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Results for “Likelihood Functions”

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PubMed1998

Recognizing protein binding sites using statistical descriptions of their 3D environments.

We have developed a new method for recognizing sites in three-dimensional protein structures. Our method is based on our previously reported algorithm for creating descriptions of protein microenvironments using physical and chemical properties at multiple levels of detail (including features at the atomic, chemical group, residue, and secondary structural levels). The recognition method takes three inputs: a set of sites that share some structural or functional role, a set of control nonsites that lack this role, and a single query site. The values of properties for the query site are compared to the distributions of values for both sites and nonsites to determine the group to which it is most similar. A log-odds scoring function, based on Bayes' Rule, computes a score that indicates the likelihood that the query region is a site of interest. In this paper, we apply the method to the task of identifying calcium binding sites in proteins. Cross-validation analysis shows that this recognition approach has high sensitivity and specificity. We also describe the results of scanning four calcium binding proteins (with the calcium removed) using a three-dimensional grid of probe points at 2 A spacing. The probe points that have high scores cluster around the true calcium binding sites, with the highest scoring points at or near the binding sites. The method fails in only one case where a calcium binding site is created by four proteins in the crystal lattice, and is thus not recognizable within the crystallographic asymmetric unit. Our results show that property-based descriptions can be used for recognizing protein sites in unannotated structures.

Bayes Theorem↗

PubMed1993

Squamous carcinoma of the head and neck: cured fraction and median survival time as functions of age, sex, histologic type, and node status.

The multivariate lognormal survival model can be used to determine the relationship of prognostic covariates to two important parameters of malignancy. Cured fraction and median survival time among uncured patients. Analysis with this model revealed that cured fraction is primarily a function of histologic type and node status, while median survival time is primarily a function of age and node status. Patient sex was also related to likelihood of cure, but this association was of marginal significance. The symmetric impact of node status on both cured fraction and median survival time is consistent with known biologic principles. The strongly asymmetric relationships of histologic grade to cured fraction and age to survival time suggest, however, that likelihood of cure and survival time may not operate by identical biologic mechanisms.

Age Factors↗

PubMed2002

Analytic approaches to twin data using structural equation models.

The classical twin study is the most popular design in behavioural genetics. It has strong roots in biometrical genetic theory, which allows predictions to be made about the correlations between observed traits of identical and fraternal twins in terms of underlying genetic and environmental components. One can infer the relative importance of these 'latent' factors (model parameters) by structural equation modelling (SEM) of observed covariances of both twin types. SEM programs estimate model parameters by minimising a goodness-of-fit function between observed and predicted covariance matrices, usually by the maximum-likelihood criterion. Likelihood ratio statistics also allow the comparison of fit of different competing models. The program Mx, specifically developed to model genetically sensitive data, is now widely used in twin analyses. The flexibility of Mx allows the modelling of multivariate data to examine the genetic and environmental relations between two or more phenotypes and the modelling to categorical traits under liability-threshold models.

Chi-Square Distribution↗

PubMed2005

Robust modeling in screening studies: estimation of sensitivity and preclinical sojourn time distribution.

In early-detection clinical trials, quantities such as the sensitivity of the screening modality and the preclinical duration of the disease are important to describe the natural history of the disease and its interaction with a screening program. Assume that the schedule of a screening program is periodic and that the sojourn time in the preclinical state has a piecewise density function. Modeling the preclinical sojourn time distribution as a piecewise density function results in robust estimation of the distribution function. Our aim is to estimate the piecewise density function and the examination sensitivity using both generalized least squares and maximum likelihood methods. We carried out extensive simulations to evaluate the performance of the methods of estimation. The different estimation methods provide complimentary tools to obtain the unknown parameters. The methods are applied to three breast cancer early-detection trials.

Adult↗

PubMed2004

Phylogenetic analysis of the formin homology 2 domain.

