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PubMed2004

The interobserver reliability of pretest probability assessment in patients with suspected pulmonary embolism.

INTRODUCTION: Pretest probability assessment and objective testing are combined to appropriately manage patients with suspected pulmonary embolism (PE). However, the interobserver reliability of pretest probability assessment has not been investigated. We sought to determine (for patients with suspected PE) the interobserver reliability of pretest probability assessment (by overall impression (gestalt) versus an explicit clinical model). MATERIALS AND METHODS: A prospective cohort study was conducted at an urban university hospital. For patients referred for ventilation and perfusion (V/Q) scanning for suspected PE, structured assessments (11 history and 4 physical examination parameters) were performed by a referring physician and a designated thrombosis physician. The referring and thrombosis physicians also assigned a pretest probability for PE (low, moderate, or high) by gestalt. An explicit seven-point clinical model for suspected PE was later applied to each structured assessment to determine the pretest probability. Assessments were performed independently and prior to diagnostic test results. Interobserver reliability (two rater unweighted Kappa (kappa) statistic) was determined for each parameter on the structured assessment and the pretest probability assessments (gestalt vs. explicit clinical model). RESULTS: One hundred and ten patients with suspected PE received duplicate assessments. Historical features demonstrated substantial to almost perfect interobserver reliability (kappa=0.60-0.95). For the physical findings, only heart rate had substantial interobserver reliability (kappa=0.60). Pretest probability assessment was not reliable when using physician's gestalt (kappa=0.33), but produced substantial interobserver reliability using the explicit clinical model (kappa=0.62). CONCLUSIONS: Given the inadequate interobserver reliability of pretest probability assessment by overall impression (or gestalt), physicians should use explicit clinical models in the diagnostic management of patients with suspected pulmonary embolism.

Adolescent↗
PubMed2003

A structured clinical model for predicting the probability of pulmonary embolism.

PURPOSE: To develop a structured model to predict the clinical probability of pulmonary embolism. METHODS: We studied 1,100 consecutive patients with suspected pulmonary embolism in whom a definite diagnosis had been established. We used logistic regression analysis to estimate the probability of pulmonary embolism based on patients' clinical characteristics; the probability was categorized as low (< or = 10%), intermediate (>10%, < or = 50%), moderately high (>50%, < or = 90%), or high (>90%). RESULTS: The overall prevalence of pulmonary embolism was 40% (n = 440). Ten characteristics were associated with an increased risk of pulmonary embolism (male sex, older age, history of thrombophlebitis, sudden-onset dyspnea, chest pain, hemoptysis, electrocardiographic signs of acute right ventricular overload, radiographic signs of oligemia, amputation of the hilar artery, and pulmonary consolidation suggestive of infarction), and five were associated with a decreased risk (prior cardiovascular or pulmonary disease, high fever, pulmonary consolidation other than infarction, and pulmonary edema on the chest radiograph). With this model, 432 patients (39%) were rated a low probability, of whom 19 (4%) had pulmonary embolism; 283 (26%) were rated an intermediate probability, of whom 62 (22%) had pulmonary embolism; 72 (7%) were rated a moderately high probability, of whom 53 (74%) had pulmonary embolism; and 313 (28%) were rated a high probability, of whom 306 (98%) had pulmonary embolism. CONCLUSION: This prediction model may be useful for estimating the probability of pulmonary embolism before obtaining definitive test results.

Adolescent↗
PubMed2003

Dependency effects in multi-locus match probabilities.

For finite populations, differences in individual histories can cause between-locus allelic dependencies even for unlinked loci. The main motivation for this study is to quantify the effect of such dependencies on genotypic match probabilities. We compare the two-locus match probability, the probability that two individuals (four gametes) chosen at random will have the same genotype at both loci, with the probability computed as the product of the one-locus match probabilities. It is demonstrated that the product rule probability always underestimates the two-locus match probability. For highly mutable minisatellite loci, these probabilities can differ by an order of magnitude or more. A simplified three-locus problem is explored, providing evidence that the degree of under-estimation worsens for more loci.

Alleles↗
PubMed1996

P300, probability, and the three-tone paradigm.

