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PubMed1985

Paternity testing. 2: Likelihood ratio tests.

It is known that the so-called paternity index is also a likelihood ratio statistic for testing that an alleged father is the true father. Unfortunately the likelihood ratio test can sometimes lead to unsatisfactory results because of its dependence on the phenotype combinations of the mother and child. A new, conditional likelihood ratio test, which we call the ancillary test, is proposed in which statistical testing is carried out conditionally on the phenotypes of the mother and alleged father. An exact procedure is available which can be executed with reasonable facility on a microcomputer.

Blood Group Antigens↗

PubMed1998

Effects of a Relative-Frequency Elicitation Question on Likelihood Judgment Accuracy: The Case of External Correspondence.

In three experiments, college students judged the likelihood that they chose the correct alternative for each of 40 two-alternative, general-knowledge items. They responded either to a relative-frequency elicitation question ("Out of 100 questions for which you felt this certain of the answer, how many would you answer correctly?") or to a probability elicitation question ("What is the probability that you chose the correct answer?"). Judgments in response to the relative-frequency elicitation question tended to be lower, exhibit less scatter, and express complete certainty less often than judgments in response to the probability elicitation question. Two types of explanation for these effects are considered. First, the effect of the relative-frequency elicitation question may be to reduce random response error in participants' likelihood judgments. Second, the relative-frequency elicitation question may encourage the use of frequency information and simpler algorithms for making likelihood judgments. Copyright 1998 Academic Press.

Journal Article↗

PubMed2000

Familiarity Bias and Belief Reversal in Relative Likelihood Judgment.

People are often called on to make an assessment of the relative likelihood of events (e.g., which of two investments is more likely to outperform the market?) and their complements (which of the two investments is more likely to perform no better than the market?). Probability theory assumes that belief orderings over events and their complements should mirror each other (i.e., P(A) >/= P(B) iff P (not-A) </= P(not-B)). This principle is violated in several surveys in which we asked people to assess the relative likelihood of familiar versus unfamiliar events. In particular, respondents are biased to view more familiar events (and their complements) as more likely than less familiar events (and their complements). Similarly, we observe that subjects are biased to view less familiar events (and their complements) as less likely than more familiar events (and their complements). Further studies demonstrate that the familiarity bias is less pronounced among subjects who are asked to judge the probability of each event rather than which event is more likely. Moreover, a greater proportion of subjects rate the more familiar event as more likely than assign a higher probability to that event. These patterns can be construed as belief reversals, analogous to the preference reversal phenomenon in decision making. The data are consistent with a contingent weighting model in which the process of judging relative likelihood biases attention toward evidence supporting the target hypothesis (and away from evidence supporting its complement). Because it is easier to recruit evidence supporting familiar events than unfamiliar events, this skewed attention causes both familiar events and their complements to be judged more likely, on average, than unfamiliar events and their complements. Copyright 2000 Academic Press.

Journal Article↗

PubMed1995

A hybrid likelihood algorithm for risk modelling.

The risk of radiation-induced cancer is assessed through the follow-up of large cohorts, such as atomic bomb survivors or underground miners who have been occupationally exposed to radon and its decay products. The models relate to the dose, age and time dependence of the excess tumour rates, and they contain parameters that are estimated in terms of maximum likelihood computations. The computations are performed with the software package EPI-CURE, which contains the two main options of person-by person regression or of Poisson regression with grouped data. The Poisson regression is most frequently employed, but there are certain models that require an excessive number of cells when grouped data are used. One example involves computations that account explicitly for the temporal distribution of continuous exposures, as they occur with underground miners. In past work such models had to be approximated, but it is shown here that they can be treated explicitly in a suitably reformulated person-by person computation of the likelihood. The algorithm uses the familiar partitioning of the log-likelihood into two terms, L1 and L0. The first term, L1, represents the contribution of the 'events' (tumours). It needs to be evaluated in the usual way, but constitutes no computational problem. The second term, L0, represents the event-free periods of observation. It is, in its usual form, unmanageable for large cohorts. However, it can be reduced to a simple form, in which the number of computational steps is independent of cohort size. The method requires less computing time and computer memory, but more importantly it leads to more stable numerical results by obviating the need for grouping the data. The algorithm may be most relevant to radiation risk modelling, but it can facilitate the modelling of failure-time data in general.

