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PubMed1999

The importance of specifying the underlying biologic model in estimating the probability of causation.

There are a number of contexts in which interested parties wish to estimate the probability that an individual's injury was caused by radiation or a toxic chemical. It has been shown, however, that such calculations cannot be made based on epidemiologic data alone, without assumption of a biologic model for the disease process and without a specific definition of causation. To illustrate the relevant theorems, we present a number of examples in which different biologic models produce different values for the probability of causation for individuals from the same population-based epidemiologic data and dose-response curves. As a result of these ambiguities, it is important that anyone attempting to calculate probability of causation for individuals explicitly state the biologic model that has been assumed, as well as state the definition of causation being used. The analyst should test the robustness of the calculations by repeating them for a broad range of underlying biologic models.

Female↗

PubMed1988

Predicting rehabilitation outcomes from clinical and statistical data: a probability model.

This research was focused on the feasibility of a Markov Chain probability model for predicting rehabilitation outcome. A combination of clinical ratings from counselors and statistical data from client files was used to predict 'successful' and 'unsuccessful' outcomes. Predictions were made at three separate time periods: Time 1, during the first week after initial interview; Time 2, during the fourth week after initial interview; and Time 3, during the thirteenth week after initial interview. The final outcome was determined at the end of six months. The research sample consisted of seventy-one clients from two private rehabilitation agencies, all of whom suffered from work-related injuries or illnesses. The results of this research indicate that a Markov Chain probability model is quite feasible for predicting rehabilitation outcomes. In addition, it was observed that the predictions generally followed a progression over time toward stronger and more accurate predictions for both 'success' and 'failure'. With only one exception, occurring at Time 1, the clinical ratings from the counselors were shown to be stronger predictors than the statistical data from case files. This finding is inconsistent with previous studies. It is suggested that a model such as this can serve to alert counselors to the possible need for different or more innovative strategies for service to clients who show a poor probability for success.

Accidents, Occupational↗

PubMed1996

Probability of heterosexual transmission of HIV: relationship to the number of unprotected sexual contacts. European Study Group in Heterosexual Transmission of HIV.

The objective of this study was to investigate the relationship between the number of unprotected heterosexual contacts with an HIV-infected person and the probability of HIV transmission. Data from a European study involving 563 heterosexual partners of HIV-infected subjects were analyzed. The number of unprotected contacts could be estimated for 525 couples (377 with male index case, 148 with female index case) from the reported frequency of unprotected contacts and an estimate of the length of the period during which transmission could have occurred. Nonparametric (isotonic regression) and parametric (Bernoulli model) analyses were performed on data at study entry and on follow-up data (121 couples). The nonparametric analysis resulted in several exposure groups, with the proportion of infected partners increasing with the number of contacts. For example, the percentage of female partners infected ranged from 10%, among those with < 10 unprotected contacts with an infected male, to 23% after 2,000 unprotected contacts. The parametric estimates of (assumed constant) per-contact infectivity were higher for male-to-female than for female-to-male transmission, but not significantly so. However, in comparison with nonparametric estimates, the model assuming constant infectivity appears to seriously underestimate the risk after very few contacts and to seriously overestimate the risk associated with a large number of contacts. Our results suggest that the association between the number of unprotected sexual contacts and the probability of infection is weak and highly inconsistent with constant per-contact infectivity. Probable explanations for these findings include large variability in infectivity between couples and within individuals over time. Estimates based on partner study data under the hypothesis of constant infectivity can, therefore, be highly misleading at a public health level, particularly when extrapolated to multiple casual contacts.

Disease Transmission, Infectious↗

PubMed2002

Age-specific survival and reproductive probabilities: evidence for senescence in male fallow deer (Dama dama).

Survival and reproduction are key features in the evolution of life-history strategies. In this study, we use capture-mark-resighting and multi-state models to examine survival senescence and reproductive senescence in six successive cohorts of fallow bucks that were studied for 16 years. We found that the overall age-specific survival probabilities of males were highly variable and the best-fitting model revealed that fallow bucks have four life-history stages: yearling, pre-reproductive, prime-age and senescent. Pre-reproductive males (2 and 3 years old) had the highest survival. Survival declined sharply after the age of 9 years, indicating that senescence had begun. When we considered reproducing and non-reproducing males separately, there was no evidence of senescence in the former, and steadily decreasing survival after the onset of social maturity in the latter. Reproduction probability also declined in older males, and thus we provide very strong evidence of senescence. Reproducers had a greater chance of reproducing again in the following year than non-reproducers. Furthermore, there were differences in the survival probabilities, with reproducers consistently surviving better than non-reproducers. In our study population, reproducers allocate more to the effort to reproduce than non-reproducers. Therefore our results indicate the generally higher phenotypic quality of reproducing males. These results, along with earlier studies on the same population, could indicate positive relationships between fitness correlates.

