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PubMed2000

Frequency versus probability formats in statistical word problems.

Three experiments examined people's ability to incorporate base rate information when judging posterior probabilities. Specifically, we tested the (Cosmides, L., & Tooby, J. (1996). Are humans good intuitive statisticians after all? Rethinking some conclusions from the literature on judgement under uncertainty. Cognition, 58, 1-73) conclusion that people's reasoning appears to follow Bayesian principles when they are presented with information in a frequency format, but not when information is presented as one case probabilities. First, we found that frequency formats were not generally associated with better performance than probability formats unless they were presented in a manner which facilitated construction of a set inclusion mental model. Second, we demonstrated that the use of frequency information may promote biases in the weighting of information. When participants are asked to express their judgements in frequency rather than probability format, they were more likely to produce the base rate as their answer, ignoring diagnostic evidence.

Adult↗

PubMed2002

Probability judgment in hierarchical learning: a conflict between predictiveness and coherence.

Why are people's judgments incoherent under probability formats? Research in an associative learning paradigm suggests that after structured learning participants give judgments based on predictiveness rather than normative probability. This is because people's learning mechanisms attune to statistical contingencies in the environment, and they use these learned associations as a basis for subsequent probability judgments. We introduced a hierarchical structure into a simulated medical diagnosis task, setting up a conflict between predictiveness and coherence. Thus, a target symptom was more predictive of a subordinate disease than of its superordinate category, even though the latter included the former. Under a probability format participants tended to violate coherence and make ratings in line with predictiveness; under a frequency format they were more normative. These results are difficult to explain within a unitary model of inference, whether associative or frequency-based. In the light of this, and other findings in the judgment and learning literature, a dual-component model is proposed.

Adult↗

PubMed1998

Probabilities for singleton and multiple pregnancies after in vitro fertilization.

OBJECTIVE: To help physicians provide risk estimates for specific pregnancy outcomes. DESIGN: Computation of exact binomial probabilities for singleton and multiple pregnancies as a function of two inputs: the number of embryos transferred and the implantation rate. Inputs were varied over the range of values reported in the literature. MAIN OUTCOME MEASURE(S): Probabilities for a singleton pregnancy (none), a multiple pregnancy (Pmult), and no pregnancy (Pnone) after one IVF cycle. RESULT(S): Given a 30% implantation rate and three embryos transferred, Pone=.44, Pmult=.22, and Pnone=.34. Although further increasing the number of embryos transferred increases the chance of pregnancy, it also raises the probability of a multiple pregnancy and lowers the chance of a singleton pregnancy. Although varying the implantation rate changes the specific probability estimates, the same trade-off persists. CONCLUSION(S): Those who consider an IVF "success" to be a singleton pregnancy should be attentive to the number of embryos transferred. Infertility therapy may be one area in medicine where more is not necessarily better.

Adult↗

PubMed1994

Probability of female-to-male transmission of HIV-1 in Thailand.

The epidemic of human immunodeficiency virus type 1 (HIV-1) infection in Thailand has allowed an estimate to be made of the probability of female-to-male HIV-1 transmission per sexual contact. In a study of 1115 21-year-old male military conscripts, of whom 77 (6.9%) were HIV-1 seropositive, sex with female prostitutes was identified as the principal mode of HIV-1 transmission. With a mathematical model including data on conscript's age at first sexual contact, frequency of sex with female prostitutes, and province of origin; as well as province-specific HIV-1 seroprevalence of prostitutes, we estimated the probability of HIV-1 transmission per sexual contact to be 0.031 (95% confidence limits [CL] 0.025-0.040). Allowing for random error in the self-reported frequency of contacts, the estimate was 0.056 (95% CL 0.041-0.075). The transmission probability was significantly greater among men with a history of sexually-transmitted diseases. These estimates are substantially higher than analogous estimates made in North America. This high per-act probability of heterosexual transmission helps to explain the rapid spread of HIV-1 in the emerging epidemic in Thailand and perhaps in other countries where HIV-1 transmission is predominantly heterosexual.

