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Results for “Likelihood Functions”

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PubMed1999

A GEE moving average analysis of the relationship between air pollution and mortality for asthma in Barcelona, Spain.

Several studies have assessed the association between air pollution and hospital admissions or emergency room visits for asthma. Because of both the presence of missing data and the small number of observations, the relationship between air pollution and mortality for respiratory causes has been rarely analysed, and when it has, the results are very inconclusive or even inconsistent. The objective of this study is to assess the relation between levels of air pollutants (black smoke, sulphur dioxide, nitrogen dioxide and ozone), meteorological variables (24th average temperature and relative humidity) and daily mortality for asthma (ICD-9 493, 2 to 45 years old) in Barcelona, Spain, during the period 1986-1989. Since the range of daily mortality for asthma (2 to 45 years old) during the period 1986-1989 was 0-1), we have preferred to consider this variable as dichotomous. First, the relationship between air pollutants, meteorological variables and daily mortality (controlled for the occurrence of asthma epidemics) was estimated using logistic regression models. As was expected, the residuals from this regression were autocorrelated, showing a complex moving average (MA) structure. If covariates were not time dependent the so-called generalized linear mixed models, could be applied. In our case the covariates vary. As a consequence the likelihood is numerically intractable because it involves the evaluation of n-fold integral. An alternative method that avoids these numerical problems is the generalized estimating equations method (GEE). It is a multivariate analogue of quasi-likelihood estimation. In the absence of a likelihood function the parameters can be estimated by solving a multivariate analogue of the quasi score function. We have modified the GEE method in this paper, allowing for a different structure in the error covariance matrix (MA). Both air pollutants and meteorological variables are related with the occurrence of a death for asthma. In this sense, nitrogen dioxide, NO(2) (ss=0.037, p<0. 05), ozone, O(3) (ss=0.021, p<0.06) and high temperature (the ss's were in the range (0.098-0.182), p<0.05) increased the probability of dying for asthma in Barcelona during the period 1986-1989.

Adolescent↗

PubMed1982

Analyses of carcinogenesis dose-response relations with dichotomous data: implications for carcinogenic risk assessment.

Dose-response data from experimental and epidemiologic carcinogenicity studies were analyzed in attempts to resolve basic questions in extrapolating from high to low doses and assessing human risk. Four models (Weibull, Mantel-Bryan, Marshall-Groer, and Mancuso-Stewart) were fit to 46 sets of experimental and 4 sets of epidemiologic data by maximizing the likelihood function with a Rosenbrock hill-climbing algorithm. The models were compared as to their adequacy in describing the data and analyzed to determine the effect of carcinogen and breeding category, species, and spontaneous tumor incidence. The shapes of the dose-response curves were analyzed, and errors in risk estimation from linear extrapolation through the origin were calculated. All models were shown to fit the data and to be comparable in accuracy. The dose-response curves were generally "stretched out," particularly for outbred strains, with one or two orders of magnitude of dose increase required to increase the proportion of tumor responders from 10% to 70%. Linear extrapolation through the origin generally underestimated the response at low doses, frequently by several orders of magnitude. The power dependence of tumor incidence on dose was generally found to be of the order of unity, substantially less than assumed in most mathematical models.

Carcinogens↗

PubMed1991

Familial aggregation of lipids and lipoproteins in families ascertained through random and nonrandom probands in the Stanford Lipid Research Clinics Family Study.

We examined the familial aggregation of lipids [total cholesterol (CH) and triglyceride (TG)] and lipoproteins [high-density lipoprotein cholesterol (HDL) and low-density lipoprotein cholesterol (LDL)] in families ascertained through random and nonrandom probands in the Stanford Lipid Research Clinics Family Study. Nonrandom probands were selected because their lipid levels at a prior screening visit exceeded a certain prespecified threshold. The statistical method is based on selection through indirect truncation on a correlated trait (in which the likelihood function is conditioned on the actual event that the proband's value is beyond the threshold). This method allows for estimation of the path model parameters in randomly and nonrandomly ascertained families jointly and separately, thus enabling tests of heterogeneity between the two types of samples. The results suggest that the multifactorial transmission is homogeneous in the random and hyperlipidemic samples for CH. However, the evidence for heterogeneity is moderate for LDL, marked HDL, and mixed for TG. The general pattern of observed results is for somewhat higher genetic heritabilities in the random than nonrandom samples, which is compatible with a higher prevalence in the random sample of certain dyslipoproteinemias associated with nonelevated lipids. Substantial genetic heritability is found for CH, HDL, and LDL, with somewhat lower estimates for TG. Cultural heritability is low but significant for all four traits. Little or no spouse resemblance or nontransmitted shared sibship effects are seen. In contrast to the findings from previous studies, little or no parental cultural transmission is seen.

