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Estimating blood phenotype probabilities and their products.

We consider two methods of estimating phenotype probabilities for a number of standard genetic markers like the ABO, MNSs, and PGM markers. The first method is based on the maximum likelihood estimates of the allele probabilities, and the second (multinomial) method uses the phenotype proportions in the sample. The latter is easy to use, the estimates are always unbiased, and simple formulae for variances are available. The former method, although giving more efficient estimates, requires the assumption of panmixia so that the Hardy-Weinberg law can be used. The two methods are compared theoretically, where possible, or by simulation. Under panmixia, the maximum likelihood estimates can be substantially more efficient than the multinomial estimates. The estimates are also compared in the codominant allele case for nonpanmictic populations. The question of efficiency is of importance when estimating the probability of obtaining a given set of phenotypes, i.e., the product of individual phenotype estimators. This problem is discussed briefly.

ABO Blood-Group System↗

Estimating population size for capture-recapture data when capture probabilities vary by time and individual animal.

There have been no estimators of population size associated with the capture-recapture model when the capture probabilities vary by time and individual animal. This work proposes a nonparametric estimation technique that is appropriate for such a model using the idea of sample coverage, which is defined as the proportion of the total individual capture probabilities of the captured animals. A simulation study was carried out to show the performance of the proposed estimation procedure. Numerical results indicate that it generally works satisfactorily when the coefficient of variation of the individual capture probabilities is relatively large. An example is also given for illustration.

Animals↗

Estimating the probability of spontaneous abortion in the presence of induced abortion and vice versa.

An integrated approach to estimate the total number of pregnancies that begin in a population during one calendar year and the probability of spontaneous abortion is described. This includes an indirect estimate of the number of pregnancies that result in spontaneous abortions. The method simultaneously takes into account the proportion of induced abortions that are censored by spontaneous abortions and vice versa in order to estimate the true annual number of spontaneous and induced abortions for a population. It also estimates the proportion of pregnancies that women intended to allow to continue to a live birth. The proposed indirect approach derives adjustment factors to make indirect estimates by combining vital statistics information on gestational age at induced abortion (from the 12 States that report to the National Center for Health Statistics) with a life table of spontaneous abortion probabilities. The adjustment factors are applied to data on induced abortions from the Alan Guttmacher Institute Abortion Provider Survey and data on births from U.S. vital statistics. For the United States in 1980 the probability of a spontaneous abortion is 19 percent, given the presence of induced abortion. Once the effects of spontaneous abortion are discounted, women in 1980 intended to allow 73 percent of their pregnancies to proceed to a live birth. One medical benefit to a population practicing induced abortion is that induced abortions avert some spontaneous abortions, leading to a lower mean gestational duration at the time of spontaneous abortion.

Abortion, Induced↗

Probability models of the rate of infection with tick-borne encephalitis virus in Ixodes persulcatus ticks.

A total of 3,254 adults of Ixodes persulcatus tick were collected in a taiga forest habitat situated in the Amgun river basin (Khabarovsk region, the Far East, USSR) and examined individually for the presence and amount of tick-borne encephalitis virus. The over-all proportion of infected ticks was 6.6% and it varied between 3.4% and 9.4% in the years 1982 to 1985. The amount of virus per tick was approximated by the gamma distribution determining a probability that the number of plaque-forming units (PFU) per tick is not greater than a selected value. The frequency distribution of infected ticks followed a model of the negative binomial distribution, enabling the estimation of probability of the occurrence of a given number of infected ticks in the area. However, the parameters of both probability models (i.e., the PFU content per tick, and the frequency of infected ticks) varied for particular years.

Animals↗

[Probability of control of the patient with diabetes exclusively treated with pharmacological therapy].

OBJECTIVE: to predict the probability of blood glucose control in patients with type-2 diabetes mellitus, exclusively treated with pharmacology therapy. MATERIAL AND METHODS: secondary analysis of a database to evaluate the therapeutic attachment in type-2 diabetics older than 60 years old. We interviewed 123 patients in their home to get information about sociodemographic aspects and diabetes characteristics. The blood glucose control was measured through glycated hemoglobin and the attachment to the pharmacological treatment was measured by the Morisky-Green test. The analysis included simple logistic regression; the calculation of probability of control for different levels of therapeutic attachment was estimated using the result of the regression equation (y) and applying the formula 1/1 + e(-y). RESULTS: Monotherapy was present in 82.1%, glibenclamide was prescribed alone in 77.2%, glycated hemoglobin average was 11.5 +/- 3.5 %, 18% of the population was controlled and 58.1% showed some attachment to the pharmacological treatment. With a total attachment to the pharmacological prescription, the control probability is 27%, and without it, it corresponds to 10%. CONCLUSION: Almost three out of ten patients with a total attachment to the pharmacological treatment have chances of being controlled.

Acarbose↗

[Empirical, free of genetic model, estimation of recurrence risks in multifactorial diseases: conditional probability approach].

