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PubMed1993

Likelihood ratios for continuous test results--making the clinicians' job easier or harder?

Clinicians' paradigms for considering diagnostic test results require decisions based on the actual test value. However, when the test result is reported on a continuous scale each possible outcome may not result in unique actions. To simplify decision making, clinicians often break down the continuous scale into dichotomous or ordered outcomes. Likelihood ratios, reported with the test outcome, help summarize the impact of diagnostic tests. Although commonly applied to dichotomous outcomes, likelihood ratios can also be applied to ordinal or continuous results. This application allows investigators to consider the effect of clinically simplifying continuous data into dichotomous or ordinal categories. The parameters of a simple logistic regression equation summarize continuous likelihood ratios, evaluate covariates, generate likelihood ratio lines, and help assess the statistical significance of more complex models. Having visually inspected likelihood ratio lines and considered statistical differences, the investigator should choose the test report format that best accounts the realities driving clinical decisions.

Diagnosis↗

PubMed2006

Serum gamma glutamyltransferase as a marker of metabolic syndrome and coronary disease likelihood in nondiabetic middle-aged and elderly adults.

The role of serum gamma glutamyltransferase (GGT) activity as a cardiovascular risk marker was studied basically cross-sectionally. After appropriate exclusions, 754 men and 802 women were available for analysis who were followed up briefly yielding only 16% of overall cases of coronary heart disease (CHD). GGT activity was measured kinetically. In multivariate analysis across 12 variables, waist circumference, sex, complement C3, moderate alcohol intake and uric acid were significant independent covariates of serum GGT. By analyzing the sample in tertiles, doubling in GGT activity was found associated with a rise of 74% in metabolic syndrome (MS) likelihood-independent of salient confounders (P < 0.001). This association was mediated by waist circumference. Individuals in the top versus the bottom tertile exhibited an odds ratio for CHD likelihood of 1.81 (95% CI 1.09; 3.02)-independent of age, sex, total cholesterol, systolic blood pressure, impaired fasting glucose, smoking status, alcohol usage and, notably, of waist circumference. This indicated that a doubling in serum GGT activity corresponded to a 45% excess in CHD likelihood, after adjustment for standard risk factors. In conclusion, waist circumference is a major determinant of serum GGT activity among Turkish adults. Doubling in activity is associated with a (largely waist girth mediated) rise by over one-half in the multiadjusted MS likelihood, and by nearly one-half in the CHD likelihood, independent of waist girth and major risk factors.

Aged↗

PubMed1998

Predicting likelihood of seeking help through the employee assistance program among salaried and union hourly employees.

AIMS: This research investigated belief, social support and background predictors of employee likelihood to use an Employee Assistance Program (EAP) for a drinking problem. DESIGN: An anonymous cross-sectional survey was administered in the home. Bivariate analyses and simultaneous equations path analysis were used to explore a model of EAP use. SETTING: Survey and ethnographic research were conducted in a unionized heavy machinery manufacturing plant in the central states of the United States. PARTICIPANTS: A random sample of 852 hourly and salaried employees was selected. MEASUREMENTS: In addition to background variables, measures included: likelihood of going to an EAP for a drinking problem, belief the EAP can help, social support for the EAP from co-workers/others, belief that EAP use will harm employment, and supervisor encourages the EAP for potential drinking problems. FINDINGS: Belief in EAP efficacy directly increased the likelihood of going to an EAP. Greater perceived social support and supervisor encouragement increased the likelihood of going to an EAP both directly and indirectly through perceived EAP efficacy. Black and union hourly employees were more likely to say they would use an EAP. Males and those who reported drinking during working hours were less likely to say they would use an EAP for a drinking problem. CONCLUSIONS: EAP beliefs and social support have significant effects on likelihood to go to an EAP for a drinking problem. EAPs may wish to focus their efforts on creating an environment where there is social support from coworkers and encouragement from supervisors for using EAP services. Union networks and team members have an important role to play in addition to conventional supervisor intervention.

Adult↗

PubMed2005

Power and related statistical properties of conditional likelihood score tests for association studies in nuclear families with parental genotypes.

