Local full likelihood estimation for the proportional hazards model.

In this paper a new approach to local likelihood estimation for censored data is proposed. This method employs the full likelihood and alternates between estimating the baseline hazard and estimating the covariate effect. The proposed methodology incorporates multidimensional data via additive models. Some results regarding inference for the covariate effect are also presented.     

Walking speed estimation using a shank-mounted inertial measurement unit

We studied the feasibility of estimating walking speed using a shank-mounted inertial measurement unit. Our approach took advantage of the inverted pendulum-like behavior of the stance leg during walking to identify a new method for dividing up walking into individual stride cycles and estimating the initial conditions for the direct integration of the accelerometer and gyroscope signals. To test its accuracy, we compared speed estimates to known values during walking overground and on a treadmill. The speed estimation method worked well across treadmill speeds and slopes yielding a root mean square speed estimation error of only 7%. It also worked well during overground walking with a 4% error in the estimated travel distance. This accuracy is comparable to that achieved from foot-mounted sensors, providing an alternative in sensor positioning for walking speed estimation. Shank mounted sensors may be of great benefit for estimating speed in walking with abnormal foot motion and for the embedded control of knee-mounted devices such as prostheses and energy harvesters.     

CodonTest: Modeling Amino Acid Substitution Preferences in Coding Sequences

Codon models of evolution have facilitated the interpretation of selective forces operating on genomes. These models, however, assume a single rate of non-synonymous substitution irrespective of the nature of amino acids being exchanged. Recent developments have shown that models which allow for amino acid pairs to have independent rates of substitution offer improved fit over single rate models. However, these approaches have been limited by the necessity for large alignments in their estimation. An alternative approach is to assume that substitution rates between amino acid pairs can be subdivided into rate classes, dependent on the information content of the alignment. However, given the combinatorially large number of such models, an efficient model search strategy is needed. Here we develop a Genetic Algorithm (GA) method for the estimation of such models. A GA is used to assign amino acid substitution pairs to a series of rate classes, where is estimated from the alignment. Other parameters of the phylogenetic Markov model, including substitution rates, character frequencies and branch lengths are estimated using standard maximum likelihood optimization procedures. We apply the GA to empirical alignments and show improved model fit over existing models of codon evolution. Our results suggest that current models are poor approximations of protein evolution and thus gene and organism specific multi-rate models that incorporate amino acid substitution biases are preferred. We further anticipate that the clustering of amino acid substitution rates into classes will be biologically informative, such that genes with similar functions exhibit similar clustering, and hence this clustering will be useful for the evolutionary fingerprinting of genes.     

Numerical discretization-based estimation methods for ordinary differential equation models via penalized spline smoothing with applications in biomedical research

Differential equations are extensively used for modeling dynamics of physical processes in many scientific fields such as engineering, physics, and biomedical sciences. Parameter estimation of differential equation models is a challenging problem because of high computational cost and high-dimensional parameter space. In this article, we propose a novel class of methods for estimating parameters in ordinary differential equation (ODE) models, which is motivated by HIV dynamics modeling. The new methods exploit the form of numerical discretization algorithms for an ODE solver to formulate estimating equations. First, a penalized-spline approach is employed to estimate the state variables and the estimated state variables are then plugged in a discretization formula of an ODE solver to obtain the ODE parameter estimates via a regression approach. We consider three different order of discretization methods, Euler's method, trapezoidal rule, and Runge-Kutta method. A higher-order numerical algorithm reduces numerical error in the approximation of the derivative, which produces a more accurate estimate, but its computational cost is higher. To balance the computational cost and estimation accuracy, we demonstrate, via simulation studies, that the trapezoidal discretization-based estimate is the best and is recommended for practical use. The asymptotic properties for the proposed numerical discretization-based estimators are established. Comparisons between the proposed methods and existing methods show a clear benefit of the proposed methods in regards to the trade-off between computational cost and estimation accuracy. We apply the proposed methods t an HIV study to further illustrate the usefulness of the proposed approaches.     