Age Factors↗

PubMed2005

Genotypic probabilities for pairs of inbred relatives.

Expressions for the joint genotypic probabilities of two related individuals are used in many population and quantitative genetic analyses. These expressions, resting on a set of 15 probabilities of patterns of identity by descent among the four alleles at a locus carried by the relatives, are generally well known. There has been recent interest in special cases where the two individuals are both related and inbred, although there have been differences among published results. Here, we return to the original 15-probability treatment and show appropriate reductions for relatives when they are drawn from a population that itself is inbred or when the relatives have parents who are related. These results have application in affected-relative tests for linkage, and in methods for interpreting forensic genetic profiles.

Breeding↗

PubMed2005

On the probability that a novel variant is a disease-causing mutation.

When a novel variant is found in a patient and not in a group of controls, it becomes a candidate for the disease-causing mutation in that patient. At present, no sampling theory exists for assessing the probability that the novel SNP might actually be a neutral variant. We have developed a population genetics-based method for calculating a P-value for a mutation-detection effort. Our method can be applied to a heterozygous patient, a homozygous patient, with or without inbreeding, or to a patient who is a compound heterozygote. Additionally, the method can be used to calculate the probability of finding a neutral variant at frequencies that differ between a group of patients and a group of controls, given some length of sequence examined. This method accounts for the multiple testing that is inherent in identification of variants through sequencing, to be used in subsequent case-control analyses. We show, for example, that for complete resequencing of 10 kb, the probability of finding a neutral variant in a patient and not in 50 controls is about 15%. Thus, discovery of a variant in a patient and not in a group of controls is, on its own, very weak evidence of involvement with disease.

Animals↗

PubMed2000

Continuous probability distributions from finite data.

Recent approaches to the problem of inferring a continuous probability distribution from a finite set of data have used a scalar field theory for the form of the prior probability distribution. This paper presents a more general form for the prior distribution that has a geometrical interpretation and can improve the specificity of likely solutions. It is also demonstrated that a numerical sampling of the posterior probability distribution can be used as an alternative to a histogram for visualization and to make probabilistic inferences from the data.

Fourier Analysis↗

PubMed1990

A probability representation for phase information from multiwavelength anomalous dispersion.

A probability distribution function, cast in the representation of Hendrickson & Lattman [Acta Cryst. (1970), B26, 136-143], has been derived for the phase information from measurements of multiwavelength anomalous diffraction (MAD). This probability function readily permits one to determine figure-of-merit weights similar to those used in isomorphous replacement, and the coefficients that characterize this distribution function facilitate the combining of MAD phasing with results from other sources of phase information. This probability representation was derived in the course of a structural analysis of selenobiotinyl streptavidin from MAD data and applications have also been made in the structure determinations of interleukin-1 alpha and a drug complex with brominated DNA.

Bacterial Proteins↗

PubMed2000

Capture-recapture when time and behavioral response affect capture probabilities.

We consider a capture-recapture model in which capture probabilities vary with time and with behavioral response. Two inference procedures are developed under the assumption that recapture probabilities bear a constant relationship to initial capture probabilities. These two procedures are the maximum likelihood method (both unconditional and conditional types are discussed) and an approach based on optimal estimating functions. The population size estimators derived from the two procedures are shown to be asymptotically equivalent when population size is large enough. The performance and relative merits of various population size estimators for finite cases are discussed. The bootstrap method is suggested for constructing a variance estimator and confidence interval. An example of the deer mouse analyzed in Otis et al. (1978, Wildlife Monographs 62, 93) is given for illustration.

Animals↗

PubMed2000

Estimating transition probabilities from aggregate samples plus partial transition data.

Longitudinal studies often collect only aggregate data, which allows only inefficient transition probability estimates. Barring enormous aggregate samples, improving the efficiency of transition probability estimates seems to be impossible without additional partial-transition data. This paper discusses several sampling plans that collect data of both types, as well as a methodology that combines them into efficient estimates of transition probabilities. The method handles both fixed and time-dependent categorical covariates and requires no assumptions (e.g., time homogeneity, Markov) about the population evolution.