Both population based and family based case control studies are used to test whether particular genotypes are associated with disease. While population based studies have more power, cryptic population stratification can produce false-positive results. Family-based methods have been introduced to control for this problem. This paper presents the full likelihood function for family-based association studies for nuclear families ascertained on the basis of their number of affected and unaffected children. The likelihood of a family factors into the probability of parental mating type, conditional on offspring phenotypes, times the probability of offspring genotypes given their phenotypes and the parental mating type. The first factor can be influenced by population stratification, whereas the latter factor, called the conditional likelihood, is not. The conditional likelihood is used to obtain score tests with proper size in the presence of population stratification (see also Clayton (1999) and Whittemore & Tu (2000)). Under either the additive or multiplicative model, the TDT is known to be the optimal score test when the family has only one affected child. Thus, the class of score tests explored can be considered as a general family of TDT-like procedures. The relative informativeness of the various mating types is assessed using the Fisher information, which depends on the number of affected and unaffected offspring and the penetrances. When the additive model is true, families with parental mating type Aa x Aa are most informative. Under the dominant (recessive) model, however, a family with mating type Aa x aa(AA x Aa) is more informative than a family with doubly heterozygous (Aa x Aa) parents. Because we derive explicit formulae for all components of the likelihood, we are able to present tables giving required sample sizes for dominant, additive and recessive inheritance models.

Case-Control Studies↗

PubMed1997

Likelihood-mapping: a simple method to visualize phylogenetic content of a sequence alignment.

We introduce a graphical method, likelihood-mapping, to visualize the phylogenetic content of a set of aligned sequences. The method is based on an analysis of the maximum likelihoods for the three fully resolved tree topologies that can be computed for four sequences. The three likelihoods are represented as one point inside an equilateral triangle. The triangle is partitioned in different regions. One region represents star-like evolution, three regions represent a well-resolved phylogeny, and three regions reflect the situation where it is difficult to distinguish between two of the three trees. The location of the likelihoods in the triangle defines the mode of sequence evolution. If n sequences are analyzed, then the likelihoods for each subset of four sequences are mapped onto the triangle. The resulting distribution of points shows whether the data are suitable for a phylogenetic reconstruction or not.

Animals↗

PubMed1997

Maximum likelihood estimation of aggregated Markov processes.

We present a maximum likelihood method for the modelling of aggregated Markov processes. The method utilizes the joint probability density of the observed dwell time sequence as likelihood. A forward-backward recursive procedure is developed for efficient computation of the likelihood function and its derivatives with respect to the model parameters. Based on the calculated forward and backward vectors, analytical formulae for the derivatives of the likelihood function are derived. The method exploits the variable metric optimizer for search of the likelihood space. It converges rapidly and is numerically stable. Numerical examples are given to show the effectiveness of the method.

Markov Chains↗

PubMed1988

Children's expected interpersonal consequences of communicating their affective state and reported likelihood of expression.

This study explored several factors associated with expected outcome of emotional expression and likelihood of expression among children. These variables were posited to be a reflection of children's affective display rules. Differences in outcome expectancies and likelihood of expression were assessed as a function of sex of parent, sex of subject, grade, and type of affect. 125 first-, fourth-, and sixth-grade children (mean ages, 6-9, 9-2, and 11-7, respectively) were randomly assigned to 1 of 2 experimental conditions involving either sad or angry affect inductions. Older boys reported less positive expectancies and lower likelihood of expression than younger boys; and boys had less positive expectancies and lower likelihood of expression for sadness than girls. A high correlation was obtained between outcome expectancy and likelihood of expression; the correlation was higher for sadness than anger, and higher among males than females. These results suggest that socialization practices tend to be directed toward the suppression of sadness among males.

Age Factors↗

PubMed2005

Eliciting information from experts on the likelihood of rapid climate change.

The threat of so-called rapid or abrupt climate change has generated considerable public interest because of its potentially significant impacts. The collapse of the North Atlantic Thermohaline Circulation or the West Antarctic Ice Sheet, for example, would have potentially catastrophic effects on temperatures and sea level, respectively. But how likely are such extreme climatic changes? Is it possible actually to estimate likelihoods? This article reviews the societal demand for the likelihoods of rapid or abrupt climate change, and different methods for estimating likelihoods: past experience, model simulation, or through the elicitation of expert judgments. The article describes a survey to estimate the likelihoods of two characterizations of rapid climate change, and explores the issues associated with such surveys and the value of information produced. The surveys were based on key scientists chosen for their expertise in the climate science of abrupt climate change. Most survey respondents ascribed low likelihoods to rapid climate change, due either to the collapse of the Thermohaline Circulation or increased positive feedbacks. In each case one assessment was an order of magnitude higher than the others. We explore a high rate of refusal to participate in this expert survey: many scientists prefer to rely on output from future climate model simulations.