Algorithms↗

PubMed1981

Evolutionary trees from DNA sequences: a maximum likelihood approach.

The application of maximum likelihood techniques to the estimation of evolutionary trees from nucleic acid sequence data is discussed. A computationally feasible method for finding such maximum likelihood estimates is developed, and a computer program is available. This method has advantages over the traditional parsimony algorithms, which can give misleading results if rates of evolution differ in different lineages. It also allows the testing of hypotheses about the constancy of evolutionary rates by likelihood ratio tests, and gives rough indication of the error of ;the estimate of the tree.

Base Sequence↗

PubMed1996

Using severity measures to predict the likelihood of death for pneumonia inpatients.

OBJECTIVE: To see whether predictions of patients, likelihood of dying in-hospital differed among severity methods. DESIGN: Retrospective cohort. PATIENTS: 18,016 persons 18 years of age and older managed medically for pneumonia; 1,732 (9.6%) in-hospital deaths. METHODS: Probability of death was calculated for each patient using logistic regression with age, age squared, sex, and each of five severity measures as the independent variables: 1) admission MedisGroups probability of death scores; 2) scores based on 17 admission physiologic variables; 3) Disease Staging's probability of mortality model; the Severity Score of Patient Management Categories (PMCs); 4) and the All Patient Refined Diagnosis-Related Groups (APR-DRGs). Patients were ranked by calculated probability of death; 5) rankings were compared across severity methods. Frequencies of 14 clinical findings considered poor prognostic indicators in pneumonia were examined for patients ranked differently by different methods. RESULTS: MedisGroups and the physiology score predicted a similar likelihood of death for 89.2% of patients. In contrast, the three code-based severity methods rated over 25% of patients differently by predicted likelihood of death when compared with the rankings of the two clinical data-based methods [MedisGroups and the physiology score]. MedisGroups and the physiology score demonstrated better clinical credibility than the three severity methods based on discharge abstract data. CONCLUSIONS: Some pairs of severity measures ranked over 25% of patients very differently by predicted probability of death. Results of outcomes studies may vary depending on which severity method is used for risk adjustment.

Adolescent↗

PubMed2001

The optimal reference population for cardiac normality in myocardial SPET in the detection of coronary artery stenoses: patients with normal coronary angiography or subjects with low likelihood of coronary artery disease?

Both subjects with a low likelihood for coronary artery disease (CAD) and patients with normal findings on coronary angiography have been used as reference populations in non-invasive stress testing, including myocardial perfusion scintigraphy. Both of these criteria of normality--low likelihood of CAD and normal coronary angiography--have been criticised, and consensus on this issue is lacking. The aim of this study was to compare two different reference populations by testing the performance of artificial neural networks designed to interpret myocardial scintigrams. The networks were trained on myocardial perfusion scintigrams from 87 patients with angiographically documented CAD and on studies from one of two different reference groups: 48 patients with no signs of CAD based on angiography or 128 healthy volunteers with a likelihood for CAD <5%. The performance of the two different networks was then tested using scintigrams from a separate test group of 68 patients. Coronary angiography was used as the gold standard in this group. The network trained on patients with no signs of CAD based on angiography showed an area under the receiver operating characteristic (ROC) curve of 93%. The ROC area for the network trained on healthy volunteers was 72%, and this difference was statistically significant (P=0.03). The results of this study using artificial neural networks suggest that normal angiography should be preferred as the reference standard in myocardial scintigraphy when a patient is examined for CAD prior to possible angiography. Whether the same is true for other indications, e.g. in prognostic evaluation, is unknown.

Adult↗

PubMed2004

Application of likelihood ratio and logistic regression models to landslide susceptibility mapping using GIS.

