Multivariate Extensions of the Mixed Model for Quantitative Traits

The mixed model for complex segregation analysis of quantitative data from three-generational nuclear families is extended to the multivariate case. Likelihood functions for hypothesis testing are derived for two types of conditional analysis of multiple traits: first when entry to the study depends on the index case's values of all the quantitative traits that are of interest, and second when entry depends on only one trait, but other correlated traits are to be studied simultaneously. Using direct products of covariance matrices, these functions are seen to be direct multivariate equivalence of the univariate functions.     

One-step targeted maximum likelihood estimation for time-to-event outcomes

Researchers in observational survival analysis are interested in not only estimating survival curve nonparametrically but also having statistical inference for the parameter. We consider right-censored failure time data where we observe n independent and identically distributed observations of a vector random variable consisting of baseline covariates, a binary treatment at baseline, a survival time subject to right censoring, and the censoring indicator. We assume the baseline covariates are allowed to affect the treatment and censoring so that an estimator that ignores covariate information would be inconsistent. The goal is to use these data to estimate the counterfactual average survival curve of the population if all subjects are assigned the same treatment at baseline. Existing observational survival analysis methods do not result in monotone survival curve estimators, which is undesirable and may lose efficiency by not constraining the shape of the estimator using the prior knowledge of the estimand. In this paper, we present a one-step Targeted Maximum Likelihood Estimator (TMLE) for estimating the counterfactual average survival curve. We show that this new TMLE can be executed via recursion in small local updates. We demonstrate the finite sample performance of this one-step TMLE in simulations and an application to a monoclonal gammopathy data.     

Estimation and Tests of Mendelian Inheritance in Small Samples of Human Families

Estimation of parameters in human genetics is usually performed by Maximum Likelihood methods for large samples relying on asymptotic results. With the aim of evaluating the importance of the bias resulting from sample size, two sets of human family data have been analysed. The bias is not very important, but programs have been elaborated, giving better estimations. The tests of hypotheses from these estimations have also been considered.     

The Role of Human Error Analysis in Occupational and Environmental Risk Assessment: A Serbian Experience

Human error analysis is certainly a challenge today for all involved in safety and environmental risk assessment. The risk assessment process should not ignore the role of humans in accidental events and the consequences that may derive from human error. This article presents a case study of the Success Likelihood Index Method (SLIM) applied to the Electric Power Company of Serbia (EPCS), with the aim to disclose the importance of human error analysis in risk assessment. A database on work-related injuries, accidents, and critical interventions that occurred over a 10-year period in the EPCS provided the basis for this study. The research comprised analysis of 1074 workplaces, with a total of 3997 employees. A detailed analysis identified 10 typical human errors, performance shaping factors (PSFs), and estimated human error probability (HEP). Based on the obtained research results one can conclude that PSF control remains crucial for human error reduction, and thus prevention of occupational injuries and fatalities (the number of injuries decreased from 58 in 2012 to 44 in 2013, no fatalities recorded). Furthermore, the case study performed at the EPCS confirmed that the SLIM is highly applicable for quantification of human errors, comprehensive, and easy to perform.     

Unified maximum likelihood estimates for closed capture-recapture models using mixtures

Agresti (1994, Biometrics 50, 494-500) and Norris and Pollock (1996a, Biometrics 52, 639-649) suggested using methods of finite mixtures to partition the animals in a closed capture-recapture experiment into two or more groups with relatively homogeneous capture probabilities. This enabled them to fit the models Mh, Mbh (Norris and Pollock), and Mth (Agresti) of Otis et al. (1978, Wildlife Monographs 62, 1-135). In this article, finite mixture partitions of animals and/or samples are used to give a unified linear-logistic framework for fitting all eight models of Otis et al. by maximum likelihood. Likelihood ratio tests are available for model comparisons. For many data sets, a simple dichotomy of animals is enough to substantially correct for heterogeneity-induced bias in the estimation of population size, although there is the option of fitting more than two groups if the data warrant it.     

MLGO: phylogeny reconstruction and ancestral inference from gene-order data

Background

The rapid accumulation of whole-genome data has renewed interest in the study of using gene-order data for phylogenetic analyses and ancestral reconstruction. Current software and web servers typically do not support duplication and loss events along with rearrangements.

Results

MLGO (Maximum Likelihood for Gene-Order Analysis) is a web tool for the reconstruction of phylogeny and/or ancestral genomes from gene-order data. MLGO is based on likelihood computation and shows advantages over existing methods in terms of accuracy, scalability and flexibility.