Acquired Immunodeficiency Syndrome↗

PubMed2002

Estimation of integrated transition hazards and stage occupation probabilities for non-Markov systems under dependent censoring.

We propose nonparametric estimators of the stage occupation probabilities and transition hazards for a multistage system that is not necessarily Markovian, using data that are subject to dependent right censoring. We assume that the hazard of being censored at a given instant depends on a possibly time-dependent covariate process as opposed to assuming a fixed censoring hazard (independent censoring). The estimator of the integrated transition hazard matrix has a Nelson-Aalen form where each of the counting processes counting the number of transitions between states and the risk sets for leaving each stage have an IPCW (inverse probability of censoring weighted) form. We estimate these weights using Aalen's linear hazard model. Finally, the stage occupation probabilities are obtained from the estimated integrated transition hazard matrix via product integration. Consistency of these estimators under the general paradigm of non-Markov models is established and asymptotic variance formulas are provided. Simulation results show satisfactory performance of these estimators. An analysis of data on graft-versus-host disease for bone marrow transplant patients is used as an illustration.

Biometry↗

PubMed2003

Modeling the dependence between number of trials and success probability in beta-binomial-Poisson mixture distributions.

Beta-binomial models are widely used for overdispersed binomial data, with the binomial success probability modeled as following a beta distribution. The number of binary trials in each binomial is assumed to be nonrandom and unrelated to the success probability. In many behavioral studies, however, binomial observations demonstrate more complex structures. In this article, a general beta-binomial-Poisson mixture model is developed, to allow for a relation between the number of trials and the success probability for overdispersed binomial data. An EM algorithm is implemented to compute both the maximum likelihood estimates of the model parameters and the corresponding standard errors. For illustration, the methodology is applied to study the feeding behavior of green-backed herons in two southeastern Missouri streams.

Algorithms↗

PubMed2001

The probability that beneficial mutations are lost in populations with periodic bottlenecks.

Population bottlenecks affect the dynamics of evolution, increasing the probability that beneficial mutations will be lost. Recent protocols for the experimental study of evolution involve repeated bottlenecks-when fresh media are inoculated during serial transfer or when chemostat tubes are changed. Unlike population reductions caused by stochastic environmental factors, these bottlenecks occur at known, regular intervals and with a fixed dilution ratio. We derive the ultimate probability of extinction for a beneficial mutation in a periodically bottlenecked population, using both discrete and continuous approaches. We show that both approaches yield the same approximation for extinction probability. From this, we derive an approximate expression for an effective population size.

Biological Evolution↗

PubMed1982

Comparison of two recently published algorithms for assessing the probability of adverse drug reactions.

1 A simple valid and reliable method for estimating the probability of adverse drug reactions (adverse drug reactions probability scale, APS) has been recently described (Naranjo et al., 1981a). 2 The results using APS were compared to those obtained with another more detailed algorithm (adverse reactions scoring system, ASS) described by Kramer et al. (1979). 3 Sixty-three randomly selected adverse drug reactions (ADRs) were rated by two observers, using APS and ASS one year apart. The cases were ordered in a random sequence. Between-raters reliability using APS (R(est) = 0.96 and ASS (R(est) = 0.86), was very high. 4 ADR scores obtained with both methods were highly correlated (r = 0.82, P less than 0.001). However, time spent using ASS was significantly longer (paired t-test, t = 1.70, P less than 0.05). 5 These results suggest that while ASS is somewhat more complex than APS both are equally reliable and will give very similar conclusions regarding the probability of ADRs. Such algorithms must be used if the clinical assessment of ADRs is to become acceptably reliable.

Drug-Related Side Effects and Adverse Reactions↗

PubMed2006

Variation in probability of first reproduction of Weddell seals.

