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Results for “Likelihood Functions”

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PubMed2002

Inferences concerning exponential distributions in the presence of randomly right censored data with missing censored values.

Inferences concerning exponential distributions are considered from a sampling theory viewpoint when the data are randomly right censored and the censored values are missing. Both one-sample and m-sample (m > or = 2) problems are considered. Likelihood functions are obtained for situations in which the censoring mechanism is informative which leads to natural and intuitively appealing estimators of the unknown proportions of censored observations. For testing hypotheses about the unknown parameters, three well-known test statistics, namely, likelihood ratio test, score test, and Wald-type test are considered.

Data Interpretation, Statistical↗
PubMed2002

A semiparametric empirical likelihood method for data from an outcome-dependent sampling scheme with a continuous outcome.

Outcome-dependent sampling (ODS) schemes can be a cost effective way to enhance study efficiency. The case-control design has been widely used in epidemiologic studies. However, when the outcome is measured on a continuous scale, dichotomizing the outcome could lead to a loss of efficiency. Recent epidemiologic studies have used ODS sampling schemes where, in addition to an overall random sample, there are also a number of supplemental samples that are collected based on a continuous outcome variable. We consider a semiparametric empirical likelihood inference procedure in which the underlying distribution of covariates is treated as a nuisance parameter and is left unspecified. The proposed estimator has asymptotic normality properties. The likelihood ratio statistic using the semiparametric empirical likelihood function has Wilks-type properties in that, under the null, it follows a chi-square distribution asymptotically and is independent of the nuisance parameters. Our simulation results indicate that, for data obtained using an ODS design, the semiparametric empirical likelihood estimator is more efficient than conditional likelihood and probability weighted pseudolikelihood estimators and that ODS designs (along with the proposed estimator) can produce more efficient estimates than simple random sample designs of the same size. We apply the proposed method to analyze a data set from the Collaborative Perinatal Project (CPP), an ongoing environmental epidemiologic study, to assess the relationship between maternal polychlorinated biphenyl (PCB) level and children's IQ test performance.

Biometry↗
PubMed2007

Shared random effects analysis of multi-state Markov models: application to a longitudinal study of transitions to dementia.

Multi-state models are appealing tools for analysing data about the progression of a disease over time. In this paper, we consider a multi-state Markov chain with two competing absorbing states: dementia and death and three transient non-demented states: cognitively normal, amnestic mild cognitive impairment (amnestic MCI), and non-amnestic mild cognitive impairment (non-amnestic MCI). The likelihood function for the data is derived and estimates for the effects of the covariates on transitions are determined when the process can be viewed as a polytomous logistic regression model with shared random effects. The presence of a shared random effect not only complicates the formulation of the likelihood but also its evaluation and maximization. Three approaches for maximizing the likelihood are compared using a simulation study; the first method is based on the Gauss-quadrature technique, the second method is based on importance sampling ideas, and the third method is based on an expansion by Taylor series. The best approach is illustrated using a longitudinal study on a cohort of cognitively normal subjects, followed annually for conversion to mild cognitive impairment (MCI) and/or dementia, conducted at the Sanders Brown Center on Aging at the University of Kentucky.

Aged↗
PubMed2004

A parametric survival model with an interval-censored covariate.

We present a parametric survival model whose particularity consists in the inclusion of an interval-censored covariate. The methodology is motivated by a study on injecting drug users in Badalona (Spain), most of whom suffered HIV infection as a result of their drug addiction. The study aims to examine the possible association between the elapsed time from first injecting drug use until HIV infection and the subsequent AIDS incubation period. Whereas the moment of HIV infection cannot be observed exactly and is therefore interval-censored, time until AIDS onset is doubly-censored. For the maximization of the resulting likelihood function, we use a numerical solver. Maximization is carried out by means of the mathematical programming language AMPL.

Acquired Immunodeficiency Syndrome↗
PubMed2006

Top-quark mass measurement from dilepton events at CDF II.