Adult↗

PubMed1997

P300 and probability: comparison of oddball and single-stimulus paradigms.

The P300 event-related brain potential (ERP) was elicited with auditory stimuli in two different tasks. The oddball paradigm presented both target and standard stimuli; the single-stimulus paradigm presented a target but no standard tone stimulus, with the inter-target interval the same as that for the oddball condition. Target stimulus probability was manipulated in the oddball task in different conditions (0.10, 0.30, 0.50, 0.70, 0.90). The single-stimulus paradigm employed the same procedures such that the inter-target interval was identical as that for the oddball condition across changes in probability. P300 amplitude and latency were similar for both the oddball and single-stimulus procedures across probability levels. Correlations between the P300 values from each task mimicked those from test-retest comparisons for the oddball paradigm. The findings suggest that P300 from the single-stimulus paradigm responds to target stimulus probability in the same fashion as the traditional oddball. The implications of the single-stimulus technique are discussed in terms of applied contexts that require very simple ERP task conditions.

Acoustic Stimulation↗

PubMedDate not supplied

Impact of survival probability, life expectancy, quality of life and patient preferences on do-not-attempt-resuscitation orders in a hospital. Resuscitation Committee.

Consensus exists that a do-not-attempt-resuscitation order (DNAR) is appropriate if a resuscitation attempt is futile. Less agreement exists when this point is reached. We investigated the influence of three major considerations for in-hospital DNAR orders: expected survival probability after resuscitation, prospects of the patients' current condition without a cardiac arrest and the patients' autonomous decision not to want resuscitation. We calculated an expected survival probability according to two multi-morbidity prediction scores for each patient, assuming the event of cardiac arrest. The prospects of the current condition without a cardiac arrest was estimated by the patients' physician, in terms of life expectancy and quality of life (level of dependency after discharge and pain). The patients' preference was documented from the medical records. A total of 470 patients were included in the study. Fifty-eight patients (12%) had a DNAR-order, 11 of these patients (19%) wanted no resuscitation. The patients' prospects (life expectancy, dependency after discharge), and age proved to be independently associated with the presence of a DNAR order. The odds ratio (OR) for the presence of a DNAR order was 37 (CL 14-107) for an estimated life expectancy less than 3 months, 13 (CL 4-41) for a life in a nursing home and four (CL 2-12) for an age of 80 years and older. Expected survival probability after resuscitation and pain were not independently associated with a DNAR order. We conclude that resuscitation is considered futile on the basis of the patients' age and prospects without cardiac arrest and that the impact of expected survival probability on these decisions is small.

Aged↗

PubMed1997

Potency probability following conformal megavoltage radiotherapy using conventional doses for localized prostate cancer.