The effects of stimulus probability on P300 from a 3-tone paradigm were examined in two experiments. Experiment 1 manipulated the probability of the non-target tone as 0.10, 0.45, or 0.80, while the target tone probability was always 0.10. Experiment 2 manipulated the probability of 3 tones as 0.10, 0.30, or 0.60, with one of the infrequent tones assigned as the target in each condition. Subjects were required to press a button in response to the target stimulus in both experiments. The results indicated that the P300 to the target and the non-target were both affected by the probability of the eliciting stimulus, such that component amplitude was inversely related to probability; no reliable P300 latency effects were found. Target tones elicited larger P300 amplitude than the non-target tones at the same probability. The findings suggest that probability effects on P300 amplitude are independent of responding to a specific target stimulus and are discussed with reference to the clinical utility of the 3-tone paradigm.

Acoustic Stimulation↗
PubMed1998

Probabilities and health risks: a qualitative approach.

Health risks, defined in terms of the probability that an individual will suffer a particular type of adverse health event within a given time period, can be understood as referencing either natural entities or complex patterns of belief which incorporate the observer's values and knowledge, the position adopted in the present paper. The subjectivity inherent in judgements about adversity and time frames can be easily recognised, but social scientists have tended to accept uncritically the objectivity of probability. Most commonly in health risk analysis, the term probability refers to rates established by induction, and so requires the definition of a numerator and denominator. Depending upon their specification, many probabilities may be reasonably postulated for the same event, and individuals may change their risks by deciding to seek or avoid information. These apparent absurdities can be understood if probability is conceptualised as the projection of expectation onto the external world. Probabilities based on induction from observed frequencies provide glimpses of the future at the price of acceptance of the simplifying heuristic that statistics derived from aggregate groups can be validly attributed to individuals within them. The paper illustrates four implications of this conceptualisation of probability with qualitative data from a variety of sources, particularly a study of genetic counselling for pregnant women in a U.K. hospital. Firstly, the official selection of a specific probability heuristic reflects organisational constraints and values as well as predictive optimisation. Secondly, professionals and service users must work to maintain the facticity of an established heuristic in the face of alternatives. Thirdly, individuals, both lay and professional, manage probabilistic information in ways which support their strategic objectives. Fourthly, predictively sub-optimum schema, for example the idea of AIDS as a gay plague, may be selected because they match prevailing social value systems.

Attitude of Health Personnel↗
PubMed2003

Probability of late rectal morbidity in 125I prostate brachytherapy.

PURPOSE: Rectal toxicity is a concern in prostate brachytherapy because it is difficult to avoid delivering a dose equal to, or greater than, the prescription dose to the anterior surface of the rectum. The purpose of this study was to define the probability that a patient will experience Grade 2 (bleeding/ulceration) late rectal morbidity after 125I prostate brachytherapy according to the rectal dosimetry. METHODS AND MATERIALS: Ninety-eight consecutive patients who received monotherapy 125I prostate implants for treatment of Stage T1-T2, favorable-risk adenocarcinoma of the prostate were evaluated for Radiation Therapy Oncology Group Grade 2 late rectal morbidity. All reported incidences of late morbidity were retrospectively confirmed by colonoscopy. All patients had at least 15 months follow-up after implantation. The median follow-up was 32 months (range 15-54). The rectal dosimetry was based on a CT scan obtained at 3-9 weeks after implantation. The rectum was contoured on each CT image between the base and apex of the prostate. A dose-surface histogram was compiled for each implant, and the relative surface area that received a dose > or =100, > or =150, > or =200, > or =300, > or =400, and > or =500 Gy was recorded. The probability of developing late rectal toxicity was calculated by logistic regression analysis as a function of dose and the percentage of the rectal surface that received that dose. RESULTS: Of the 98 patients, 10 developed Grade 2 late rectal morbidity. The percentage of the rectal surface that received 100, 150, 200, and 300 Gy was significantly greater (p < or =0.02) for patients who experienced late rectal morbidity. The probability of late rectal morbidity increased with both the dose and the percentage of the rectal surface that received that dose. The probability was < or =1% when 20%, 7%, and 0% of the rectal surface received 100, 150, and 200 Gy, respectively. The probability increased to < or =5% when 31%, 19%, and 9% of the rectal surface received these doses. The probability of late rectal morbidity can also be expressed in terms of the maximal rectal dose. The probability of late morbidity was 0.4%, 1.2%, and 4.7% when the maximal rectal dose was 150, 200, and 300 Gy, respectively. CONCLUSION: The percentage of the rectal surface that receives a dose > or =100 Gy is predictive of Grade 2 (bleeding/ulceration) late rectal morbidity after 125I prostate brachytherapy. The probability of late morbidity depends on both the dose and the percentage of the rectal surface that received that dose. Our results indicate that the rectum can tolerate doses of 100, 150, and 200 Gy to approximately 30%, 20%, and 10% of the rectal surface with a < or =5% risk of late morbidity. Our results also indicate that the practical guideline for limiting the incidence of late morbidity to 1%, 3%, or 5% is to keep the maximal rectal dose to <200, 250, and 300 Gy, respectively.