Adult↗

PubMed1989

Summary measures for evaluating the evidence for linkage.

Two summary measures for evaluating the evidence for linkage are the maximum lod score and the average of the likelihood function (antilod score). The average antilod score can be used to calculate an exact probability of there being no linkage. Use of subjective prior probabilities in the calculation will only influence the final conclusion in any important way if evidence from the sample is not particularly conclusive. It is shown how results from two-point analyses for linkage of the test locus with each marker locus can be easily combined to give an approximate probability of there being no linkage. Some examples using bipolar affective disorder data and marker loci are presented.

Bipolar Disorder↗

PubMed1992

Using an autoregressive model to detect departures from steady states in unequally spaced tumour biomarker data.

A new method, based on a continuous time autoregressive [CAR(1)] model of time series data, is provided for detecting departures of tumour markers from steady states in breast cancer patients following surgery. A Kalman filter recursive algorithm is used to calculate the likelihood function arising from the CAR(1) model and to calculate recursive residuals, which are monitored by a Shewhart-Cusum scheme. This approach can be used to monitor the serial marker data of large numbers of patients even when the series are short and the data are serially correlated and unequally spaced. Further, the methodology can be used to recommend appropriate testing intervals.

Algorithms↗

PubMed1995

Identification of protein coding regions in genomic DNA.

We have developed a computer program, GeneParser, which identifies and determines the fine structure of protein genes in genomic DNA sequences. The program scores all subintervals in a sequence for content statistics indicative of introns and exons, and for sites that identify their boundaries. This information is weighted by a neural network to approximate the log-likelihood that each subinterval exactly represents an intron or exon (first, internal or last). A dynamic programming algorithm is then applied to this data to find the combination of introns and exons that maximizes the likelihood function. Using this method, we can rapidly generate ranked suboptimal solutions, each of which is the optimum solution containing a given intron-exon junction. We have tested the system on a large collection of human genes. On sequences not used in training, we achieved a correlation coefficient for exon nucleotide prediction of 0.89. For a subset of G + C-rich genes, a correlation coefficient of 0.94 was achieved. We have also quantified the robustness of the method to substitution and frame-shift errors and show how the system can be optimized for performance on sequences with known levels of sequencing errors.

Base Composition↗

PubMed1983

Affinity spectra: a novel way for the evaluation of equilibrium binding experiments.

For equilibrium binding isotherms of radioreceptor assays, the affinity spectrum is defined as a plot of the number of binding sites against their corresponding dissociation constants. A numerical procedure for direct calculation of affinity spectra from untransformed binding data is presented and illustrated with experimental values. The advantage of the new method in comparison to non-linear regression analysis is the fact that no starting values and mathematical models have to be supplied and that statistical assessment of the results is straightforward from a detailed graphical display of a likelihood function. Affinity spectra thus show directly all information formerly obtained by means of both graphical plots and regression analysis.

Animals↗

PubMed1989

On the maximum likelihood method for estimating molecular trees: uniqueness of the likelihood point.

Studies are carried out on the uniqueness of the stationary point on the likelihood function for estimating molecular phylogenetic trees, yielding proof that there exists at most one stationary point, i.e., the maximum point, in the parameter range for the one parameter model of nucleotide substitution. The proof is simple yet applicable to any type of tree topology with an arbitrary number of operational taxonomic units (OTUs). The proof ensures that any valid approximation algorithm be able to reach the unique maximum point under the conditions mentioned above. An algorithm developed incorporating Newton's approximation method is then compared with the conventional one by means of computer simulation. The results show that the newly developed algorithm always requires less CPU time than the conventional one, whereas both algorithms lead to identical molecular phylogenetic trees in accordance with the proof.

Algorithms↗

PubMed1991

Myxoma virus expresses a secreted protein with homology to the tumor necrosis factor receptor gene family that contributes to viral virulence.