Conclusions

To the best of our knowledge, it is the first web tool for analysis of large-scale genomic changes including not only rearrangements but also gene insertions, deletions and duplications. The web tool is available from http://www.geneorder.org/server.php.     

Multilocus Phylogeny of Lycodon and the Taxonomic Revision of Oligodon multizonatum

Classification of the Asian snake genera Lycodon and Oligodon has proven challenging. We conducted a molecular phylogenetic analysis to estimate the phylogenetic relationships in the genus of Lycodon and clarify the taxonomic status of Oligodon multizonatum using mitochondrial（cyt b, ND4） and nuclear（c-mos） genes. Phylogenetic trees estimated using Maximum Likelihood and Bayesian Inference indicated that O. multizonatum is actually a species of Lycodon. Comparing morphological data from O. multizonatum and its closest relatives also supported this conclusion. Our results imply that a thorough review of the evolutionary relationships in the genus of Lycodon is strong suggested.     

Estimation of components of genetic variance and heritability for flowering time and yield in gerbera using Derivative-Free Restricted Maximum Likelihood (DFRML)

Summary Additive genetic components of variance and narrow-sense heritabilities were estimated for flowering time (FT) and cut-flower yield (Y) for six generations of the Davis Population of gerbera using Derivative-Free Restricted Maximum Likelihood (DFRML). Additive genetic variance accounted for 54% of the total variability for FT and 30% of the total variability for Y. The heritability of FT (0.54) agreed with previous ANOVA-based estimates. However, the heritability of Y (0.30) was substantially lower than estimates using ANOVA. The advantages of DFRML and its applications in the estimation of components of genetic variance and heritabilities of plant populations are discussed.     

Spatial dependence modeling of latent susceptibility and time to joint damage in psoriatic arthritis

Important scientific insights into chronic diseases affecting several organ systems can be gained from modeling spatial dependence of sites experiencing damage progression. We describe models and methods for studying spatial dependence of joint damage in psoriatic arthritis (PsA). Since a large number of joints may remain unaffected even among individuals with a long disease history, spatial dependence is first modeled in latent joint-specific indicators of susceptibility. Among susceptible joints, a Gaussian copula is adopted for dependence modeling of times to damage. Likelihood and composite likelihoods are developed for settings, where individuals are under intermittent observation and progression times are subject to type K interval censoring. Two-stage estimation procedures help mitigate the computational burden arising when a large number of processes (i.e., joints) are under consideration. Simulation studies confirm that the proposed methods provide valid inference, and an application to the motivating data from the University of Toronto Psoriatic Arthritis Clinic yields important insights which can help physicians distinguish PsA from arthritic conditions with different dependence patterns.     

Likelihood methods for detecting temporal shifts in diversification rates

Maximum likelihood is a potentially powerful approach for investigating the tempo of diversification using molecular phylogenetic data. Likelihood methods distinguish between rate-constant and rate-variable models of diversification by fitting birth-death models to phylogenetic data. Because model selection in this context is a test of the null hypothesis that diversification rates have been constant over time, strategies for selecting best-fit models must minimize Type I error rates while retaining power to detect rate variation when it is present. Here I examine model selection, parameter estimation, and power to reject the null hypothesis using likelihood models based on the birth-death process. The Akaike information criterion (AIC) has often been used to select among diversification models; however, I find that selecting models based on the lowest AIC score leads to a dramatic inflation of the Type I error rate. When appropriately corrected to reduce Type I error rates, the birth-death likelihood approach performs as well or better than the widely used gamma statistic, at least when diversification rates have shifted abruptly over time. Analyses of datasets simulated under a range of rate-variable diversification scenarios indicate that the birth-death likelihood method has much greater power to detect variation in diversification rates when extinction is present. Furthermore, this method appears to be the only approach available that can distinguish between a temporal increase in diversification rates and a rate-constant model with nonzero extinction. I illustrate use of the method by analyzing a published phylogeny for Australian agamid lizards.     

Design and Inference for Cancer Biomarker Study with an Outcome and Auxiliary‐Dependent Subsampling

Summary In cancer research, it is important to evaluate the performance of a biomarker (e.g., molecular, genetic, or imaging) that correlates patients' prognosis or predicts patients' response to treatment in a large prospective study. Due to overall budget constraint and high cost associated with bioassays, investigators often have to select a subset from all registered patients for biomarker assessment. To detect a potentially moderate association between the biomarker and the outcome, investigators need to decide how to select the subset of a fixed size such that the study efficiency can be enhanced. We show that, instead of drawing a simple random sample from the study cohort, greater efficiency can be achieved by allowing the selection probability to depend on the outcome and an auxiliary variable; we refer to such a sampling scheme as outcome and auxiliary‐dependent subsampling (OADS). This article is motivated by the need to analyze data from a lung cancer biomarker study that adopts the OADS design to assess epidermal growth factor receptor (EGFR) mutations as a predictive biomarker for whether a subject responds to a greater extent to EGFR inhibitor drugs. We propose an estimated maximum‐likelihood method that accommodates the OADS design and utilizes all observed information, especially those contained in the likelihood score of EGFR mutations (an auxiliary variable of EGFR mutations) that is available to all patients. We derive the asymptotic properties of the proposed estimator and evaluate its finite sample properties via simulation. We illustrate the proposed method with a data example.     