Journal Article↗

PubMed1994

Further studies of a maximum-likelihood yes-no procedure.

Absolute thresholds were estimated for pure tones of 500, 1000, and 2000 Hz using both a maximum-likelihood yes-no procedure and a traditional three-down one-up forced-choice adaptive procedure. Threshold estimates obtained with the two procedures were highly correlated. In the maximum-likelihood yes-no procedure, the false-alarm probability was poorly estimated. A simple change in that procedure produced less-biased estimates of the false-alarm rate. In a second experiment, the influence of the false-alarm rate on the threshold estimates was investigated. The listeners' absolute thresholds were estimated when they adopted either a liberal or conservative criterion for detecting the signals. Data were collected using both a constant-stimulus yes-no procedure and a maximum-likelihood yes-no procedure. Threshold estimates are 5 to 6 dB higher for the low than for the high false-alarm rates. Psychometric functions based on a stimulus-power model provided the best fit to the data obtained with the constant-stimulus method. This stimulus-power model was used to produce the assumed psychometric function in the maximum-likelihood yes-no procedure. Computer simulations were conducted to determine how threshold estimates were affected by the listener's inattention or by mismatches between the slope parameter of the listener's psychometric function and that assumed in the maximum-likelihood procedure.

Attention↗

PubMed1983

Extensions to pedigree analysis. V. Optimal calculation of Mendelian likelihoods.

Mendelian likelihoods are computed from human pedigree data for purposes of gene mapping, risk prediction in genetic counseling, and hypothesis testing in genetic epidemiology. The Mendelian likelihood of an extended pedigree can be written as a sum of products, the sum ranging over all possible genotypic combinations for the individuals in the pedigree. Exclusion of genotypes incompatible with the phenotypic information and pedigree structure reduces the ranges of summation and simplifies the likelihood calculation. To evaluate the likelihood with the fewest possible arithmetic operations requires carrying out the summations over one individual at a time and the intervening multiplications in some appropriate order. Each such removal of an individual reduces the likelihood evaluation to another evaluation of the same numerical form. Greedy-type algorithms are suggested for determining an order in which the summations and multiplications may be carried out. The greedy methods are fast and appear to generate good removal sequences. They are shown to work well when applied to a large, complex pedigree.

ABO Blood-Group System↗

PubMed2006

Variation in preoperative assessment of cardiac output reserve and likelihood of transfusion among anaesthetists: a pilot study.

The aim of this pilot study was to investigate anaesthetists' assessment of the ability of patients to increase cardiac output over a range of clinical scenarios and of their perceived 'likelihood of transfusion' in these scenarios. Specialist anaesthetists were given a questionnaire with clinical cues in the form of diagnoses about theoretical patients. They were asked to use 100 mm visual analogue scales (VAS) for their assessments of each patient's cardiac reserve and their 'likelihood of transfusion' of these patients; the endpoints of the VAS being 'Very low' (0 mm) to 'High' (100 mm), and 'Do not transfuse' (0 mm) to 'Transfuse' (100 mm) respectively. The assessment of patients' cardiac output reserve by anaesthetists (n = 54) showed great variation; for example, a patient with severe aortic stenosis was perceived overall to have a limited ability to increase cardiac output (mean VAS 16 mm) but there was considerable variation between anaesthetists (25-75 percentiles 10 mm to 21 mm). Assessment of 'likelihood of transfusion' (n = 42) also had great variation; as an example a patient with 'angina' with a haemoglobin of 95 g l(-1) was perceived overall to have an average likelihood of transfusion of 50 mm, but the 25-75 percentiles ranged from 33 mm to 71 mm. This study suggests that inter-anaesthetist variability in the assessment of a patient's 'cardiac output reserve' and his 'likelihood of transfusion' is large.

Anesthesia↗

PubMed2006

Likelihood of home death associated with local rates of home birth: influence of local area healthcare preferences on site of death.

