crack growth law they may be of value in assessing the likely clinical wear resistance of new formulations. Consideration, however, should always be given to what levels are deemed acceptable for the intended clinical application of the material. Thus, before this technique can be employed fully, to the evaluation of new restorative materials, further work is necessary to determine appropriate design criteria.

Composite Resins↗

Aging, stimulus identification and the effect of probability: an event-related potential study.

Event-related potentials (ERPs) of younger and older subjects were compared in a simple reaction time (SRT) and in two GoNogo (20% and 80% target probability) tasks. At the T5 location, the NA component (the difference between the ERPs elicited by the frequent stimuli in the GoNogo tasks on the one hand, and the ERPs in the SRT task on the other hand) emerged earlier in the younger group. The N2b was larger in the younger group, and in this group the rare stimuli of the 80% GoNogo task elicited an enlarged N2. When compared to the older group, the stimulus probability in the younger group had a larger effect on the amplitude of the late positivity. The results show age-related changes at an early stage of the information processing activity, and larger sensitivity of the orienting system in the younger subjects.

Adolescent↗