Anthropometric Cutoff Points for Predicting Chronic Diseases in the Mexican National Health Survey 2000

Objective: To determine optimum anthropometric cutoffs for predicting the likelihood ratios of type 2 diabetes mellitus (DM) and hypertension (HT) in Mexicans. Research Methods and Procedures: Data from a randomly selected, nationally representative health survey (2000) with 11, 730 men [37.4 (± 12.9) years] and 26, 647 women [37.3(± 12.9) years] were assessed for values of body mass index (BMI) and waist circumference (WC) for predicting DM or HT by receiver operating characteristic curve analyses. Likelihood ratios for DM and HT were calculated, and BMIs or WCs for public‐health screening were developed. Subanalyses included regional data. Results: Likelihood ratios of DM and HT increased from BMI values of 22 to 24 kg/m² in both sexes and with WC values of 75 to 80 cm in men and 70 to 80 cm in women. The best BMI cutoffs for predicting DM were 26.3 to 27.4 kg/m² in men and 27.7 to 28.9 kg/m² in women, with similar values for HT, i.e., 26.2 to 27.0 kg/m² and 27.7 to 28.5 kg/m², for men and women, respectively; WC cutoffs for DM were 93 to 98 cm in men and 94 to 99 cm in women, and cutoffs for HT were 92 to 96 cm and 93 to 96 cm for men and women, respectively. The WC cutoffs had higher sensitivity and specificity than those of BMI. Discussion: The risk for DM and HT starts at lower levels of BMI and WC than those suggested by WHO. WC is a better discriminator than BMI measures for use in public health.     

Impact of character correlation and variable groupings on modern human population tree resolution

Relationships among modern human populations are often explored through the use of linear measurements taken on the cranium and expressed in the form of dendrograms. However, craniometric variables are strongly correlated and thereby violate the assumption of independence that most statistical analyses require. This study explores the relationship between differing methods of variable treatment and the statistical robustness of the outcomes they yield, as depicted in interpopulational trees of relatedness among modern humans. Three methods of grouping variables are examined. The first method leaves them ungrouped, the second groups variables on the basis of the developmental and/or functional complex of the cranium to which they are thought to belong, and the last method reduces variables by using principal components analysis. The strength of each of these methods is tested through the use of the Continuous Character Maximum Likelihood (CONTML) program in the PHYLIP phylogeny inference package. This program produces output in the form of trees, and the resolution of the branching topology is given as a log-likelihood value, with statistical confidence intervals supporting each branch placement on the tree. The results indicate that leaving variables ungrouped provides misleadingly strong results by failing to account for character correlation. Of the alternative two grouping methods, the covarying components method yields the best-resolved tree with stronger statistical support for its topology than the approach of grouping variables on the basis of their location on the cranium. Finally, the implications for interpreting population histories based on such methods are discussed.     

Plausibility Inference for Generalized Poisson Distribution

The two parameter generalized Poisson distribution (GPD) has been usefully applied to many biological and genetic problems and important interpretations have been given to both the parameters; however, reliable interval estimates for them are not available. A number of results on the plausibility inference for the GPD have been provided. Likelihood intervals and likelihood regions are also considered for the two parameters of the GPD. Expressions needed to compute the intervals and regions are given. These results are then applied to two biological problems to derive the relevant regions and intervals for the parameters of interest.     