We report a measurement of the top-quark mass using events collected by the CDF II detector from pp collisions at square root of s = 1.96 TeV at the Fermilab Tevatron. We calculate a likelihood function for the top-quark mass in events that are consistent with tt --> bl(-)nu(l)bl'+ nu'(l) decays. The likelihood is formed as the convolution of the leading-order matrix element and detector resolution functions. The joint likelihood is the product of likelihoods for each of 33 events collected in 340 pb(-1) of integrated luminosity, yielding a top-quark mass M(t) = 165.2 +/- 6.1(stat) +/- 3.4(syst) GeV/c2. This first application of a matrix-element technique to tt --> bl+ nu(l)bl'- nu(l') decays gives the most precise single measurement of M(t) in dilepton events. Combined with other CDF run II measurements using dilepton events, we measure M(t) = 167.9 +/- 5.2(stat) +/- 3.7(syst) GeV/c2.

Journal Article↗
PubMed2006

Weinberg's differential rule reconsidered.

A central problem in research on twins is the estimation of the rates of monozygotic and dizygotic twin maternities. The estimation usually follows Weinberg's differential rule. According to this rule, the rate of dizygotic twinning is twice the rate of twin maternities in which the twins are of opposite sex. The monozygotic twinning rate is the difference between the rates of same-sex and opposite-sex twin sets. Weinberg's differential rule is implicitly based on the assumptions that the probability of a male equals the probability of a female and that the sexes in a dizygotic twin set are independent. Although Weinberg's differential rule has been the target of continuing discussions, the reliability of these assumptions has never been conclusively verified or rejected. In this study we present new variance formulas for the monozygotic and dizygotic twinning rates obtained using Weinberg's differential rule and stress that these new formulas have to be used. We analyze the accuracy of Weinberg's differential rule by considering alternative attempts. Especially, we build a general likelihood function and show that the maximum-likelihood estimates differ only slightly from the rates obtained using Weinberg's differential rule. In addition, our methods are applied to twinning data from Finland and Sweden. We compare our results with findings in the literature. In conclusion, our findings indicate that Weinberg's differential rule is rather robust and that despite its simplicity, it gives reliable results when official birth registers are analyzed.

Birth Rate↗
PubMed1995

Approximate solutions for the maximum-likelihood estimates in models of univariate human twin data.

We present numerical results concerning the accuracy of approximate maximum-likelihood estimators of variance components for several models of univariate human twin data. The approximations are obtained via a spectral decomposition of the twin model covariance matrix. The results apply to likelihood functions for univariate twin data based on either the Wishart distribution or the bivariate normal distribution. For sample sizes of 100 twin pairs for each zygosity group, if the difference of the traces of the sample covariance matrices is 10% or less of the sum of the traces, the approximate solutions can be used as the maximum-likelihood estimators for some models.

Analysis of Variance↗
PubMed1997

Modeling the lifespan of human T lymphocyte subsets.

T lymphocytes may be classified as naive or memory cells, depending on whether they possess immunological memory. The central tenet of this work is that memory lymphocytes revert to naive lymphocytes in vivo. This phenomenon is modeled by a mechanism qualitatively similar to Demoivre's law of human mortality. Additionally, both lymphocyte subsets undergo decay. Model parameters and their standard errors are estimated by maximizing a likelihood function constructed by Kalman filtering of the experimental data on the assumption that it is contaminated by measurement noise of constant relative error.

Cell Death↗
PubMed2000

A direct optimization approach to hidden Markov modeling for single channel kinetics.