1. For many species, when to begin reproduction is an important life-history decision that varies by individual and can have substantial implications for lifetime reproductive success and fitness. 2. We estimated age-specific probabilities of first-time breeding and modelled variation in these rates to determine age at first reproduction and understand why it varies in a population of Weddell seals in Erebus Bay, Antarctica. We used multistate mark-recapture modelling methods and encounter histories of 4965 known-age female seals to test predictions about age-related variation in probability of first reproduction and the effects of annual variation, cohort and population density. 3. Mean age at first reproduction in this southerly located study population (7.62 years of age, SD=1.71) was greater than age at first reproduction for a Weddell seal population at a more northerly and typical latitude for breeding Weddell seals (mean=4-5 years of age). This difference suggests that age at first reproduction may be influenced by whether a population inhabits the core or periphery of its range. 4. Age at first reproduction varied from 4 to 14 years, but there was no age by which all seals recruited to the breeding population, suggesting that individual heterogeneity exists among females in this population. 5. In the best model, the probability of breeding for the first time varied by age and year, and the amount of annual variation varied with age (average variance ratio for age-specific rates=4.3%). 6. Our results affirmed the predictions of life-history theory that age at first reproduction in long-lived mammals will be sensitive to environmental variation. In terms of life-history evolution, this variability suggests that Weddell seals display flexibility in age at first reproduction in order to maximize reproductive output under varying environmental conditions. Future analyses will attempt to test predictions regarding relationships between environmental covariates and annual variation in age at first reproduction and evaluate the relationship between age at first reproduction and lifetime reproductive success.

Age Factors↗

PubMed1998

A risk score to predict the probability of postoperative vomiting in adults.

BACKGROUND: The aim of this study was to identify factors most relevant for postoperative vomiting (PV) and to develop a risk score to predict the probability of PV. METHODS: Adult inpatients scheduled for elective ear, nose and throat (ENT) surgery under general anaesthesia were offered to participate in a prospective study for PV over 24 h. No prophylactic antiemetics were used. The data of 1137 patients were randomized and split into an evaluation set (n=553) and a validation set (n=584). The evaluation set was subjected to logistic regression analysis to quantify the relative impact of anaesthetic, surgical and individual factors and to develop a risk score. The score was then tested by applying it to the validation set. The area under a receiver operation characteristic (ROC) curve was calculated and the predicted and actual incidences of patients were correlated. RESULTS: In the evaluation set, patient-related factors (female gender, young age, non-smoking, history of PV or motion sickness) and a high duration of anaesthesia were independent risk factors for PV. The probability of PV could be estimated from the equation: PV=1/(1+exp(-z)) where z=1.28 (gender)-0.029 (age)-0.74 x (smoking)+0.63 x (history of PV or motion sickness)+0.26 x (duration)-0.92. In the validation set this score achieved an area under the ROC-curve of 0.78 and the actual incidence correlated strongly with the predicted risks (R2=0.93, P<0.001). CONCLUSION: The data suggest that the probability of PV following ENT surgery under inhalational anaesthesia with low-dose opioids can be predicted by a score mainly based upon patient-related risk factors.

Adult↗

PubMed1978

Effect of 5-bromodeoxyuridine on differentiation. I. Probability distribution of BUdR-containing DNA-strands in subsequent divisions.

The consequences on transcription of BUdR substitution of the normal thymidine in nuclear DNA are analyzed from a probabilistic point of view. The probability that at any stage subsequent to the administration of BUdR, a randomly chosen cell will be able to make good transcripts is calculated both under the assumption that incorporation of BUdR is complete and under the assumption that incorporation is partial. In the latter case both gradually increasing and decreasing incorporation rates are considered. The presented calculations may be of value for the investigation of any type of differentiating cells. Using the example of the sea urchin embryo it is shown how to calculate the probability that a particular group of cells, which in further development differentiate to a certain organ, will inherit as sufficient number of essential genes unaffected by BUdR in order to ensure a normal development. It is shown that the probability that the four macromeres (or micromeres) in the vegetal half of the 16-cell stage of the sea urchin embryo will contain at least one, two or four plus (or minus) strands of DNA uninfluenced by BUdR gradually decreases the earlier BUdR is administered. The theoretical calculations are in agreement with experimental observations on sea urchin embryos (described in part II).

Animals↗

PubMed1978

On the probability of demonstrating differential fertility in genetic studies.

Computer simulation has been used to investigate the probability of detecting genetic differences in fertility in small cohorts. It was found that in cohorts of size 200 which have the demographic characteristics of females born in the United States in 1921--5, the probability is approximately 0.50 of detecting, by analysis of variance, either a 20% reduction in the monthly probability of conception or a 15--20% increase in the rate of foetal loss in the first month after conception. Consideration is given to the relative sensitivities of various observable measures of fertility to variation in underlying fertility components.

Abortion, Spontaneous↗