PURPOSE: Impotence is a familiar sequela of definitive external beam radiation therapy (EBRT) for localized prostate cancer; however, nerve-sparing radical prostatectomy (NSRP) has offered potency rates as high as 70% for selected for patients in several large series. To the authors' knowledge, age and stage-matched comparisons between the effects of EBRT and NSRP upon the normal age trend of impotence have not been performed. Herein, we report the change in potency over time in an EBRT-treated population, determine the significantly predisposing health factors affecting potency in this population, and compare age and stage-matched potency rates with those of normal males and prostatectomy patients. METHODS AND MATERIALS: Our results are obtained from a retrospective study of 114 patients ranging in age from 52 to 85 (mean, 68) who were diagnosed with clinical stages A-C C (T1-T4N0M0) prostate cancer and then treated conformally with megavoltage x-rays to 6500-7000 cGy (180-200 cGy per fraction) using the four-field box technique. Information concerning pre-RT potency, medical and surgical history, and medications was documented for each patient as was time of post-RT change in potency during regular follow-up. The median follow-up time was 18.5 months. RESULTS: The actuarial probability of potency for all patients gradually decreased throughout post-RT follow-up. At months 1, 12, 24, and 36, potency rates were 98, 92, 75, and 66%, respectively. For those patients who became impotent, the median time to impotence was 14 months. Factors identified from logistic regression analysis as significant predictors of post-EBRT impotence include pre-EBRT partial potency (p < 0.001), vascular disease (p < 0.001), and diabetes (p = 0.003). Next, an actuarial plot of potency probability to patient age for the EBRT-treated population was compared to that obtained from the Massachusetts Male Aging Study of normal males. The two curves were not significantly different (logrank test, p = 0.741) between ages 50 and 65. Finally, potency probability after follow-up of 1 year or more in EBRT-treated patients was stratified by age and substratified by clinical stage and then compared to similarly stratified potencies for patients treated with NSRP. The prostatectomy data were derived from the pooled data of six large (total n, 952), independent series conducted at academic centers. For patients older than 70 years, 79.1% of EBRT patients and 32.9% of NSRP patients remained potent after treatment. For patients with stage B2 disease, 75.0% of EBRT patients and 49.3% of NSRP patients remained potent after treatment. Overall EBRT patient potency was 76.1% vs. 66.2% for NSRP patients. CONCLUSIONS: 1) By 36 months after completion of EBRT for localized prostate cancer, fully one-third of all patients becomes impotent; however, for patients younger than 70 years, the probability of impotence does not depart significantly from that for normal males. 2) In the EBRT-treated population, pre-EBRT partial potency, vascular disease, and diabetes are the most significant predispositions to the development of impotence. Patients with these predispositions, though, do not become impotent significantly earlier than other patients. 3) When comparing age and stage-stratified potency rates for EBRT and NSRP patients, potency is roughly equal for both modalities for most age and stage groups; however, for patients older than 70 years or with stage B2 disease, EBRT offers notably higher posttreatment potency rates than NSRP. Thus, for the treatment of localized prostate cancer, EBRT may not affect the normal age trend of impotence in younger patients and may induce impotence less frequently than NSRP in older patients or in patients with later stage disease.

Actuarial Analysis↗

PubMed1998

Hodgkin's disease: correlation of clinical characteristics with probabilities for negative lymphangiogram vs. negative laparotomy findings in patients with Stage I supradiaphragmatic presentations vs. those in patients with Stage II.

PURPOSE: At a time both when late complications and second malignancies have become a growing concern and when staging laparotomy has been largely abandoned and comparative studies for staging Hodgkin's disease by state of the art computed tomography (CT) vs. lymphangiography have revealed minimal differences in results for these procedures, our purpose for undertaking this study was twofold. Our initial reason was to determine and compare probabilities for negative abdominal findings for patients with Stage I presentations with those for patients with Stage II as determined by lymphangiography and subsequently by laparotomy for those patients who had negative lymphangiograms. Our second reason, being an extension of the first, was to create a resource that can be used in conjunction with other information for arriving at appropriate treatment decisions including giving either more or particularly less than standard institutional therapy and especially with respect to the abdomen. METHODS AND MATERIALS: Data on 714 patients with prelymphangiogram Stage I-II upper torso presentations of Hodgkin's disease were entered prospectively in our database between 1968 and 1987. Twenty-eight with lymphocyte predominant disease, who had both negative lymphangiogram and negative laparotomy findings and 17 with questionable diagnoses of lymphocyte-depleted or unclassified disease were excluded from subsequent analyses of 669 patients with nodular sclerosis (NS) and mixed cellularity (MC) diagnoses. RESULTS: Stage I: in final logistic models, negative lymphangiogram findings were associated strongly with a combination of no constitutional symptoms and nodular sclerosis histology, whereas negative laparotomy findings correlated strongly with a combination of no constitutional symptoms and female sex. Predicted probabilities depended on the ratios of favorable to unfavorable characteristics. Stage II: in final logistic models, negative lymphangiogram findings were associated strongly with a combination of no constitutional symptoms, nodular sclerosis histology, age <40 years, and <4 involved sites, whereas negative laparotomy findings correlated strongly with a combination of <4 involved sites and mediastinal disease. Predicted probabilities again depended on the ratios of favorable to unfavorable characteristics. CONCLUSION: This study demonstrated that probabilities for negative abdominal findings for patients with supradiaphragmatic presentations of NS and MC Hodgkin's disease depended on: 1) whether the disease presented as Stage I or as Stage II; 2) whether staging was limited to a lymphangiogram or whether it included a laparotomy; and 3) or whether the clinical features associated with the presenting stage and methods of staging were favorable or unfavorable.