Poxviruses are known to contain a large number of open reading frames, particularly near the termini of the viral genome, that are not required for growth in tissue culture. However, many of these gene products are believed to play important roles in determining the virulence of the virus by modulating the host immune response to the infection. Recently it has been shown that Shope fibroma virus encodes, within the terminal inverted repeats, a protein (T2) related to the cellular tumor necrosis factor receptor (TNFR) and which specifically binds both TNF alpha and TNF beta. We have sequenced the terminal regions of two other Leporipoxviruses (myxoma virus and malignant rabbit fibroma virus) that are extremely invasive and capable of inducing extensive immunosuppression in rabbits and demonstrate that they also encode a closely related T2 homolog with all the structural motifs predicted for a secreted TNF binding protein. To investigate the biological role of the T2 protein, we have inactivated the myxoma virus T2 gene within each copy of the viral TIR by the insertion of a dominant selectable marker (Escherichia coli guanosine phosphoribosyltransferase) and selection of the recombinant virus in the presence of mycophenolic acid. The success of the inactivation of both copies of T2 was confirmed by the loss a broad protein band (52-56 kDa) of the predicted size for T2 from the profile of proteins secreted from mutant virus-infected BGMK cells at early times after infection. Although the T2-minus recombinant myxoma virus grew normally in tissue culture, upon infection of susceptible rabbits the viral disease was observed to be significantly attenuated. The majority of infected rabbits were able to mount an effective immune response to the infection and completely recovered. These survivor rabbits became immune to subsequent challenge with wild type myxoma virus. We conclude that the T2 viral protein is an important secreted virulence factor and that it in all likelihood functions by compromising the antiviral effects of TNF. We propose the term "viroceptor" to describe viral-encoded homologs of cellular lymphokine receptors whose function is to intercept the activity of the cognate lymphokine in order to short circuit the host immune response to the viral infection.

Amino Acid Sequence↗

PubMed1985

Assessment of the hot-plate antinociceptive test in mice. A new method for the statistical treatment of graded data.

The use of graded data from hot-plate antinociceptive tests is complicated by the problem of how to treat responses that are greater than the cut-off time. This paper describes a statistical procedure for analysis of antinociceptive data that circumvents this problem. The method is based upon the likelihood function and the data is assumed to follow a Weibull distribution. The technique can be implemented with the use of a computer and provides a more comprehensive assessment of antinociceptive data.

Analgesics↗

PubMed1985

A computer program for an illness-death process with time-dependent covariates.

This paper presents a computer program for estimating transition probabilities between states in a stochastic model for an illness-death process which incorporates time-dependent covariates. Parameters are estimated by the method of maximum likelihood using the Newton-Raphson iterative procedure. The program provides the standard normal deviate statistics as well as the value of the maximum of the likelihood function which can be used on repeated applications to test hypotheses concerning coefficients associated with covariates. Although this program is demonstrated by using a model with two 'illness' states and two 'death' states, it is also suitable for analyzing data with models involving fewer states, such as the analysis of survival time with covariates assuming a proportional hazard model.

Computers↗

PubMed1991

An optimization strategy for a biokinetic model of inhaled radionuclides.

Models for material disposition and dosimetry involve predictions of the biokinetics of the material among compartments representing organs and tissues in the body. Because of a lack of human data for most toxicants, many of the basic data are derived by modeling the results obtained from studies using laboratory animals. Such a biomathematical model is usually developed by adjusting the model parameters to make the model predictions match the measured retention and excretion data visually. The fitting process can be very time-consuming for a complicated model, and visual model selections may be subjective and easily biased by the scale or the data used. Due to the development of computerized optimization methods, manual fitting could benefit from an automated process. However, for a complicated model, an automated process without an optimization strategy will not be efficient, and may not produce fruitful results. In this paper, procedures for, and implementation of, an optimization strategy for a complicated mathematical model is demonstrated by optimizing a biokinetic model for 144Ce in fused aluminosilicate particles inhaled by beagle dogs. The optimized results using SimuSolv were compared to manual fitting results obtained previously using the model simulation software GASP. Also, statistical criteria provided by SimuSolv, such as likelihood function values, were used to help or verify visual model selections.

Administration, Inhalation↗

PubMed1993

Optimization issues in physiological toxicokinetic modeling: a case study with benzene.

This paper compares two methods for global optimization of physiologically based toxicokinetic models: Monte Carlo optimization, which searches randomly for the optimum; and the simplex method, which updates systematically an array of parameter values. Two measures of goodness-of-fit are also contrasted: criterion function and likelihood. A 14-parameter model of benzene distribution in rats is used to illustrate these techniques. Simplex optimization yields better fits overall. However, the measurement of uncertainty offered by Monte Carlo simulations is a major argument in favor of their use.