Substitution Model of Sequence Evolution for the Human Immunodeficiency Virus Type 1 Subtype B gp120 Gene over the C2-V5 Region

Phylogenetic analyses frequently rely on models of sequence evolution that detail nucleotide substitution rates, nucleotide frequencies, and site-to-site rate heterogeneity. These models can influence hypothesis testing and can affect the accuracy of phylogenetic inferences. Maximum likelihood methods of simultaneously constructing phylogenetic tree topologies and estimating model parameters are computationally intensive, and are not feasible for sample sizes of 25 or greater using personal computers. Techniques that initially construct a tree topology and then use this non-maximized topology to estimate ML substitution rates, however, can quickly arrive at a model of sequence evolution. The accuracy of this two-step estimation technique was tested using simulated data sets with known model parameters. The results showed that for a star-like topology, as is often seen in human immunodeficiency virus type 1 (HIV-1) subtype B sequences, a random starting topology could produce nucleotide substitution rates that were not statistically different than the true rates. Samples were isolated from 100 HIV-1 subtype B infected individuals from the United States and a 620 nt region of the env gene was sequenced for each sample. The sequence data were used to obtain a substitution model of sequence evolution specific for HIV-1 subtype B env by estimating nucleotide substitution rates and the site-to-site heterogeneity in 100 individuals from the United States. The method of estimating the model should provide users of large data sets with a way to quickly compute a model of sequence evolution, while the nucleotide substitution model we identified should prove useful in the phylogenetic analysis of HIV-1 subtype B env sequences. Received: 4 October 2000 / Accepted: 1 March 2001     

Correcting the Bias of Empirical Frequency Parameter Estimators in Codon Models

Markov models of codon substitution are powerful inferential tools for studying biological processes such as natural selection and preferences in amino acid substitution. The equilibrium character distributions of these models are almost always estimated using nucleotide frequencies observed in a sequence alignment, primarily as a matter of historical convention. In this note, we demonstrate that a popular class of such estimators are biased, and that this bias has an adverse effect on goodness of fit and estimates of substitution rates. We propose a “corrected” empirical estimator that begins with observed nucleotide counts, but accounts for the nucleotide composition of stop codons. We show via simulation that the corrected estimates outperform the de facto standard estimates not just by providing better estimates of the frequencies themselves, but also by leading to improved estimation of other parameters in the evolutionary models. On a curated collection of sequence alignments, our estimators show a significant improvement in goodness of fit compared to the approach. Maximum likelihood estimation of the frequency parameters appears to be warranted in many cases, albeit at a greater computational cost. Our results demonstrate that there is little justification, either statistical or computational, for continued use of the -style estimators.     

Accuracy of rate estimation using relaxed-clock models with a critical focus on the early metazoan radiation

In recent years, a number of phylogenetic methods have been developed for estimating molecular rates and divergence dates under models that relax the molecular clock constraint by allowing rate change throughout the tree. These methods are being used with increasing frequency, but there have been few studies into their accuracy. We tested the accuracy of several relaxed-clock methods (penalized likelihood and Bayesian inference using various models of rate change) using nucleotide sequences simulated on a nine-taxon tree. When the sequences evolved with a constant rate, the methods were able to infer rates accurately, but estimates were more precise when a molecular clock was assumed. When the sequences evolved under a model of auto-correlated rate change, rates were accurately estimated using penalized likelihood and by Bayesian inference using lognormal and exponential models of rate change, while other models did not perform as well. When the sequences evolved under a model of uncorrelated rate change, only Bayesian inference using an exponential rate model performed well. Collectively, the results provide a strong recommendation for using the exponential model of rate change if a conservative approach to divergence time estimation is required. A case study is presented in which we use a simulation-based approach to examine the hypothesis of elevated rates in the Cambrian period, and it is found that these high rate estimates might be an artifact of the rate estimation method. If this bias is present, then the ages of metazoan divergences would be systematically underestimated. The results of this study have implications for studies of molecular rates and divergence dates.     

Estimation of kinetic parameters in a structured yeast model using regularisation.

In this work, a procedure for estimating kinetic parameters in biochemically structured models was developed. The approach is applicable when the structure of a kinetic model has been set up and the kinetic parameters should be estimated. The procedure consists of five steps. First, initial values were found in or calculated from literature. Hereafter using sensitivity analysis the most sensitive parameters were identified. In the third step physiological knowledge was combined with the parameter sensitivities to manually tune the most sensitive parameters. In step four, a global optimisation routine was applied for simultaneous estimation of the most sensitive parameters identified during the sensitivity analysis. Regularisation was included in the simultaneous estimation to reduce the effect of insensitive parameters. Finally, confidence intervals for the estimated parameters were calculated. This parameter estimation approach was demonstrated on a biochemically structured yeast model containing 11 reactions and 37 kinetic constants as a case study.     