Hidden Markov modeling (HMM) provides an effective approach for modeling single channel kinetics. Standard HMM is based on Baum's reestimation. As applied to single channel currents, the algorithm has the inability to optimize the rate constants directly. We present here an alternative approach by considering the problem as a general optimization problem. The quasi-Newton method is used for searching the likelihood surface. The analytical derivatives of the likelihood function are derived, thereby maximizing the efficiency of the optimization. Because the rate constants are optimized directly, the approach has advantages such as the allowance for model constraints and the ability to simultaneously fit multiple data sets obtained at different experimental conditions. Numerical examples are presented to illustrate the performance of the algorithm. Comparisons with Baum's reestimation suggest that the approach has a superior convergence speed when the likelihood surface is poorly defined due to, for example, a low signal-to-noise ratio or the aggregation of multiple states having identical conductances.

Algorithms↗
PubMed1999

Hazard models for line transect surveys with independent observers.

The likelihood function for data from independent observer line transect surveys is derived, and a hazard model is proposed for the situation where animals are available for detection only at discrete time points. Under the assumption that the time points of availability follow a Poisson point process, we obtain an analytical expression for the detection function. We discuss different criteria for choosing the hazard function and consider in particular two different parametric families of hazard functions. Discrete and continuous hazard models are compared and the robustness of the discrete model is investigated. Finally, the methodology is applied to data from a survey for minke whales in the northeastern Atlantic.

Animals↗
PubMed1993

Using autoregressive and random walk models to detect trends and shifts in unequally spaced tumour biomarker data.

Continuous time autoregressive (CAR(1)) and random walk models of time series data are provided for detecting non-random shifts and trends of tumour markers in breast cancer patients following resection for cure. The continuous time random walk model with observation error is extended to the case of multiple patient time series. These models can be used to monitor large numbers of patients with time series with few sampling events that are serially correlated and unequally spaced. Further, the methodologies can be used to recommend appropriate testing intervals. A Kalman filter recursive algorithm is used to calculate the likelihood functions arising from the CAR(1) and random walk models and to calculate recursive residuals, which are monitored by Shewhart-cusum schemes.

Antigens, Tumor-Associated, Carbohydrate↗
PubMed2005

Simultaneous modelling of survival and longitudinal data with an application to repeated quality of life measures.

In biomedical studies, interest often focuses on the relationship between patient's characteristics or some risk factors and both quality of life and survival time of subjects under study. In this paper, we propose a simultaneous modelling of both quality of life and survival time using the observed covariates. Moreover, random effects are introduced into the simultaneous models to account for dependence between quality of life and survival time due to unobserved factors. EM algorithms are used to derive the point estimates for the parameters in the proposed model and profile likelihood function is used to estimate their variances. The asymptotic properties are established for our proposed estimators. Finally, simulation studies are conducted to examine the finite-sample properties of the proposed estimators and a liver transplantation data set is analyzed to illustrate our approaches.

Algorithms↗
PubMed1999

[Inheritance of quantitative traits in hybrid pedigrees: mixed models].

Mixed models have been extended to make them applicable to description of inheritance of quantitative traits in pedigrees obtained via interbreed or interpopulation hybridization. Additional assumptions specify definite relationships between the parameters that characterize the inheritance of the trait in two parental populations. It is assumed that (1) parental populations differ from each other only in the allelic frequencies in the major gene locus and polygenic loci and (2) the patterns of phenotype formation based on an individual genotype and the transmission of genes to the next generation are the same in both parental populations, as well as in their hybrids. Based on these assumptions, the likelihood function for a hybrid pedigree is derived, and the heterosis effect is formalized. The results of this study offer new possibilities for estimating the contribution of the major gene effect to interpopulation and interbreed differences in the expression of quantitative traits.

Female↗
PubMed2005

A composite-likelihood approach for detecting directional selection from DNA sequence data.