Animals↗

PubMed1991

Bayesian image processing in magnetic resonance imaging.

In the past several years, image processing techniques based on Bayesian models have received considerable attention. In our earlier work, we developed a novel Bayesian approach which was primarily aimed at the processing and reconstruction of images in positron emission tomography. In this paper, we describe how the technique has been adopted to process magnetic resonance images in order to reduce noise and artifacts, thereby improving image quality. In this framework, the image is assumed to be a statistical variable whose posterior probability density conditional on the observed image is modeled by the product of the likelihood function of the observed data with a prior density based our prior knowledge. A Gibbs random field incorporating local continuity information and with edge-detection capability is used as the prior model. Based on the formalism of the posterior density, we can compute an estimate of the image using an iterative technique. We have implemented this technique and applied it to phantom and clinical images. Our results indicate that the approach works reasonably well for reducing noise, enhancing edges, and removing ringing artifact.

Algorithms↗

PubMed1997

Analyses on the temporal patterns of spikes of auditory neurons of the macaque monkey by means of an artificial neural network and tree-based models.

The time scale over which information in the primary auditory cortex is processed was estimated. An artificial neural network was used to learn the temporal patterns of spikes. After learning, test patterns were input to the network. Comparison of the accuracy of the network with that of the maximum likelihood function computed from the spike count reveals that the temporal patterns of spikes are closely related to stimulus discrimination. Next, a tree-based model from a subset of the spike trains with a fixed time resolution was constructed and validated the model with another. By repeating this for different bin widths, it was found that there are no simple models for the time bin width larger than 50 ms. This indicates that the time scale in the auditory cortex is not larger than 50 ms.

Animals↗

PubMed1976

Point and interval estimation in the combination of bioassay results.

A procedure for combining evidence from different biological assays is shown to be equivalent both to generalized least-squares and to maximum-likelihood estimation. By appropriate nesting of hypotheses, the likelihood function can be used to test the agreement between the assays and to obtain probability limits for the combined estimate of potency. The properties of these limits are examined, with particular reference to the situation, unusual but not impossible in practice, in which the values of relative potency that they define consist of several disjoint segments instead of a single interval. The connection with general theory of estimating linear functional relations is pointed out.

Biological Assay↗

PubMed1990

A Bayesian method for synthesizing evidence. The Confidence Profile Method.

This article describes a collection of meta-analysis techniques based on Bayesian statistics for interpreting, adjusting, and combining evidence to estimate parameters and outcomes important to the assessment of health technologies. The result of an analysis by the Confidence Profile Method is a joint posterior probability distribution for the parameters of interest, from which marginal distributions for any particular parameter can be calculated. The method can be used to analyze problems involving a variety of types of outcomes, a variety of measures of effect, and a variety of experimental designs. This article presents the elements necessary for analysis, including prior distributions, likelihood functions, and specific models for experimental designs that include adjustment for biases.

Bayes Theorem↗

PubMed2001

Introduction to Bayesian reasoning.

Interest in Bayesian analyses has increased recently, in part as a response to policy makers wanting sound scientific bases for health technology assessments, and associated healthcare funding decisions. This paper provides a brief and simplified description of Bayesian reasoning. Bayes is illustrated in a clinical setting of an expert helping a woman understand the potential risk of passing on an inheritable disease (hemophilia) to her next child, based on disease occurrence in two living children. The illustration describes fundamental concepts and derivations, such as Bayes theorem, likelihood functions, prior probability, and posterior probability. A second illustration shows the use of Bayes for interpreting clinical trial results. The uncertainty in the clinical effect before and after the trial analyses has been completed is characterized by the Bayes prior and posterior probabilities, respectively. Techniques are also shown for estimating the potential loss (e.g., in lives lost) for making the wrong decision with and without knowledge of the trial results, an estimation that cannot be carried out using techniques of hypotheses testing associated with the frequentist school of statistics. Information from Bayes analysis then may be used to help policy makers decide, or justify, whether the analyses provides a sufficient basis for making a treatment recommendation, or whether there remains a need to request more information. Subsequent papers in this volume offer additional examples and clarification of the use of Bayes in clinical practice and in interpretation of clinical studies.

Bayes Theorem↗