Abdomen↗

PubMed2000

Beyond traditional paternity and identification cases. Selecting the most probable pedigree.

The paper extends on the traditional methodology used to quantify DNA evidence in paternity or identification cases. By extending we imply that there are more than two alternatives to choose between. In a standard paternity case the two competing explanations H(1): "John Doe is the father of the child and H(2): "A random man is the father of the child, are typically considered. A paternity index of 100000 implies that the data is 100000 more likely assuming hypothesis H(1) rather than H(2). If H(2) is replaced by "A brother of John Doe is the father", the LR may change dramatically. The main topic of this paper is to determine the most probable pedigree given a certain set of data including DNA profiles. In the previous example this corresponds to determining the most likely relation between John Doe and the child. Based on DNA obtained from victims of a fire, bodies found in an ancient grave or from individuals seeking to confirm their anticipated family relations, we would like to determine the most probable pedigree. The approach we present provides the possibility to combine non-DNA evidence, say age of individuals, and DNA profiles. The program familias, obtainable as shareware from http://www.nr.no/familias, delivers the probabilities for the various family constellations. More precisely, the information (if any) prior to DNA is combined with the DNA-profiles in a Bayesian manner to deliver the posterior probabilities. We exemplify using the well published Romanov data where the accepted solution emerges among 4536 possibilities considered. Various other applications based on forensic case work are discussed. In addition we have simulated data to resemble an incest case. Since the true family relation is known in this case, we may evaluate the method.

Adult↗

PubMed2002

Probability interrelations between pre-/post-stimulus intervals and ERD/ERS during a memory task.

OBJECTIVES: To investigate the functional relationship between oscillatory electroencephalographic (EEG) components (pre-/post-stimulus intervals) with audio-event-related desynchronization/synchronization (ERD/ERS). METHODS: In an experimental study (9 subjects), the probability-classification analysis of single-trial spectral EEG changes was utilized. Results were compared with auditory ERD/ERS. RESULTS: It was shown that (1) variability of EEG spectral patterns was considerable, (2) EEG activity was different at various task stages, (3) probability measures were different from the results of conventional frequency analysis, (4) probability of trials with alpha- and theta-patterns was characteristically different in various task stages, (5) the occurrence of alpha- and theta-trials were most probable, but not frequent enough to characterize all the trials. The results suggest that the ERD/ERS responses are influenced by EEG characteristics in the pre-stimulus interval, which also have a strong influence on the EEG in the post-stimulus interval. CONCLUSIONS: Alpha- and theta-ERD/ERS responses during memory task performance are not typical for all trials. They reflect EEG changes only in approximately 39% for alpha-activity and approximately 43% for theta-oscillations of all trials, what reflects piecewise stationary EEG structure.

Acoustic Stimulation↗

PubMed2003

A hypergeometric probability model for protein identification and validation using tandem mass spectral data and protein sequence databases.

We present a new probability-based method for protein identification using tandem mass spectra and protein databases. The method employs a hypergeometric distribution to model frequencies of matches between fragment ions predicted for peptide sequences with a specific (M + H)+ value (at some mass tolerance) in a protein sequence database and an experimental tandem mass spectrum. The hypergeometric distribution constitutes null hypothesis-all peptide matches to a tandem mass spectrum are random. It is used to generate a score characterizing the randomness of a database sequence match to an experimental tandem mass spectrum and to determine the level of significance of the null hypothesis. For each tandem mass spectrum and database search, a peptide is identified that has the least probability of being a random match to the spectrum and the corresponding level of significance of the null hypothesis is determined. To check the validity of the hypergeometric model in describing fragment ion matches, we used chi2 test. The distribution of frequencies and corresponding hypergeometric probabilities are generated for each tandem mass spectrum. No proteolytic cleavage specificity is used to create the peptide sequences from the database. We do not use any empirical probabilities in this method. The scores generated by the hypergeometric model do not have a significant molecular weight bias and are reasonably independent of database size. The approach has been implemented in a database search algorithm, PEP_PROBE. By using a large set of tandem mass spectra derived from a set of peptides created by digestion of a collection of known proteins using four different proteases, a false positive rate of 5% is demonstrated.