For landslide susceptibility mapping, this study applied and verified a Bayesian probability model, a likelihood ratio and statistical model, and logistic regression to Janghung, Korea, using a Geographic Information System (GIS). Landslide locations were identified in the study area from interpretation of IRS satellite imagery and field surveys; and a spatial database was constructed from topographic maps, soil type, forest cover, geology and land cover. The factors that influence landslide occurrence, such as slope gradient, slope aspect, and curvature of topography, were calculated from the topographic database. Soil texture, material, drainage, and effective depth were extracted from the soil database, while forest type, diameter, and density were extracted from the forest database. Land cover was classified from Landsat TM satellite imagery using unsupervised classification. The likelihood ratio and logistic regression coefficient were overlaid to determine each factor's rating for landslide susceptibility mapping. Then the landslide susceptibility map was verified and compared with known landslide locations. The logistic regression model had higher prediction accuracy than the likelihood ratio model. The method can be used to reduce hazards associated with landslides and to land cover planning.

Databases, Factual↗

PubMed1983

Estimating the likelihood of significant coronary artery disease.

Among 23 clinical characteristics examined in 3,627 consecutive, symptomatic patients referred for cardiac catheterization between 1969 and 1979, nine were found to be important for estimating the likelihood a patient had significant coronary artery disease. A model using these characteristics accurately estimated the likelihood of disease when applied prospectively to 1,811 patients referred since 1979 and when used to estimate the prevalence of disease in subgroups reported in the literature. Since accurate estimates of the likelihood of significant disease that are based on clinical characteristics are reproducible, they should be used in interpreting the results of additional noninvasive tests and in quantitating the added diagnostic value.

Adult↗

PubMed1986

Maximum likelihood alignment of DNA sequences.

The optimal alignment problem for pairs of molecular sequences under a probabilistic model of evolutionary change is equivalent to the problem of estimating the maximum likelihood time required to transform one sequence to the other. When this time has been estimated, various alignments of high posterior probability may be written down. A simple model with two parameters is presented and a method is described by which the likelihood may be computed. Maximum likelihood estimates for some pairs of tRNA genes illustrate the method and allow us to obtain the best alignments under the model.

Animals↗

PubMed1996

Maximum likelihood estimation of spontaneous mutation rates from large initial populations.

When estimating a spontaneous mutation rate from either a single culture (C=1) or from the C parallel cultures (C>1) of a fluctuation experiment, the use of a large initial population size N0 to seed each culture will permit a gaussian approximation for the probability distribution of the number M of mutants at the time when the culture(s) has (have) grown to size N=N02g, i.e., experienced g doublings. Using this gaussian approximation we find that the maximum likelihood estimate mu of the expected number mu of mutants present in a culture in generation g is (exactly) (equation: see text) where r = 2g / g and M 2 is the average of the squares of the C mutant counts. The maximum likelihood estimate p of the unknown mutation rate p is p = 2 mu / gN assuming an 'ideal' experiment and that there were no mutants in the initial population. A well-behaved maximum likelihood estimate is known to be efficient in large samples and we illustrate by Monte Carlo simulation that indeed p is better (has smaller mean squared error) than our previous (Rossman et al., 1995) estimator (equation: see text) (M is the average mutant count) provided N0 is of the order 1/p or larger. This advantage exists even without a fluctuation experiment, i.e., for C = 1.

Animals↗

PubMed1991

Likelihood ratios with confidence: sample size estimation for diagnostic test studies.

Confidence intervals are important summary measures that provide useful information from clinical investigations, especially when comparing data from different populations or sites. Studies of a diagnostic test should include both point estimates and confidence intervals for the tests' sensitivity and specificity. Equally important measures of a test's efficiency are likelihood ratios at each test outcome level. We present a method for calculating likelihood ratio confidence intervals for tests that have positive or negative results, tests with non-positive/non-negative results, and tests reported on an ordinal outcome scale. In addition, we demonstrate a sample size estimation procedure for diagnostic test studies based on the desired likelihood ratio confidence interval. The renewed interest in confidence intervals in the medical literature is important, and should be extended to studies analyzing diagnostic tests.