Adenocarcinoma↗
PubMed1999

Inclusion of geometrical uncertainties in radiotherapy treatment planning by means of coverage probability.

PURPOSE: Following the ICRU-50 recommendations, geometrical uncertainties in tumor position during radiotherapy treatments are generally included in the treatment planning by adding a margin to the clinical target volume (CTV) to yield the planning target volume (PTV). We have developed a method for automatic calculation of this margin. METHODS AND MATERIALS: Geometrical uncertainties of a specific patient group can normally be characterized by the standard deviation of the distribution of systematic deviations in the patient group (Sigma) and by the average standard deviation of the distribution of random deviations (sigma). The CTV of a patient to be planned can be represented in a 3D matrix in the treatment room coordinate system with voxel values one inside and zero outside the CTV. Convolution of this matrix with the appropriate probability distributions for translations and rotations yields a matrix with coverage probabilities (CPs) which is defined as the probability for each point to be covered by the CTV. The PTV can then be chosen as a volume corresponding to a certain iso-probability level. Separate calculations are performed for systematic and random deviations. Iso-probability volumes are selected in such a way that a high percentage of the CTV volume (on average > 99%) receives a high dose (> 95%). The consequences of systematic deviations on the dose distribution in the CTV can be estimated by calculation of dose histograms of the CP matrix for systematic deviations, resulting in a so-called dose probability histogram (DPH). A DPH represents the average dose volume histogram (DVH) for all systematic deviations in the patient group. The consequences of random deviations can be calculated by convolution of the dose distribution with the probability distributions for random deviations. Using the convolved dose matrix in the DPH calculation yields full information about the influence of geometrical uncertainties on the dose in the CTV. RESULTS: The model is demonstrated to be fast and accurate for a prostate, cervix, and lung cancer case. A CTV-to-PTV margin size which ensures at least 95% dose to (on average) 99% of the CTV, appears to be equal to about 2Sigma + 0.7sigma for three all cases. Because rotational deviations are included, the resulting margins can be anisotropic, as shown for the prostate cancer case. CONCLUSION: A method has been developed for calculation of CTV-to-PTV margins based on the assumption that the CTV should be adequately irradiated with a high probability.

Female↗
PubMed2003

Cumulative probability of neodymium: YAG laser posterior capsulotomy after phacoemulsification.

PURPOSE: To retrospectively analyze the cumulative probability of neodymium:YAG (Nd:YAG) laser posterior capsulotomy after phacoemulsification and to evaluate the risk factors. SETTING: Ando Eye Clinic, Kanagawa, Japan. METHODS: In 3997 eyes that had phacoemulsification with an intact continuous curvilinear capsulorhexis, the cumulative probability of posterior capsulotomy was computed by Kaplan-Meier survival analysis and risk factors were analyzed using the Cox proportional hazards regression model. The variables tested were sex; age; type of cataract; preoperative best corrected visual acuity (BCVA); presence of diabetes mellitus, diabetic retinopathy, or retinitis pigmentosa; type of intraocular lens (IOL); and the year the operation was performed. The IOLs were categorized as 3-piece poly(methyl methacrylate) (PMMA), 1-piece PMMA, 3-piece silicone, and acrylic foldable. RESULTS: The cumulative probability of capsulotomy after cataract surgery was 1.95%, 18.50%, and 32.70% at 1, 3, and 5 years, respectively. Positive risk factors included a better preoperative BCVA (P =.0005; risk ratio [RR], 1.7; 95% confidence interval [CI], 1.3-2.5) and the presence of retinitis pigmentosa (P<.0001; RR, 6.6; 95% CI, 3.7-11.6). Women had a significantly greater probability of Nd:YAG laser posterior capsulotomy (P =.016; RR, 1.4; 95% CI, 1.1-1.8). The type of IOL was significantly related to the probability of Nd:YAG laser capsulotomy, with the foldable acrylic IOL having a significantly lower probability of capsulotomy. The 1-piece PMMA IOL had a significantly higher risk than 3-piece PMMA and 3-piece silicone IOLs. CONCLUSIONS: The probability of Nd:YAG laser capsulotomy was higher in women, in eyes with a better preoperative BCVA, and in patients with retinitis pigmentosa. The foldable acrylic IOL had a significantly lower probability of capsulotomy.