Towards accurate estimation of the proportion of true null hypotheses in multiple testing

BACKGROUND: Biomedical researchers are now often faced with situations where it is necessary to test a large number of hypotheses simultaneously, eg, in comparative gene expression studies using high-throughput microarray technology. To properly control false positive errors the FDR (false discovery rate) approach has become widely used in multiple testing. The accurate estimation of FDR requires the proportion of true null hypotheses being accurately estimated. To date many methods for estimating this quantity have been proposed. Typically when a new method is introduced, some simulations are carried out to show the improved accuracy of the new method. However, the simulations are often very limited to covering only a few points in the parameter space. RESULTS: Here I have carried out extensive in silico experiments to compare some commonly used methods for estimating the proportion of true null hypotheses. The coverage of these simulations is unprecedented thorough over the parameter space compared to typical simulation studies in the literature. Thus this work enables us to draw conclusions globally as to the performance of these different methods. It was found that a very simple method gives the most accurate estimation in a dominantly large area of the parameter space. Given its simplicity and its overall superior accuracy I recommend its use as the first choice for estimating the proportion of true null hypotheses in multiple testing.     

A tiered approach to estimate inventory data and impacts of chemical products and mixtures

Purpose

Mixtures of organic chemicals are a part of virtually all life cycles, but LCI data exist for only relatively few chemicals. Thus, estimation methods are required. However, these are often either very time-consuming or deliver results of low quality. This article compares existing and new methods in two scenarios and recommends a tiered approach of different methods for an efficient estimation of the production impacts of chemical mixtures.

Methods

Four approaches to estimate impacts of a large number of chemicals are compared in this article: extrapolation from existing data, substitution with generic datasets on chemicals, molecular structure-based models (MSMs, in this case the Finechem tool), and using process-based estimation methods. Two scenarios were analyzed as case studies: soft PVC plastic and a tobacco flavor, a mixture of 20 chemicals.

Results

Process models have the potential to deliver the best estimations, as existing information on production processes can be integrated. However, their estimation quality suffers when such data are not available and they are time-consuming to apply, which is problematic when estimating large numbers of chemicals. Extrapolation from known to unknown components and use of generic datasets are generally not recommended. In both case studies, these two approaches significantly underestimated the impacts of the chemicals compared to the process models. MSMs were generally able to estimate impacts on the same level as the more complex process models. A tiered approach using MSMs to determine the relevance of individual components in mixtures and applying process models to the most relevant components offered a simpler and faster estimation process while delivering results on the level of most process models.

Conclusions

The application of the tiered combination of MSMs and process models allows LCA practitioners a relatively fast and simple estimation of the LCIA results of chemicals, even for mixtures with a large number of components. Such mixtures previously presented a problem, as the application of process models for all components was very time-consuming, while the existing, simple approaches were shown to be inadequate in this study. We recommend the tiered approach as a significant improvement over previous approaches for estimating LCA results of chemical mixtures.     

Analysis of cytoplasmic and maternal effects. II. Genetic models for triploid endosperms

Genetic models for quantitative traits of triploid endosperms are proposed for the analysis of direct gene effects, cytoplasmic effects, and maternal gene effects. The maternal effect is partitioned into maternal additive and dominance components. In the full genetic model, the direct effect is partitioned into direct additive and dominance components and high-order dominance component, which are the cumulative effects of three-allele interactions. If the high-order dominance effects are of no importance, a reduced genetic model can be used. Monte Carlo simulations were conducted in this study for demonstrating unbiasedness of estimated variance and covariance components from the MINQUE (0/1) procedure, which is a minimum norm quadratic unbiased estimation (MINQUE) method setting 0 for all the prior covariances and 1 for all the prior variances. Robustness of estimating variance and covariance components for the genetic models was tested by simulations. Both full and reduced genetic models are shown to be robust for estimating variance and covariance components under several situations of no specific effects. Efficiency of predicting random genetic effects for the genetic models by the MINQUE (0/1) procedure was compared with the best linear unbiased prediction (BLUP). A worked example is given to illustrate the use of the reduced genetic model for kernel growth characteristics in corn (Zea mays L.).     

Approximate methods for estimating the pattern of nucleotide substitution and the variation of substitution rates among sites

We propose two approximate methods (one based on parsimony and one on pairwise sequence comparison) for estimating the pattern of nucleotide substitution and a parsimony-based method for estimating the gamma parameter for variable substitution rates among sites. The matrix of substitution rates that represents the substitution pattern can be recovered through its relationship with the observable matrix of site pattern frequences in pairwise sequence comparisons. In the parsimony approach, the ancestral sequences reconstructed by the parsimony algorithm were used, and the two sequences compared are those at the ends of a branch in the phylogenetic tree. The method for estimating the gamma parameter was based on a reinterpretation of the numbers of changes at sites inferred by parsimony. Three data sets were analyzed to examine the utility of the approximate methods compared with the more reliable likelihood methods. The new methods for estimating the substitution pattern were found to produce estimates quite similar to those obtained from the likelihood analyses. The new method for estimating the gamma parameter was effective in reducing the bias in conventional parsimony estimates, although it also overestimated the parameter. The approximate methods are computationally very fast and appear useful for analyzing large data sets, for which use of the likelihood method requires excessive computation.      