Epidemiology↗

PubMed2005

Factors associated with the likelihood of receiving second line therapy for advanced non-small cell lung cancer.

Second-line (SL) treatment has been shown to improve survival and quality of life outcomes for patients with stage IIIB/IV non-small cell lung cancer. However, only a minority of patients will receive SL therapy and the characteristics of this population have not been well described in the literature. In an effort to define the factors that predict who is likely to receive second line treatment, we performed an analysis on 230 patients with stage IIIB or IV non-small cell lung cancer who received first line therapy with carboplatin and paclitaxel. The median age of these patients was 63, and 144 (63%) were male, 200 (87%) had stage IV disease, 106 (46%) had a KPS of 90-100% and 124 (54%) had a KPS of 70-80%. The median number of cycles of first line chemotherapy was 4. Of these patients, 101 (44%) received second line therapy (median age 57 (range 45-76), 50% male and 37% KPS 90-100%). In the univariate analysis, younger age (P = 0.015), high baseline performance status (P = 0.002), non-squamous histology (P = 0.027), female gender (P = 0.0003), two or more cycles of therapy (P = 0.0004), four or more cycles of therapy (P = 0.001), and grade 2 or greater neuropathy (P = 0.024) were significantly associated with an increased likelihood of receiving SL therapy. In the multivariate model, high baseline performance status (OR = 2.05, P = 0.015), female gender (OR = 2.69, P = 0.001), non-squamous histology (OR = 1.98, P = 0.066), and two or more cycles of therapy (OR = 5.89, P = 0.002) remained significant. In conclusion, less than 50% of patients with stage IIIB/IV non-small cell lung cancer received SL treatment. Factors increasing the likelihood of second-line therapy include high performance status, female gender and non-squamous histology, while early termination of first-line therapy decreased the likelihood of further therapy.

Adult↗

PubMed1999

An experimental study of influences on the perceived likelihood of seeking genetic testing: "nondirectiveness" may be misleading.

It has been suggested that decision making involves the implicit weighing up of those advantages and disadvantages of possible options considered relevant at the time the decision is made. If this is so, the information that people have most readily available at the time of the decision would influence the decision outcome. The study reported here experimentally evaluates the effect of manipulating the issues on which individuals focus as a way of investigating subtle directive influences. Participants (n = 104) were interviewed about their anticipated likelihood of opting for testing for hereditary hemochromatosis. All participants were given standard information about hemochromatosis, including a description of the disorder as causing progressive damage over many years and an explanation that treatment is most effective if begun before the age of 30 years. Individuals were randomly allocated to groups according to age group (30 years and under, or over 30 years) and gender. Those allocated to the positive group were then encouraged to focus on positive aspects of the previously given information by considering the extent to which statements applied to them, whereas the negative group focused on negative aspects. The control group focused on an unrelated disease. Analyses of variance indicated that the focusing manipulation affected the likelihood of opting for testing. This effect interacted with age of respondent: in participants over 30, the positive group ratings of likelihood of testing increased, whereas in the negative group they decreased; in participants 30 and under, both the positive and negative groups showed an increased desire to be tested. The control group did not alter significantly. The relevance of these findings to "nondirective" approaches to genetic counseling is considered.

Adult↗

PubMed1998

Likelihood of spontaneous conversion of atrial fibrillation to sinus rhythm.