Acrylic Resins↗
PubMed2002

An empirical comparison of discrete ratings and subjective probability ratings.

RATIONALE AND OBJECTIVES: The authors compared receiver operating characteristic (ROC) data from a five-category discrete scale with that from a 101-category subjective probability scale to determine how well the latter categories define the ROC curve. MATERIALS AND METHODS: The authors analyzed data from a pilot study performed for another purpose in which 10 radiologists provided both a five-point confidence rating and a subjective probability rating of abnormality for each interpretation. ROC operating points were plotted for a five-category scale and a 101-category scale to determine how well the observed points covered the range of false-positive probabilities. ROC curves were fitted to the subjective probability data according to the standard ROC model. RESULTS: For these data, subjective probability ratings were somewhat more effective in populating the range of false-positive probability with ROC points. For three observers, the ROC curves inappropriately crossed the chance line. For another four, prevention of such crossing seemed to depend on one or two ROC points near the upper right corner of the ROC space, points based on discriminations within the discrete category "no abnormality to report." CONCLUSION: Subjective probability rating should provide substantially better coverage of the ROC space with operating points, preventing inappropriate crossing of the chance line. Unfortunately, the protection offered by subjective probability ratings was unreliable and depended on ROC points derived from discriminations not directly related to apparent abnormality. The use of proper ROC models to fit data may offer a better solution.

Observer Variation↗
PubMed1999

Probabilities of marriage in two outer Hebridean islands, 1861-1990.

A study has been made of the probabilities of marriage of females and males aged 15-49 (either as a whole or in 5-year age groups) in two Outer Hebridean islands, Harris and Barra. The results were compared with ages of marriage and with the frequencies of permanent celibacy. The marriages took place between 1861 and 1990. Median ages of marriage rose to maxima in the 1930s and 1940s, then fell steeply, levelling out latterly. Permanent celibacy was consistently high among females, but rose from much lower levels in males to maxima in the 1970s and 1980s. It is concluded that in these populations age at marriage and the extent of permanent celibacy are largely independent of one another. In both islands the overall probabilities of females marrying fell until the 1920s, and then rose. The last decades showed stability (Barra) and a fall (Harris). Males showed only slight falls to about 1910; data were absent for between 1911 and 1960, but subsequently there was little rise in probability. These overall changes seemed to be associated with reciprocal variations in probabilities in the younger and older age groups. Declining overall probabilities were associated with declines in younger and increases in older age-group probabilities, and vice versa. Non-parametric correlations between median ages of marriage and probability of marriage were negative and generally significant for the 15-19 age group. Among the older age groups coefficients were generally positive. There was some evidence of an association between probability of marriage and sex ratio in any group of potential mates. The effect appeared more marked among 15- to 19-year-old females. Local factors which might explain at least part of the decline in nuptiality for the greater part of the period under study include the decline in the fishing industry and the 'land hunger' which existed until the late 1920s. This decline is interpreted as a 'Malthusian' response to economic and social conditions, but it coexisted with a 'neo-Malthusian' strategy, in the shape of declining marital fertility. The 'Malthusian' strategy seems to have been largely abandoned around the 1950s, but it may have reappeared during the 1980s.

Adolescent↗
PubMed2006

Directional verbal probabilities: inconsistencies between preferential judgments and numerical meanings.

Verbal probability expressions (e.g., it is possible or doubtful) convey not only vague numerical meanings (i.e., probability) but also semantic functions, called directionality. We performed two experiments to examine whether preferential judgments are consistent with numerical meanings of verbal probabilities regardless of directionality. The results showed that because of the effects of directionality, perceived degrees of certainty for verbal probabilities differed between a binary choice and a numerical translation (Experiment 1), and decisions based on a verbal probability do not correspond to those based on a numerical translation for verbal probabilities (Experiment 2). These findings suggest that directionality of verbal probabilities is an independent feature from numerical meanings; hence numerical meanings of verbal probability alone remain insufficient to explain the effects of directionality on preferential judgments.

Choice Behavior↗
PubMed1999

Naive probability: a mental model theory of extensional reasoning.

This article outlines a theory of naive probability. According to the theory, individuals who are unfamiliar with the probability calculus can infer the probabilities of events in an extensional way: They construct mental models of what is true in the various possibilities. Each model represents an equiprobable alternative unless individuals have beliefs to the contrary, in which case some models will have higher probabilities than others. The probability of an event depends on the proportion of models in which it occurs. The theory predicts several phenomena of reasoning about absolute probabilities, including typical biases. It correctly predicts certain cognitive illusions in inferences about relative probabilities. It accommodates reasoning based on numerical premises, and it explains how naive reasoners can infer posterior probabilities without relying on Bayes's theorem. Finally, it dispels some common misconceptions of probabilistic reasoning.