Incorporating capture heterogeneity in the estimation of autoregressive coefficients of animal population dynamics using capture–recapture data

Population dynamic models combine density dependence and environmental effects. Ignoring sampling uncertainty might lead to biased estimation of the strength of density dependence. This is typically addressed using state‐space model approaches, which integrate sampling error and population process estimates. Such models seldom include an explicit link between the sampling procedures and the true abundance, which is common in capture–recapture settings. However, many of the models proposed to estimate abundance in the presence of capture heterogeneity lead to incomplete likelihood functions and cannot be straightforwardly included in state‐space models. We assessed the importance of estimating sampling error explicitly by taking an intermediate approach between ignoring uncertainty in abundance estimates and fully specified state‐space models for density‐dependence estimation based on autoregressive processes. First, we estimated individual capture probabilities based on a heterogeneity model for a closed population, using a conditional multinomial likelihood, followed by a Horvitz–Thompson estimate for abundance. Second, we estimated coefficients of autoregressive models for the log abundance. Inference was performed using the methodology of integrated nested Laplace approximation (INLA). We performed an extensive simulation study to compare our approach with estimates disregarding capture history information, and using R‐package VGAM, for different parameter specifications. The methods were then applied to a real data set of gray‐sided voles Myodes rufocanus from Northern Norway. We found that density‐dependence estimation was improved when explicitly modeling sampling error in scenarios with low process variances, in which differences in coverage reached up to 8% in estimating the coefficients of the autoregressive processes. In this case, the bias also increased assuming a Poisson distribution in the observational model. For high process variances, the differences between methods were small and it appeared less important to model heterogeneity.     

Estimating the hidden learning representations

Successful adaptation relies on the ability to learn the consequence of our actions in different environments. However, understanding the neural bases of this ability still represents one of the great challenges of system neuroscience. In fact, the neuronal plasticity changes occurring during learning cannot be fully controlled experimentally and their evolution is hidden. Our approach is to provide hypotheses about the structure and dynamics of the hidden plasticity changes using behavioral learning theory. In fact, behavioral models of animal learning provide testable predictions about the hidden learning representations by formalizing their relation with the observables of the experiment (stimuli, actions and outcomes). Thus, we can understand whether and how the predicted learning processes are represented at the neural level by estimating their evolution and correlating them with neural data. Here, we present a bayesian model approach to estimate the evolution of the internal learning representations from the observations of the experiment (state estimation), and to identify the set of models' parameters (parameter estimation) and the class of behavioral model (model selection) that are most likely to have generated a given sequence of actions and outcomes. More precisely, we use Sequential Monte Carlo methods for state estimation and the maximum likelihood principle (MLP) for model selection and parameter estimation. We show that the method recovers simulated trajectories of learning sessions on a single-trial basis and provides predictions about the activity of different categories of neurons that should participate in the learning process. By correlating the estimated evolutions of the learning variables, we will be able to test the validity of different models of instrumental learning and possibly identify the neural bases of learning.     

Estimation of evolutionary parameters with phylogenetic trees

An important issue in the phylogenetic analysis of nucleotide sequence data using the maximum likelihood (ML) method is the underlying evolutionary model employed. We consider the problem of simultaneously estimating the tree topology and the parameters in the underlying substitution model and of obtaining estimates of the standard errors of these parameter estimates. Given a fixed tree topology and corresponding set of branch lengths, the ML estimates of standard evolutionary model parameters are asymptotically efficient, in the sense that their joint distribution is asymptotically normal with the variance–covariance matrix given by the inverse of the Fisher information matrix. We propose a new estimate of this conditional variance based on estimation of the expected information using a Monte Carlo sampling (MCS) method. Simulations are used to compare this conditional variance estimate to the standard technique of using the observed information under a variety of experimental conditions. In the case in which one wishes to estimate simultaneously the tree and parameters, we provide a bootstrapping approach that can be used in conjunction with the MCS method to estimate the unconditional standard error. The methods developed are applied to a real data set consisting of 30 papillomavirus sequences. This overall method is easily incorporated into standard bootstrapping procedures to allow for proper variance estimation.     

The Treatment of Missing Values in Logistic Regression

The efficiencies of the estimators in the linear logistic regression model are examined using simulations under six missing value treatments. These treatments use either the maximum likelihood or the discriminant function approach in the estimation of the regression coefficients. Missing values are assumed to occur at random. The cases of multivariate normal and dichotomous independent variables are both considered. We found that in general, there is no uniformly best method. However, mean substitution and discriminant function estimation using existing pairs of values for correlations turn out to be favourable for the cases considered.     