Amino Acid Sequence↗

PubMed2006

Vertical distribution and probability of encountering intertidal Exxon Valdez oil on shorelines of three embayments within Prince William Sound, Alaska.

We examined 32 shorelines selected at random in 2003 from shorelines in Herring Bay, Lower Pass, and Bay of Isles in Prince William Sound, Alaska, to examine the vertical distribution of oil remaining from the 1989 Exxon Valdez oil spill and to estimate the probability that sea otters and ducks would encounter oil while foraging there. On each shoreline, sampling was stratified by 1-m tide height intervals and randomly located 0.25 m2 sampling quadrats were examined for evidence of surface and subsurface oil. Oil from the T/V Exxon Valdezwasfound on 14 shorelines, mainly in Herring Bay and Lower Pass, with an estimated 0.43 ha covered by surface oil and 1.52 ha containing subsurface oil. Surface and subsurface oil were most prevalent near the middle of the intertidal and had nearly symmetrical distributions with respect to tide height. Hence, about half the oil is in the biologically rich lower intertidal, where predators may encounter it while disturbing sediments in search of prey. The overall probability of encountering surface or subsurface oil is estimated as 0.0048, which is only slightly greaterthan our estimated probability of encountering subsurface oil in the lower intertidal of Herring Bay or Lower Pass. These encounter probabilities are sufficient to ensure that sea otters and ducks that routinely excavate sediments while foraging within the intertidal would likely encounter subsurface oil repeatedly during the course of a year.

Accidents↗

PubMed2000

A two-locus forensic match probability for subdivided populations.

A two-locus match probability is presented that incorporates the effects of within-subpopulation inbreeding (consanguinity) in addition to population subdivision. The usual practice of calculating multi-locus match probabilities as the product of single-locus probabilities assumes independence between loci. There are a number of population genetics phenomena that can violate this assumption: in addition to consanguinity, which increases homozygosity at all loci simultaneously, gametic disequilibrium will introduce dependence into DNA profiles. However, in forensics the latter problem is usually addressed in part by the careful choice of unlinked loci. Hence, as is conventional, we assume gametic equilibrium here, and focus instead on between-locus dependence due to consanguinity. The resulting match probability formulae are an extension of existing methods in the literature, and are shown to be more conservative than these methods in the case of double homozygote matches. For two-locus profiles involving one or more heterozygous genotypes, results are similar to, or smaller than, the existing approaches.

Alleles↗

PubMed2000

Framing of outcome and probability of recurrence: breast cancer patients' choice of adjuvant chemotherapy (ACT) in hypothetical patient scenarios.

PURPOSE: To examine the effects of framing of outcome and probabilities of cancer occurrence on the treatment preference which breast cancer patients indicate for hypothetical patient scenarios. METHODS: A modified version of the Decision Board Instrument (Levine et al. 1992) was administered to 35 breast cancer patients with past ACT experience. Patients expressed their choice regarding ACT for six scenarios which were characterized by either negative or positive framing of outcome and by one of the three levels of probability of recurrence (high, medium, low). RESULTS: The framing had no influence on ACT choices over all three probability levels. The majority chose ACT for high and medium risk and one third switched from ACT to No ACT in the low-risk condition. This switch was statistically significant. CONCLUSION: Hypothetical treatment decisions against ACT occur only when the probability of recurrence is low and the benefit of ACT is small. This finding for patients with past experience of ACT is similar to those reported for other oncological patient groups still in treatment.

Adult↗

PubMed2001

Probabilities of transition among health states for older adults.