OBJECTIVES: We tested whether local cultural and social values regarding the use of health care are associated with the likelihood of home death, using variation in local rates of home births as a proxy for geographic variation in these values. METHODS: For each of 351110 adult decedents in Washington state who died from 1989 through 1998, we calculated the home birth rate in each zip code during the year of death and then used multivariate regression modeling to estimate the relation between the likelihood of home death and the local rate of home births. RESULTS: Individuals residing in local areas with higher home birth rates had greater adjusted likelihood of dying at home (odds ratio [OR]=1.04 for each percentage point increase in home birth rate; 95% confidence interval [CI] = 1.03, 1.05). Moreover, the likelihood of dying at home increased with local wealth (OR=1.04 per $10000; 95% CI=1.02, 1.06) but decreased with local hospital bed availability (OR=0.96 per 1000 beds; 95% CI=0.95, 0.97). CONCLUSIONS: The likelihood of home death is associated with local rates of home births, suggesting the influence of health care use preferences.

Adult↗

PubMed2004

Asymptotic optimality of likelihood-based cross-validation.

Likelihood-based cross-validation is a statistical tool for selecting a density estimate based on n i.i.d. observations from the true density among a collection of candidate density estimators. General examples are the selection of a model indexing a maximum likelihood estimator, and the selection of a bandwidth indexing a nonparametric (e.g. kernel) density estimator. In this article, we establish a finite sample result for a general class of likelihood-based cross-validation procedures (as indexed by the type of sample splitting used, e.g. V-fold cross-validation). This result implies that the cross-validation selector performs asymptotically as well (w.r.t. to the Kullback-Leibler distance to the true density) as a benchmark model selector which is optimal for each given dataset and depends on the true density. Crucial conditions of our theorem are that the size of the validation sample converges to infinity, which excludes leave-one-out cross-validation, and that the candidate density estimates are bounded away from zero and infinity. We illustrate these asymptotic results and the practical performance of likelihood-based cross-validation for the purpose of bandwidth selection with a simulation study. Moreover, we use likelihood-based cross-validation in the context of regulatory motif detection in DNA sequences.

Journal Article↗

PubMed2004

Likelihood ratios: a simple and flexible statistic for empirical psychologists.

Empirical studies in psychology typically employ null hypothesis significance testing to draw statistical inferences. We propose that likelihood ratios are a more straightforward alternative to this approach. Likelihood ratios provide a measure of the fit of two competing models; the statistic represents a direct comparison of the relative likelihood of the data, given the best fit of the two models. Likelihood ratios offer an intuitive, easily interpretable statistic that allows the researcher great flexibility in framing empirical arguments. In support of this position, we report the results of a survey of empirical articles in psychology, in which the common uses of statistics by empirical psychologists is examined. From the results of this survey, we show that likelihood ratios are able to serve all the important statistical needs of researchers in empirical psychology in a format that is more straightforward and easier to interpret than traditional inferential statistics.

Empirical Research↗

PubMed1997

[Impact of androgen deprivation prior to radical prostatectomy for T1, T2 prostate cancer on the likelihood of curative surgery].

BACKGROUND: Extracapsular extension is commonly seen in patients undergoing radical prostatectomy for localized prostate cancer due to understaging of disease. One possible approach to reduce the likelihood of extracapsular disease is androgen deprivation prior to radical prostatectomy, neoadjuvant therapy. However, adequate application is not clear. We analyzed the outcome of neoadjuvant therapy and radical prostatectomy in an attempt to expand our understanding on indications of neoadjuvant therapy. METHODS: Forty-six selected patients with clinical T1 or T2 prostate cancer were retrospectively reviewed. Twenty-two patients underwent neoadjuvant therapy (group N) that mainly consists of LH-RH agonist. The duration of neoadjuvant therapy, varied from 1 to 12 months with the mean being 4 months. Twenty-four underwent radical prostatectomy alone (group S). RESULTS: In the group N and group S, 59% and 33% had either organ confined disease (OCD) or specimen confined disease (SCD) respectively. When the patients had OCD or SCD, they were defined as surgically cured patients. In the patients with clinical stage T1b, T1c, and T2 disease, likelihood of surgical cure were 100%, 50%, 46.7% in group N, 100%, 20%, 11%, in group S respectively. In the patients with initial serum PSA less than 10 ng/ml and more than 10.1 ng/ml, likelihood of surgical cure were 83.3% and 50% in group N, 63.6% and 15.4% in group S, respectively. Likelihood of surgical cure was higher in the patients with well differentiated carcinoma both in group N and group S. All the patients with serum PSA less than 0.1 ng/ml after neoadjuvant therapy had OCD. CONCLUSION: Neoadjuvent therapy could be beneficial either in the patients with moderately or in the poorly differentiated adenocarcinoma of prostate especially in the group with initial serum PSA more than 10.1 ng/ml. However, in patients both with well differentiated adenocarcinoma and the initial serum PSA less than 10 ng/ml, no evidence of beneficial effect on the likelihood of OCD or SCD was observed. PSA after neoadjuvant therapy could be useful predictor for the pathological outcome.