OBJECTIVES: We sought to determine the likelihood and predictors of spontaneous conversion to sinus rhythm of recent-onset atrial fibrillation (symptoms <72 h). BACKGROUND: Although spontaneous conversion of recent-onset atrial fibrillation is common, the likelihood and clinical and echocardiographic predictors have not been fully defined. Such data would be important for management of patients in whom early cardioversion is desired: Cardioversion could be delayed in patients with a high likelihood of spontaneous conversion, and it could be expeditiously pursued if spontaneous conversion is unlikely. METHODS: We screened 1,822 consecutive adults admitted to the hospital with atrial fibrillation and prospectively identified 356 patients (45% male, mean age +/- SD 68 +/- 16 years) with atrial fibrillation of <72-h duration. The occurrence of spontaneous conversion to sinus rhythm and clinical and echocardiographic data were identified through retrospective chart review. RESULTS: Spontaneous conversion to sinus rhythm occurred in 68% of the study group (n = 242; 95% confidence interval [CI] 63% to 73%). Among patients with spontaneous conversion, the total duration of atrial fibrillation was <24 h in 159 (66%), 24 to 48 h in 42 (17%) and >48 h in 41 (17%) (p < 0.001). Logistic regression analysis of clinical data identified presentation <24 h from onset of symptoms as the only predictor of spontaneous conversion (odds ratio 1.8, 95% CI 1.4 to 2.4, p < 0.0001). Normal left ventricular systolic function was more common among patients with spontaneous conversion (p = 0.03), but it was not an independent predictor of conversion. Left atrial dimension was similar between groups. CONCLUSIONS: Spontaneous conversion to sinus rhythm occurs in almost 70% of patients presenting with atrial fibrillation of <72-h duration. Presentation with symptoms of <24-h duration is the best predictor of spontaneous conversion.

Aged↗

PubMed1997

Bayesian nonparametric population models: formulation and comparison with likelihood approaches.

Population approaches to modeling pharmacokinetic and/or pharmacodynamic data attempt to separate the variability in observed data into within- and between-individual components. This is most naturally achieved via a multistage model. At the first stage of the model the data of a particular individual is modeled with each individual having his own set of parameters. At the second stage these individual parameters are assumed to have arisen from some unknown population distribution which we shall denote F. The importance of the choice of second stage distribution has led to a number of flexible approaches to the modeling of F. A nonparametric maximum likelihood estimate of F was suggested by Mallet whereas Davidian and Gallant proposed a semiparametric maximum likelihood approach where the maximum likelihood estimate is obtained over a smooth class of distributions. Previous Bayesian work has concentrated largely on F being assigned to a parametric family, typically the normal or Student's t. We describe a Bayesian nonparametric approach using the Dirichlet process. We use Markov chain Monte Carlo simulation to implement the procedure. We discuss each procedure and compare our approach with those of Mallet and Davidian and Gallant, using simulated data for a pharmacodynamic dose-response model.

Bayes Theorem↗

PubMed2000

Beyond valence in the perception of likelihood: the role of emotion specificity.

Positive and negative moods have been shown to increase likelihood estimates of future events matching these states in valence (e.g., E. J. Johnson & A. Tversky, 1983). In the present article, 4 studies provide evidence that this congruency bias (a) is not limited to valence but functions in an emotion-specific manner, (b) derives from the informational value of emotions, and (c) is not the inevitable outcome of likelihood assessment under heightened emotion. Specifically, Study 1 demonstrates that sadness and anger, 2 distinct, negative emotions, differentially bias likelihood estimates of sad and angering events. Studies 2 and 3 replicate this finding in addition to supporting an emotion-as-information (cf. N. Schwarz & G. L. Clore, 1983), as opposed to a memory-based, mediating process for the bias. Finally, Study 4 shows that when the source of the emotion is salient, a reversal of the bias can occur given greater cognitive effort aimed at accuracy.

Analysis of Variance↗

PubMed1995

Neural computation of log likelihood in control of saccadic eye movements.

The latency between the appearance of a visual target and the start of the saccadic eye movement made to look at it varies from trial to trial to an extent that is inexplicable in terms of ordinary 'physiological' processes such as synaptic delays and conduction velocities. An alternative interpretation is that it represents the time needed to decide whether a target is in fact present: decision processes are necessarily stochastic, because they depend on extracting information from noisy sensory signals. In one such model, the presence of a target causes a signal in a decision unit to rise linearly at a rate r from its initial value s0 until it reaches a fixed threshold theta, when a saccade is initiated. One can regard this decision signal as a neural estimate of the log likelihood of the hypothesis that the target is present, the threshold being the significance criterion or likelihood level at which the target is presumed to be present. Experiments manipulating the prior probability of the target's appearing confirm this notion: the latency distribution then changes in the way expected if s0 simply reflects the prior log likelihood of the stimulus.

Humans↗