GOAL: To estimate the probabilities of transition among self-rated health states for older adults, and examine how they vary by age and sex. METHODS: We used self-rated health (excellent, very good, good, fair, poor, dead) collected in two longitudinal studies of older adults (mean age 75) to estimate the probability of transition in 2 years. We used the estimates to project future health for selected cohorts. FINDINGS: These older adults were most likely to be in the same health state 2 years later, but a substantial proportion changed in both directions. Transition probabilities varied by initial health state, age and sex. Men were more likely than women to transition to excellent or dead. Women were more likely than men to transition to good or fair health. Although women aged 70 will have more years of life and more years of healthy life than men, they also have more years of unhealthy life, and the proportion of remaining life that is healthy is slightly higher for men. When observed and predicted years of healthy life (YHL) were compared in various subgroups, the YHL of persons with less favorable baseline characteristics was lower than predicted, and vice-versa. Differences, however, were small (about 5%). CONCLUSIONS: These transition probability estimates can be used to predict the future health of individuals or groups as a function of current age, sex, and self-rated health.

Age Factors↗

PubMed2002

Forecasting trial outcomes: lawyers assign higher probability to possibilities that are described in greater detail.

The study of judgment under uncertainty has revealed that people judge the probability of an event to be higher when the event is described as a disjunction of constituent events or when they judge constituent events separately. These observations have motivated the development of support theory (Y. Rottenstreich & A. Tversky, 1997; A. Tversky & D. J. Koehler, 1994), a descriptive model of judgment under uncertainty. The major predictions of support theory are that (1) the judged probabilities of complementary events sum to 1; (2) the judged probabilities of n > 2 exclusive and exhaustive events generally sum to more than 1; and (3) the judged probability of an event generally increases when it is described as a disjunction of specific possibilities. We test these predictions in 6 studies of experienced attorneys who judged the likelihood of particular trial outcomes or were asked to offer advice on whether or not to accept a settlement offer. The results demonstrate that attorneys are indeed susceptible to bias in forecasting trial outcomes, consistent with support theory.

Forecasting↗

PubMed2003

Using thermal inactivation kinetics to calculate the probability of extreme spore longevity: implications for paleomicrobiology and lithopanspermia.

Thermal inactivation kinetics with extrapolation were used to model the survival probabilities of spores of various Bacillus species over time periods of millions of years at the historical ambient temperatures (25-40 degrees C) encountered within the 250 million-year-old Salado formation, from which the putative ancient spore-forming bacterium Salibacillus marismortui strain 2-9-3 was recovered. The model indicated extremely low-to-moderate survival probabilities for spores of mesophiles. but surprisingly high survival probabilities for thermophilic spores. The significance of the results are discussed in terms of the survival probabilities of (i) terrestrial spores in ancient geologic samples and (ii) spores transported between planets within impact ejecta.

Bacillus↗

PubMed2003

Facilitating normative judgments of conditional probability: frequency or nested sets?

Recent probability judgment research contrasts two opposing views. Some theorists have emphasized the role of frequency representations in facilitating probabilistic correctness; opponents have noted that visualizing the probabilistic structure of the task sufficiently facilitates normative reasoning. In the current experiment, the following conditional probability task, an isomorph of the "Problem of Three Prisoners" was tested. "A factory manufactures artificial gemstones. Each gemstone has a 1/3 chance of being blurred, a 1/3 chance of being cracked, and a 1/3 chance of being clear. An inspection machine removes all cracked gemstones, and retains all clear gemstones. However, the machine removes 1/2 of the blurred gemstones. What is the chance that a gemstone is blurred after the inspection?" A 2 x 2 design was administered. The first variable was the use of frequency instruction. The second manipulation was the use of a roulette-wheel diagram that illustrated a "nested-sets" relationship between the prior and the posterior probabilities. Results from two experiments showed that frequency alone had modest effects, while the nested-sets instruction achieved a superior facilitation of normative reasoning. The third experiment compared the roulette-wheel diagram to tree diagrams that also showed the nested-sets relationship. The roulette-wheel diagram outperformed the tree diagrams in facilitation of probabilistic reasoning. Implications for understanding the nature of intuitive probability judgments are discussed.

Adult↗