Conditional probability approach in estimation of recurrence risks in sibships of different parental phenotypic matings with the different set of affected and normal siblings is considered. The formulae are presented for calculation of recurrence risks in cases of equal and different susceptibility of two sexes under different ways of sampling of family data: direct selection of offsprings through the parents; indirect selection of offsprings through affected siblings--the probands, under different ascertainment probability--from pi = 1.0 ("exhaustive selection") up to pi----0 ("single selection"); for the case of different susceptibility of the two sexes a possibility of the differences in the ascertainment probabilities of men (pi m) and of women (pi w) is allowed, unlike "independent ascertainment model", which requires the constancy of pi. The case of multiple incompatible subforms is considered for estimation of the recurrence risks of the specified subforms. The methods of the risks estimation proposed are free of genetic models being universal both for classical mendelian traits (with the constant risks) and for multifactorial ones (with variable risks).

Causality↗

[Integral-probability assessment of development of occupational diseases using Bayes' formula in building-land improvement and car repair industry].

Integral probability technique used for the assessment of occupational diseases facilitated the evaluation of variability in the parameters of unfavorable industrial factors, as well as their complex action, the occupational pathologic developments "probability and risk groups identification. The technique proved valuable in charting the priority list of hygienic and health improvement measures to prevent the hazardous factors" influence depending on their probability indices.

Bayes Theorem↗

[A method for the quantitative evaluation of the probability of ischemic heart disease in epidemiological research on workers exposed to harmful effects].

A method for quantitative evaluation of the probability for ischaemic disease of the heart in epidemiological studies is recommended and the state of risk is determined by riskogram, including 3 parts: 1. Assessment of the electrocardiographic changes after Minnesota code. 2. Integral quantitative interpretation of ECG-changes with the data from the Rose test. 3. Classified quantitative assessment of the probability for ischaemic disease of the heart. The quantitative interpretation of the probability for ischaemic disease of the heart allows the use of various statistical methods, mathematical models and computer processing of data, received at the epidemiological studies. By tracing the dependences "dose-effect" and "dose-response" the maximum admissible duration of the length of service could be predicted in specific conditions of professional exposure, in order to prevent injury of the cardiovascular system from harmful industrial factors.

Bulgaria↗

[The dependence of hippocampal electrical activity on the probability of the reinforcement of a conditioned food stimulus].

In three dogs the dynamics was studied of changes in the number of instrumental motor reactions, the heart rate and the hippocampus theta rhythm was studied at the change of constant reinforcement to various regimes of probable reinforcement of alimentary conditioned stimulus. At 70 and 50% levels of the reinforcement the instrumental reflex appeared in response to all presentations of the signal stimulus. The greatest decrease in the number of reactions took place at 5% probability. The heart rate both in the intersignal period and at getting of empty feeder depended on the used probability of reinforcement and individual characteristics of animals. The frequency of the theta rhythm in all dogs was the highest at the 30% level and the lowest values were found at the 5% level of reinforcement. The obtained facts testify once more to complex genesis of emotional excitation, the value of which depends both on informational (uncertainty) and motivational (significance of reinforcement) factors.

Animals↗

[Dependence of search activities on the probability of random execution of instrumental reaction].

The increase in rat search activity was found to develop in early stages of the learning when probability of random performance of instrumental reaction to light was equal to 0.25. This phenomenon was not depended on duration of conditioned signal and/or/of intersignal period at the invariable probability. The probability of random performance of instrumental reaction is suggested to determine search activity and to be able to influence leaning rate.

Animals↗

Use of the concept of subjective probability in undergraduate training in differential diagnosing.

In teaching clinical problem solving the probabilistic component should be emphasized. In the domain of empirical medical knowledge to be utilized in diagnostic strategies the prediction according to clinicians' subjective probabilities is used in medical decision making concerning patient problem definition and diagnosis. Two approaches in teaching differential diagnosing by decision models using short case studies are compared. The first is traditional one with the concept of one "true" diagnosis selected from proposed diagnoses group in a MCQ-test. The second approach reflects more the medical practice reality: the students have to predict quantified subjective probabilities of each diagnosis in a suggested diagnoses group considering all the diagnoses probable and not excluding each other. The advantages of the second procedure are evaluated.

Cohort Studies↗

Words or numbers? The evaluation of probability expressions in general practice.

A sample of 56 general practitioners were asked to rate, on a percentage scale, 23 words or phrases which denote frequency or likelihood. The hypothetical context of the exercise was that of communicating to patients the probability of a side-effect (headache) arising from an unspecified prescription medicine. Median phrase ratings ranged from 'never' at 0% to 'certain' at 95% with a 50% rating given to the phrase 'reasonable chance'. Despite relatively large variance in ratings between respondents, the median ratings of a number of phrases were similar, and some identical, to other studies from different medical professionals. Although the clinical context in which a given expression of probability is used may affect its meaning, the results are encouraging and suggest that phrases denoting likelihood might be systematically codified to enhance communication between doctor and patient. To move towards this objective more research is needed to evaluate how patients interpret expressions of probability, and the relative effectiveness of different modes of communicating likelihood.