Aged↗

PubMed1996

A likelihood approach to meta-analysis with random effects.

In a meta-analysis of a set of clinical trials, a crucial but problematic component is providing an estimate and confidence interval for the overall treatment effect theta. Since in the presence of heterogeneity a fixed effect approach yields an artificially narrow confidence interval for theta, the random effects method of DerSimonian and Laird, which incorporates a moment estimator of the between-trial components of variance sigma B2, has been advocated. With the additional distributional assumptions of normality, a confidence interval for theta may be obtained. However, this method does not provide a confidence interval for sigma B2, nor a confidence interval for theta which takes account of the fact that sigma B2 has to be estimated from the data. We show how a likelihood based method can be used to overcome these problems, and use profile likelihoods to construct likelihood based confidence intervals. This approach yields an appropriately widened confidence interval compared with the standard random effects method. Examples of application to a published meta-analysis and a multicentre clinical trial are discussed. It is concluded that likelihood based methods are preferred to the standard method in undertaking random effects meta-analysis when the value of sigma B2 has an important effect on the overall estimated treatment effect.

Antihypertensive Agents↗

PubMed1999

Likelihoods and TDT for the case-parents design.

Association studies using diseased cases and their parents avoid biases due to population stratification, and the transmission/disequilibrium test (TDT) is a popular method of analysis. Sample size and power calculations for the TDT method have been reported, but often for the special situation of multiplicative effects of alleles on the genotype relative risks. Furthermore, some of the proposed calculations ignore the dependence of transmitted alleles from a pair of heterozygous parents when the effects are not multiplicative, which can lead to erroneous sample size calculations. We demonstrate how to calculate sample size and power for the TDT method for general genotype relative risks. As an alternative to the TDT method, we present likelihood methods for a variety of genotype relative risk models. Exact likelihood methods are presented to allow for accurate small-sample analyses. We demonstrate by numerical comparisons: (1) that the TDT method is inefficient for recessive patterns of relative risks, (2) for alleles that are not rare, falsely assuming a multiplicative model can lead to gross underestimation of the required sample size for the TDT statistic, and (3) for common alleles, if the true genotype relative risks have an approximately dominant pattern, then the TDT method can be grossly inefficient compared to likelihood methods. An alternative likelihood ratio statistic, based on two degrees of freedom, tends to be robust for a wide range of genotype relative risk models. Finally, we discuss how to use standard software for conditional logistic regression to accurately assess effects of alleles as well as genotype-environment interaction.

Genome, Human↗

PubMedDate not supplied

Modelling spatial disease rates using maximum likelihood.

This paper concerns maximum likelihood estimation for a generalized linear mixed model (GLMM) useful for modelling spatial disease rates. The model allows for log-linear covariate adjustment and local smoothing of rates through estimation of spatially correlated random effects. The covariance structure of the random effects is based on a recently proposed model which parameterizes spatial dependence through the inverse covariance matrix. A Markov chain Monte Carlo algorithm for performing maximum likelihood estimation for this model is described. Results of a computer simulation study that compared maximum likelihood (ML) and penalized quasi-likelihood (PQL) estimators are presented. Compared with PQL, ML produced less biased estimates of the intercept but the ML estimates were slightly more variable. Estimates of the other regression coefficients were unbiased and nearly identical for the two methods. ML estimators of the random effects standard deviation and spatial correlation were more biased than the corresponding PQL estimators. The conclusion is that ML estimators for GLMMs cannot be expected to perform better than PQL for small samples.

Algorithms↗