Performance-based selection of likelihood models for phylogeny estimation

Phylogenetic estimation has largely come to rely on explicitly model-based methods. This approach requires that a model be chosen and that that choice be justified. To date, justification has largely been accomplished through use of likelihood-ratio tests (LRTs) to assess the relative fit of a nested series of reversible models. While this approach certainly represents an important advance over arbitrary model selection, the best fit of a series of models may not always provide the most reliable phylogenetic estimates for finite real data sets, where all available models are surely incorrect. Here, we develop a novel approach to model selection, which is based on the Bayesian information criterion, but incorporates relative branch-length error as a performance measure in a decision theory (DT) framework. This DT method includes a penalty for overfitting, is applicable prior to running extensive analyses, and simultaneously compares all models being considered and thus does not rely on a series of pairwise comparisons of models to traverse model space. We evaluate this method by examining four real data sets and by using those data sets to define simulation conditions. In the real data sets, the DT method selects the same or simpler models than conventional LRTs. In order to lend generality to the simulations, codon-based models (with parameters estimated from the real data sets) were used to generate simulated data sets, which are therefore more complex than any of the models we evaluate. On average, the DT method selects models that are simpler than those chosen by conventional LRTs. Nevertheless, these simpler models provide estimates of branch lengths that are more accurate both in terms of relative error and absolute error than those derived using the more complex (yet still wrong) models chosen by conventional LRTs. This method is available in a program called DT-ModSel.     

A method for assessing patterns of familial resemblance in complex human pedigrees, with an application to the nevus-count data in Utah kindreds.

An analytic method is described for estimating phenotypic correlations between pairs of members of specific relationships in pedigrees. In estimating correlations, this new method allows simultaneous adjustment for available covariates such as age, gender, environmental factors, and variables reflecting ascertainment mode, through mean- and variance-regression models. The estimated correlations and regression coefficients corresponding to covariates are consistent and asymptotically normally distributed. Differing from a full-likelihood approach, this new method does not require the assumption of a particular joint distribution of phenotypes from a pedigree, such as the multivariate normal distribution, but instead only requires correct specification of mean- and variance-regression models. Within this framework, missing data, if they are missing completely at random, can be ignored without biasing estimates. The method is illustrated by an application using nevus-count data from 28 Utah kinships. The results from the analysis are that covariate-adjusted nevus counts are correlated between parents and children (correlation .22; P less than .001) and between siblings (correlation .32; P less than .001), while the correlation of -.04 between husband and wife is not significantly different (P = .31) from 0. This result is consistent with a genetic etiology of nevus count.     

Marginal structural models for estimating principal stratum direct effects under the monotonicity assumption

In epidemiological and clinical research, investigators are frequently interested in estimating the direct effect of a treatment on an outcome that is not relayed by intermediate variables. In 2009, VanderWeele presented marginal structural models (MSMs) for estimating direct effects based on interventions on the mediator. This paper focuses on direct effects based on principal stratification, i.e. principal stratum direct effects (PSDEs), which are causal effects within latent subgroups of subjects where the mediator is constant, regardless of the exposure status. We propose MSMs for estimating PSDEs. We demonstrate that the PSDE can be estimated readily using MSMs under the monotonicity assumption.     

Detecting femur–insert collisions to improve precision of fluoroscopic knee arthroplasty analysis

Fluoroscopic analysis is an important tool for assessing in vivo kinematics of knee prostheses. Most commonly, a single-plane fluoroscopic setup is used to capture the motion of prostheses during a particular task. Unfortunately, single-plane fluoroscopic analysis is imprecise in the out-of-plane direction. This can result in reconstructing physically impossible poses, in which—for example—the femoral component intersects with the insert, as the normal pose estimation process does not take into account the relation between the components. In the proposed method, the poses of both components are estimated simultaneously, while preventing femur–insert collisions. In a phantom study, the accuracy and precision of the new method in estimating the relative pose of the femoral component were compared to those of the original method. With reverse engineered models, the errors in estimating the out-of-plane position decreased from 2.0±0.7 to 0.1±0.1 mm, without effects on the errors in rotations and the in-plane positions. With CAD models, the errors in estimating the out-of-plane position decreased from 5.3±0.7 mm (mean±SD) to 0.0±0.4 mm, at the expense of a decreased precision for the other position or orientation parameters. In conclusion, collision detection can prevent reconstructing impossible poses and it improves the position and motion estimation in the out-of-plane direction.