We present a novel composite-likelihood-ratio test (CLRT) for detecting genes and genomic regions that are subject to recurrent natural selection (either positive or negative). The method uses the likelihood functions of Hartl et al. (1994) for inference in a Wright-Fisher genic selection model and corrects for nonindependence among sites by application of coalescent simulations with recombination. Here, we (1) characterize the distribution of the CLRT statistic (Lambda) as a function of the population recombination rate (R=4Ner); (2) explore the effects of bias in estimation of R on the size (type I error) of the CLRT; (3) explore the robustness of the model to population growth, bottlenecks, and migration; (4) explore the power of the CLRT under varying levels of mutation, selection, and recombination; (5) explore the discriminatory power of the test in distinguishing negative selection from population growth; and (6) evaluate the performance of maximum composite-likelihood estimation (MCLE) of the selection coefficient. We find that the test has excellent power to detect weak negative selection and moderate power to detect positive selection. Moreover, the test is quite robust to bias in the estimate of local recombination rate, but not to certain demographic scenarios such as population growth or a recent bottleneck. Last, we demonstrate that the MCLE of the selection parameter has little bias for weak negative selection and has downward bias for positively selected mutations.

Base Sequence↗
PubMed2006

A copula model for repeated measurements with non-ignorable non-monotone missing outcome.

A normal copula-based selection model is proposed for continuous longitudinal data with a non-ignorable non-monotone missing-data process. The normal copula is used to combine the distribution of the outcome of interest and that of the missing-data indicators given the covariates. Parameters in the model are estimated by a pseudo-likelihood method. We first use the GEE with a logistic link to estimate the parameters associated with the marginal distribution of the missing-data indicator given the covariates, assuming that covariates are always observed. Then we estimate other parameters by inserting the estimates from the first step into the full likelihood function. A simulation study is conducted to assess the robustness of the assumed model under different missing-data processes. The proposed method is then applied to one example from a community cohort study to demonstrate its capability to reduce bias.

Aged↗
PubMed1997

Testing for treatment related trend with partially exchangeable clustered data.

When testing for treatment related effect, it is common to focus on data that describe some primary response, even though an experiment might yield data on secondary, less conspicuous effects. An example of such an experiment can be found in developmental toxicity studies, where a primary response might be the presence of skeletal malformation in a fetus, and a secondary effect might be reduced weight. In such studies, weight reduction may occur not only among malformed fetuses, but also among normal fetuses. In this paper, we use a likelihood ratio procedure to construct treatment related trend tests for developmental experiments with such outcomes. We assume that within each cluster, data are partially exchangeable and we use the presence or absence of malformations as categorical covariates. Two models are considered for the covariance structures: In the general model, partially exchangeable covariance matrices are used for each cluster within dose groups. In the homogeneous model, a common exchangeable covariance matrix is used for all clusters. Maximum likelihood estimates (MLEs) of unknown parameters in the general model are obtained by directly maximizing the log-likelihood function through careful numerical consideration, while MLEs of parameters of teh homogeneous model are obtained through an iterative procedure. Two applications to developmental toxicity data are described.

Abnormalities, Drug-Induced↗
PubMed2005

Comparison of Bayesian and maximum-likelihood inference of population genetic parameters.

UNLABELLED: Comparison of the performance and accuracy of different inference methods, such as maximum likelihood (ML) and Bayesian inference, is difficult because the inference methods are implemented in different programs, often written by different authors. Both methods were implemented in the program MIGRATE, that estimates population genetic parameters, such as population sizes and migration rates, using coalescence theory. Both inference methods use the same Markov chain Monte Carlo algorithm and differ from each other in only two aspects: parameter proposal distribution and maximization of the likelihood function. Using simulated datasets, the Bayesian method generally fares better than the ML approach in accuracy and coverage, although for some values the two approaches are equal in performance. MOTIVATION: The Markov chain Monte Carlo-based ML framework can fail on sparse data and can deliver non-conservative support intervals. A Bayesian framework with appropriate prior distribution is able to remedy some of these problems. RESULTS: The program MIGRATE was extended to allow not only for ML(-) maximum likelihood estimation of population genetics parameters but also for using a Bayesian framework. Comparisons between the Bayesian approach and the ML approach are facilitated because both modes estimate the same parameters under the same population model and assumptions.

Bayes Theorem↗