Cognition↗
PubMed2006

Three-month stability of delay and probability discounting measures.

Psychopharmacologists are interested in delay and probability discounting because the tendency to discount the value of future and uncertain rewards has been linked with drug dependency. However, relatively little is known about the long-term stability of discounting measures typically studied in clinical psychopharmacology. To evaluate the stability of discounting over a 3-month period, the authors compared points of subjective equality (indifference points) with those collected from the same subjects 3 months earlier. Seven delay periods, ranging from 1 week to 25 years, and 7 probability values, ranging from .95 to .05, were assessed in an undergraduate sample (n=22, delay discounting; n=18, probability discounting). The authors examined both differential stability (stability of individual differences) and absolute stability (stability of the group mean) of delay and probability discounting measures as well as their respective indifference points. The results demonstrate that standard delay and probability discounting parameters (e.g., hyperbolic k and area under the curve) had both differential stability and absolute stability across 3 months. Moreover, most indifference points in the delay and probability discounting tasks demonstrated both differential and absolute stability. All together, these results suggest that delay and probability parameters are stable enough to predict future behavior, such as substance abuse. Additional findings indicated that a hyperbolic function fitted the data better than an exponential function and that delay and probability discounting parameters were not significantly correlated.

Adult↗
PubMed1981

Deviations from Michaelis-Menten kinetics. Computation of the probabilities of obtaining complex curves from simple kinetic schemes.

1. It is possible to calculate the intrinsic probability associated with any curve shape that is allowed for rational functions of given degree when the coefficients are independent or dependent random variables with known probability distributions. 2. Computations of such probabilities are described when the coefficients of the rational function are generated according to several probability distribution functions and in particular when rate constants are varied randomly for several simple model mechanisms. 3. It is concluded that each molecular mechanism is associated with a specific set of curve-shape probabilities, and this could be of value in discriminating between model mechanisms. 4. It is shown how a computer program can be used to estimate the probability of new complexities such as extra inflexions and turning points as the degree of rate equations increases. 5. The probability of 3 : 3 rate equations giving 2 : 2 curve shapes is discussed for unrestricted coefficients and also for the substrate-modifier mechanisms. 6. The probability associated with the numerical values of coefficients in rate equations is also calculated for this mechanism, and a possible method for determining the approximate magnitude of product-release steps is given. 7. The computer programs used in the computations have been deposited as Supplement SUP 50113 (21 pages) with the British Library Lending Division, Boston Spa, Wetherby, West Yorkshire LS23 7BQ, U.K., from whom copies can be obtained on the terms indicated in Biochem, J. (1978) 169, 5.

Binding Sites↗
PubMed1981

The probability that complex enzyme kinetic curves can be caused by activators of inhibitors.

Numerous chemical compounds are known that alter the rate of conversion of substrates into products in enzyme-catalysed reactions by interacting with the enzyme rather than substrates. Where this takes place in such a way that the effect is reversible on removing the compound, say by dialysis, and where the compound is unchanged chemically by the enzyme system, we refer to such a compound as a modifier. So protons, inorganic salts, activators, inhibitors or even specific allosteric effectors would all be modifiers, and any chemically reasonable kinetic scheme that is proposed to account for such effects is referred to as modifier mechanism. Three versions of a modifier mechanism of enzyme action are studied. The implicit representation is 2:2 in [S] (with alpha(0)=0) and 2:2 in [M] (with alpha(0) not equal0), and this is a short-hand scheme for the minimum chemical formulation, the explicit one, involving discrete ES and EP species, which is 2:2 in [S] (with alpha(0)=0) and 3:3 in [M] (with alpha(0) not equal0). If m extra steps are allowed between interconversion of ES and EP species, the degree of the rate equation remains 2:2 in [S] (with alpha(0)=0), but increases to degree (m+3):(m+3) in modifier (with alpha(0) not equal0). It is proved that this increase in degree is genuine and that highly complex v([M]) (i.e. v-versus-[M]) curves can occur. Computation of the probabilities of the five possible double-reciprocal plots in 1/v versus 1/[S] show that all of these formulations of the modifier mechanism give similar probabilities, and these are characteristic for the mechanism and quite distinct from the intrinsic curve-shape probabilities. It is also established that the probabilities of alternative complex v([M]) plots are similar for the various formulations, and again the probabilities of the allowed complex curves for the mechanism are quite distinct from the instrinsic probabilities of the ten possible v([M]) curves for a 2:2 function (with alpha(0) not equal0). The computer studies reported lead to several conclusions about the probability of modifiers leading to inhibition or activation or causing changes in v([S]) curve shapes, and suggest that differentiation between model mechanisms may be facilitated by knowledge of the intrinsic curve-shape probabilities for the appropriate degree rational function and the characteristic way that this is altered by specific mechanisms. It is shown that, although in some instances new curve-shape complexities are possible when schemes are considered that allow for interconversion of ES and EP species, these are highly improbable and, for theoretical purposes, schemes formulated with node compression provide good approximations to the more complicated explicit schemes. By node compression we refer to the procedure whereby enzyme kinetic schemes are simplified by replacing sequences of steps such as ESright harpoon over left harpoonX(1)right harpoon over left harpoonX(2)right harpoon over left harpoon...right harpoon over left harpoonEP... by a single step... ES/EP... that does not formally recognize the existence of the intermediate species. We show that the modifier mechanism studied is one where this process alters the form of the rate equation.