Communication↗

Hip fracture in women. Incidence, in-hospital mortality, and five-year survival probabilities in members of a prepaid health plan.

The problem of hip fracture is especially serious for women, who live longer than men and who have a higher risk of the condition. Data on women older than 49 years enrolled in a prepaid medical care program were analyzed to determine the incidence of hospitalization for hip fracture, in-hospital death rate, and five-year probability of survival after hip fracture. The cumulative lifetime probability of hip fracture for women alive at age 50 years was calculated, taking into account current estimates of survival in women. As in other studies, the incidence of hip fracture increased exponentially with age. In-hospital death rate after hip fracture was low in this population (3.7%). Survival after hip fracture was correlated with age at hospitalization. About 12% of women alive at age 50 years will be hospitalized for a hip fracture at least once before they die. In this population, the incidence of hospitalization, in-hospital death rate, and lifetime probability of hip fracture were lower than in some other reports.

Actuarial Analysis↗

The probability of tsetse acquiring trypanosome infection from single blood meal in different localities in Kenya.

The probability of tsetse, Glossina pallidipes, acquiring a trypanosome infection from a single blood meal was estimated in five localities on the Kenya coast which were selected for differences in habitat and host availability. The probability that one blood meal contained infective Trypanosoma congolense was 0.0077 in rural areas with domestic animals, 0.0019 in extensive areas of natural habitat with wild hosts and 0.0013 in an area with domestic animals under regular chemoprophylaxis. The respective probabilities for T. vivax were 0.0010, 0.0024 and 0.0021.

Age Factors↗

Diagnosis of acute myocardial infarction from two measurements of creatine kinase isoenzyme MB with use of nonparametric probability estimation.

By using bivariate probability estimation for the diagnosis of acute myocardial infarction (AMI) we show how to overcome the difficulties encountered for patients whose clinical presentation is atypical and those encountered when multiple isoenzyme determinations are treated by univariate methods. We use the values for creatine kinase isoenzyme MB measured at the time of admission and 12 h later to estimate the Bayes factors in favor of AMI. The Bayes factors are compiled into a table that the clinician can use to estimate the posterior probability that a patient has AMI. The table of Bayes factors is based on data for a sample of 802 non-AMI patients and 180 AMI patients. Further to validate the method, we randomly chose 200 of the non-AMI and 50 of the AMI patients as an evaluation sample, then used the remaining 602 non-AMI and 130 AMI patients to recompute the Bayes factors. These Bayes factors were used to find the probability of AMI for each of the 250 patients in the evaluation sample. The method resulted in only one false positive and no false negatives. For the misclassified patient the measurements at admission and 12 h later were 1 and 11 U/L; the posterior odds were 15 to 1 in favor of AMI, but in fact the patient was non-AMI.

Creatine Kinase↗

Directional probability information and Down syndrome: a training study.

In previous studies we have found that subjects with Down syndrome did not respond to changes in directional probability within a complex motor task in the manner of other subjects with mental retardation (Blais & Kerr, 1986; Kerr & Blais, 1985). Only after extended practice were significant changes noted in their reaction time (RT) performance; however, movement time (MT) data remained relatively unchanged (Kerr & Blais, 1987). In the present study, subjects were given training relative to the directional probability component of the task (choice of direction). The subjects with Down syndrome did improve their subsequent performance, but primarily in terms of MT. Although they did adopt a pattern of responding to changes in directional probability (RT) similar to that of subjects without mental retardation, the nature of the change reflected the extent of previous exposure to the task.

Adolescent↗

Empirical validation of the Essen-Möller probability of paternity.

The validity of the Essen-Möller formulation probability of paternity is supported by demonstrating its correctness in a model genetic system--the ABO system. An analysis was made of 1,393 paternity cases typed uniformly for HLA-A and -B, ABO, Rh, and MNSs, in which the mother named one man only as the child's father and in which both mother and putative father identified themselves as Caucasian. For purposes of analysis, putative fathers not excluded from paternity by the four systems tested were regarded as actual fathers. The joint distribution of observed triplets of ABO phenotypes is shown to be statistically consistent with expected values, and the fractions of "true" fathers for a given triplet closely approximated the probability of paternity calculated using a realistic prior probability. Recent allegations of fallaciousness of the method by Li and Chakravarty and Aickin are discussed in terms of the results presented.

ABO Blood-Group System↗

The calculation of probabilities in rejecting bioequivalence.

Methods are given for deriving the lower and upper bounds of the probabilities for rejecting bioequivalence. Except when two formulations are nearly equal, the lower and upper bounds become very close and thus give an exact probability. The methods can be used in two- or higher-way crossover or parallel groups designs. One can also determine the sample size from the equations. The results are compared with the probabilities obtained by simulation.

Clinical Trials as Topic↗