Formin proteins are key regulators of eukaryotic actin filament assembly and elongation, and many species possess multiple formin isoforms. A nomenclature system based on fundamental features would be desirable, to aid the rapid identification and characterization of novel formins. In this article, we attempt to systematize the formin family by performing phylogenetic analyses of the formin homology 2 (FH2) domain, an independently folding region common to all formins, which alone can influence actin dynamics. Through database searches, we identify 101 FH2 domains from 26 eukaryotic species, including 15 in mice. Sequence alignments reveal a highly conserved yeast-specific insert in the "knob loop" region of the FH2 domain, with unknown functional consequences. Phylogenetic analysis using minimum evolution (ME), maximum parsimony (MP), and maximum likelihood (ML) algorithms strongly supports the existence of seven metazoan groups. Yeast FH2 domains segregate from all other eukaryotes, including metazoans, other fungi, plants, and protists. Sequence comparisons of non-FH2 regions support relationships between three metazoan groups (Dia, DAAM, and FRL) and examine previously identified coiled-coil and Diaphanous auto-regulatory domain sequences. This analysis allows for a formin nomenclature system based on sequence relationships, as well as suggesting strategies for the determination of biochemical and cellular activities of these proteins.

Adaptor Proteins, Signal Transducing↗

PubMed2001

Polylink: to support two-point linkage analysis in autotetraploids.

SUMMARY: Polylink runs under Microsoft Windows (95 or later). It performs various calculations that are useful for investigating two-point linkage analysis for autopolyploids, based on the random chromosome pairing model. These include calculation of offspring phenotypic probabilities as functions of the recombination fraction, calculation of theoretical standard errors for the maximum likelihood estimator of and numerical computation of maximum likelihood estimates. It also includes simulation facilities. AVAILABILITY: Polylink is free and available from Xiangming Xu via email

Computational Biology↗

PubMed2006

Smoothing spline-based score tests for proportional hazards models.

We propose "score-type" tests for the proportional hazards assumption and for covariate effects in the Cox model using the natural smoothing spline representation of the corresponding nonparametric functions of time or covariate. The tests are based on the penalized partial likelihood and are derived by viewing the inverse of the smoothing parameter as a variance component and testing an equivalent null hypothesis that the variance component is zero. We show that the tests have a size close to the nominal level and good power against general alternatives, and we apply them to data from a cancer clinical trial.

Analysis of Variance↗

PubMed1991

A method of non-parametric back-projection and its application to AIDS data.

The method of back-projection has been used to estimate the unobserved past incidence of infection with the human immunodeficiency virus (HIV) and to obtain projections of future AIDS incidence. Here a new approach to back-projection, which avoids parametric assumptions about the form of the HIV infection intensity, is described. This approach gives the data greater opportunity to determine the shape of the estimated intensity function. The method is based on a modification of an EM algorithm for maximum likelihood estimation that incorporates smoothing of the estimated parameters. It is easy to implement on a computer because the computations are based on explicit formulae. The method is illustrated with applications to AIDS data from Australia, U.S.A. and Japanese haemophiliacs.

Acquired Immunodeficiency Syndrome↗

PubMed2004

Shared frailty models for recurrent events and a terminal event.

There has been an increasing interest in the analysis of recurrent event data (Cook and Lawless, 2002, Statistical Methods in Medical Research 11, 141-166). In many situations, a terminating event such as death can happen during the follow-up period to preclude further occurrence of the recurrent events. Furthermore, the death time may be dependent on the recurrent event history. In this article we consider frailty proportional hazards models for the recurrent and terminal event processes. The dependence is modeled by conditioning on a shared frailty that is included in both hazard functions. Covariate effects can be taken into account in the model as well. Maximum likelihood estimation and inference are carried out through a Monte Carlo EM algorithm with Metropolis-Hastings sampler in the E-step. An analysis of hospitalization and death data for waitlisted dialysis patients is presented to illustrate the proposed methods. Methods to check the validity of the proposed model are also demonstrated. This model avoids the difficulties encountered in alternative approaches which attempt to specify a dependent joint distribution with marginal proportional hazards and yields an estimate of the degree of dependence.

Algorithms↗

PubMed2004

A parametric model for studying organism fitness using step-stress experiments.