Computers↗
PubMed2001

Risk communication and older people-understanding of probability and risk information by medical inpatients aged 75 years and older.

OBJECTIVE: To determine older people's understanding of probability and risk information, and the impact of pictorial representation of risk. DESIGN: A researcher-administered questionnaire. SUBJECTS: 50 inpatients aged > or =75 years on elderly medicine wards at Huddersfield Royal Infirmary, Huddersfield, UK. RESULTS: Older people understand percentage probability better than fractional probability, and a wide range of incorrect responses indicated significant over- and underestimation of probabilities. Visual data about percentages were well received and understood, and were perceived as a good idea by participants. CONCLUSIONS: We have demonstrated a wide variation in understanding of risk and probability information by older people, with over- and underestimations of probability, along with confusion between fractional and percentage probability. Pictorial representation of probability was well understood. It could be developed as a simple, yet powerful communication tool to be used in daily clinical practice to help older people understand information on risks and benefits when making decisions about treatment choices.

Aged↗
PubMed2001

Trends in the incidence of births and multiple births and the factors that determine the probability of multiple birth after IVF treatment.

BACKGROUND: We aimed to review trends in the probability of birth and multiple birth before and after the legal restriction limiting the maximum allowable number of embryos transferred, and to examine factors that determine the probability of multiple birth following IVF treatment. METHODS: We analysed data relating to 7170 IVF and 530 intracytoplasmic sperm injection cycles reaching embryo transfer undertaken by 4417 women at a single tertiary referral assisted conception centre in the UK between 1984 and 1997. Probability of birth, and of proportion of multiple births among those who gave birth, was explored using logistic regression analysis. RESULTS: Between 1984 and 1997 there was a significant increase in probability of birth but no change in the probability of multiple birth. The trend in probability of birth was almost wholly explained by the significant increase in number of embryos created per cycle. Pooling all the data, risk factors for increased chance of birth and multiple birth were: younger age (<35 years), diagnoses other than tubal infertility, fewer than three previous unsuccessful cycles, previous IVF live birth and a large number of embryos created. Given these factors, increasing the number of embryos transferred did not increase the chance of a birth, but did increase the chance of a multiple birth. CONCLUSIONS: The probability of birth has increased and the probability of multiple birth has remained unchanged, despite legislation limiting the number of embryos transferred in the UK. Efforts should be made to reduce the incidence of multiple births by transferring fewer embryos, especially in the presence of good prognostic factors for birth.

Adult↗
PubMed1993

Probability-summation model of multiple laser-exposure effects.

A probability-summation model is introduced to provide quantitative criteria for discriminating independent from interactive effects of multiple laser exposures on biological tissue. Data that differ statistically from predictions of the probability-summation model indicate the action of sensitizing (synergistic/positive) or desensitizing (hardening/negative) biophysical interactions. Interactions are indicated when response probabilities vary with changes in the spatial or temporal separation of exposures. In the absence of interactions, probability-summation parsimoniously accounts for "cumulative" effects. Data analyzed using the probability-summation model show instances of both sensitization and desensitization of retinal tissue by laser exposures. Other results are shown to be consistent with probability-summation. The relevance of the probability-summation model to previous laser-bioeffects studies, models, and safety standards is discussed and an appeal is made for improved empirical estimates of response probabilities for single exposures.

Humans↗