We propose a method based on parametric survival analysis to analyze step-stress data. Step-stress studies are failure time studies in which the experimental stressor is increased at specified time intervals. While this protocol has been frequently employed in industrial reliability studies, it is less common in the life sciences. Possible biological applications include experiments on swimming performance of fish using a step function defining increasing water velocity over time, and treadmill tests on humans. A likelihood-ratio test is developed for comparing the failure times in two groups based on a piecewise constant hazard assumption. The test can be extended to other piecewise distributions and to include covariates. An example data set is used to illustrate the method and highlight experimental design issues. A small simulation study compares this analysis procedure to currently used methods with regard to type I error rate and power.

Analysis of Variance↗

PubMed2001

Predictive approaches for choosing hyperparameters in gaussian processes.

Gaussian processes are powerful regression models specified by parameterized mean and covariance functions. Standard approaches to choose these parameters (known by the name hyperparameters) are maximum likelihood and maximum a posteriori. In this article, we propose and investigate predictive approaches based on Geisser's predictive sample reuse (PSR) methodology and the related Stone's cross-validation (CV) methodology. More specifically, we derive results for Geisser's surrogate predictive probability (GPP), Geisser's predictive mean square error (GPE), and the standard CV error and make a comparative study. Within an approximation we arrive at the generalized cross-validation (GCV) and establish its relationship with the GPP and GPE approaches. These approaches are tested on a number of problems. Experimental results show that these approaches are strongly competitive with the existing approaches.

Likelihood Functions↗

PubMedDate not supplied

Estimating genetic covariance functions assuming a parametric correlation structure for environmental effects.

A random regression model for the analysis of "repeated" records in animal breeding is described which combines a random regression approach for additive genetic and other random effects with the assumption of a parametric correlation structure for within animal covariances. Both stationary and non-stationary correlation models involving a small number of parameters are considered. Heterogeneity in within animal variances is modelled through polynomial variance functions. Estimation of parameters describing the dispersion structure of such model by restricted maximum likelihood via an "average information" algorithm is outlined. An application to mature weight records of beef cow is given, and results are contrasted to those from analyses fitting sets of random regression coefficients for permanent environmental effects.

Age Distribution↗

PubMed2002

Maximum likelihood estimation of a survival function with a change point for truncated and interval-censored data.

This paper considers estimation of a survival function when there exists a change point and the survival time of interest is defined as elapsed time between two related events. Furthermore, there exists censoring on observations on the occurrences of both events and truncation on observations on the occurrence of the second event and thus the survival time of interest. To obtain the maximum likelihood estimator of a survival function, an EM algorithm is developed when the survival function is completely unknown before the change point and known up to a vector of unknown parameters after the change point. The idea is a generalization of that discussed in Moeschberger and Klein. Simulations and an example are used to evaluate and illustrate the algorithm.

Acquired Immunodeficiency Syndrome↗

PubMed1997

Multivariate methods for clustered ordinal data with applications to survival analysis.

Clustered data are the rule in many clinical specialties such as ophthalmology. Methods have been developed for the treatment of clustered continuous or binary outcome data. Less attention has been given to ordinal outcomes which occur frequently in ophthalmology. For example, grading systems of cataract and diabetic retinopathy are commonly used where a photograph is graded by comparison with a series of reference photographs of increasing severity. Some commonly used methods for the analysis of ordered categorical data include the proportional odds and continuation ratio models. It is difficult, however, to incorporate clustering effects into these models. Instead, for clusters of size two, we propose a generalization of the adjacent category model given by log[Pr(i + 1,j)/Pr(i,j)] = ui + (j - 1) lambda + beta' x, where Pr(i,j) denotes the probability that the right (left) eye has grade i(j), x is a vector of (person or eye-specific) covariates for the right eye, u and beta are vectors of location and covariate parameters and lambda is a clustering parameter. Based on this model, and a similar model interchanging the role of i and j, we derived a closed-form expression for Pr(i,j) as a function of u, lambda and beta and use Newton-Raphson method to maximize the likelihood. An extension of the method allows for extra agreement along the diagonal and is then a generalization of the agreement plus linear-by-linear association model proposed by Agresti in the setting of no covariates. We apply these methods to a data set of 43 diabetic subjects from the Harvard Clinical Cataract Research Center, where cortical cataract grade was the outcome. We also extend this methodology to a survival setting, where both censored and uncensored outcomes are available for individual cluster members, and one wishes to take clustering into account. We apply the survival analysis model to a data set of 1807 children (two ears per child) in the greater Boston area, who were followed for the development of otitis media over the first year of life.

Boston↗

PubMed1999

A Markov model for measuring vaccine efficacy for both susceptibility to infection and reduction in infectiousness for prophylactic HIV vaccines.

We use a discrete-time non-homogeneous Markov chain to model data from augmented human immunodeficiency virus (HIV) vaccine trials. For this design, the study population consists of primary participants some of whom have steady sexual partners who are also enrolled to augment the trial. The state space consists of the infection status of primary participants without steady partners and the infection status of both persons in the steady partnerships. The transition probabilities are functions of the two parameters: vaccine efficacy for susceptibility (VES) and infectiousness (VEI). We use likelihood methods to estimate VES and VEI from time-to-event data. We then use stochastic simulations to explore the bias and precision of the estimators under various plausible conditions for HIV vaccine trials. We show that both the VES and VEI are estimable with reasonable precision for the conditions that may exist for planned HIV vaccine trials. We show that exams conducted every six months will likely provide sufficient information to estimate the VE parameters accurately, and that there is little gain in precision for more frequent exams. Finally, we show that joint estimation of the VES and VEI will likely be feasible in a currently planned HIV vaccine trial among injecting drug users in Bangkok, Thailand, if one augments the information about the primary participants in the trial with information about their steady sexual partners.

AIDS Vaccines↗

PubMed2001

Modelling bivariate ordinal responses smoothly with examples from ophthalmology and genetics.

A non-parametric implementation of the bivariate Dale model (BDM) is presented as an extension of the generalized additive model (GAM) of Hastie and Tibshirani. The original BDM is an example of a bivariate generalized linear model. In this paper smoothing is introduced on the marginal as well as on the association level. Our non-parametric procedure can be used as a diagnostic tool for identifying parametric transformations of the covariates in the linear BDM, hence it also provides a kind of goodness-of-fit test for a bivariate generalized linear model. Cubic smoothing spline functions for the covariates are estimated by maximizing a penalized version of the log-likelihood. The method is applied to two studies. The first study is the classical Wisconsin Epidemiologic Study of Diabetic Retinopathy. The second study is a twin study, where the association between the elements of twin pairs is of primary interest. The results show that smoothing on the association level can give a significant improvement to the model fit.

Adolescent↗

PubMed2003

Followup of cocaine-dependent men and women with antisocial personality disorder.

Long-term outcomes following drug treatment were examined for cocaine-dependent men (N = 453) and women (N = 254) with and without antisocial personality disorder (ASP). In-depth assessments were conducted at treatment intake in 1991-93 and at 1 and 5 years following treatment discharge. Overall, 47.2% of the males and 34.3% of females were diagnosed with ASP using DSM-III-R criteria derived from the Diagnostic Interview Schedule. All groups reduced their cocaine, marijuana, and alcohol use; reduced their levels of psychological distress; and improved in functioning (e.g., employment, arrests, residential status). At Year 5 ASP was associated with an increased likelihood of heavy alcohol use and additional substance abuse treatment among men, whereas women with ASP were more likely to report psychological problems and to receive mental health treatment and other services than either women without ASP or men with ASP. The findings suggest the need to address the specific treatment needs of male and female cocaine abusers with ASP.

Activities of Daily Living↗

PubMed2001

Inference for reliability and stress-strength for a scaled Burr type X distribution.

Inference for R = P(Y < X) is considered when X and Y are independently distributed as scaled Burr type X random variables. Under this model, exact inference procedures for R cannot be found. Hence, based on the expected Fisher information matrix which is derived here, asymptotic inference procedures for R and other general functions of the parameters are developed. A bootstrap method to estimate variance for the maximum likelihood estimators is also discussed. To illustrate these techniques, an example using carbon fiber strength data is given. Simulations to assess the effectiveness of these techniques, as well as other concerns, are presented.

Carbon↗