Tumor Necrosis Factor Inhibition and Head and Neck Cancer Recurrence and Death in Rheumatoid Arthritis

The objective of this retrospective cohort study was to determine the effect of tumor necrosis factor inhibitor (TNFi) therapy on the risk of head and neck cancer (HNC) recurrence or HNC-attributable death in patients with rheumatoid arthritis (RA). RA patients with HNC were assembled from the US national Veterans’ Affairs (VA) administrative databases, and diagnoses confirmed and data collected by electronic medical record review. The cohort was divided into those treated with non-biologic disease-modifying anti-rheumatic drugs (nbDMARDs) versus TNF inhibitors (TNFi) after a diagnosis of HNC. Likelihood of a composite endpoint of recurrence or HNC-attributable death was determined by Cox proportional hazards regression. Of 180 patients with RA and HNC, 31 were treated with TNFi and 149 with nbDMARDs after the diagnosis of HNC. Recurrence or HNC-attributable death occurred in 5/31 (16.1%) patients in the TNFi group and 44/149 (29.5%) patients in the nbDMARD group (p = 0.17); it occurred in 2/16 (13%) patients who received TNFi in the year prior to HNC diagnosis but not after. Overall stage at diagnosis (p = 0.03) and stage 4 HNC (HR 2.49 [CI 1.06–5.89]; p = 0.04) were risk factors for recurrence or HNC-attributable death; treatment with radiation or surgery was associated with a lower risk (HR 0.35 [CI 0.17–0.74]; p = 0.01 and HR 0.39 [CI 0.20–0.76]; p = 0.01 respectively). Treatment with TNFi was not a risk factor for recurrence or HNC-attributable death (HR 0.75; CI 0.31–1.85; p = 0.54). We conclude that treatment with TNFi may be safe in patients with RA and HNC, especially as the time interval between HNC treatment and non-recurrence increases. In this study, TNF inhibition was not associated with an increase in recurrence or HNC-attributable death.     

Application of Artificial Bee Colony Algorithm to Maximum Likelihood DOA Estimation

Maximum Likelihood (ML) method has an excellent performance for Direction-Of-Arrival (DOA) estimation, but a multidimensional nonlinear solution search is required which complicates the computation and prevents the method from practical use. To reduce the high computational burden of ML method and make it more suitable to engineering applications, we apply the Artificial Bee Colony (ABC) algorithm to maximize the likelihood function for DOA estimation. As a recently proposed bio-inspired computing algorithm, ABC algorithm is originally used to optimize multivariable functions by imitating the behavior of bee colony finding excellent nectar sources in the nature environment. It offers an excellent alternative to the conventional methods in ML-DOA estimation. The performance of ABC-based ML and other popular meta-heuristic-based ML methods for DOA estimation are compared for various scenarios of convergence, Signal-to-Noise Ratio (SNR), and number of iterations. The computation loads of ABC-based ML and the conventional ML methods for DOA estimation are also investigated. Simulation results demonstrate that the proposed ABC based method is more efficient in computation and statistical performance than other ML-based DOA estimation methods.     

Coalescent-based species tree inference from gene tree topologies under incomplete lineage sorting by maximum likelihood

Incomplete lineage sorting can cause incongruence between the phylogenetic history of genes (the gene tree) and that of the species (the species tree), which can complicate the inference of phylogenies. In this article, I present a new coalescent-based algorithm for species tree inference with maximum likelihood. I first describe an improved method for computing the probability of a gene tree topology given a species tree, which is much faster than an existing algorithm by Degnan and Salter (2005). Based on this method, I develop a practical algorithm that takes a set of gene tree topologies and infers species trees with maximum likelihood. This algorithm searches for the best species tree by starting from initial species trees and performing heuristic search to obtain better trees with higher likelihood. This algorithm, called STELLS (which stands for Species Tree InfErence with Likelihood for Lineage Sorting), has been implemented in a program that is downloadable from the author's web page. The simulation results show that the STELLS algorithm is more accurate than an existing maximum likelihood method for many datasets, especially when there is noise in gene trees. I also show that the STELLS algorithm is efficient and can be applied to real biological datasets.     

Prediction of distal residue participation in enzyme catalysis

A scoring method for the prediction of catalytically important residues in enzyme structures is presented and used to examine the participation of distal residues in enzyme catalysis. Scores are based on the Partial Order Optimum Likelihood (POOL) machine learning method, using computed electrostatic properties, surface geometric features, and information obtained from the phylogenetic tree as input features. Predictions of distal residue participation in catalysis are compared with experimental kinetics data from the literature on variants of the featured enzymes; some additional kinetics measurements are reported for variants of Pseudomonas putida nitrile hydratase (ppNH) and for Escherichia coli alkaline phosphatase (AP). The multilayer active sites of P. putida nitrile hydratase and of human phosphoglucose isomerase are predicted by the POOL log ZP scores, as is the single-layer active site of P. putida ketosteroid isomerase. The log ZP score cutoff utilized here results in over-prediction of distal residue involvement in E. coli alkaline phosphatase. While fewer experimental data points are available for P. putida mandelate racemase and for human carbonic anhydrase II, the POOL log ZP scores properly predict the previously reported participation of distal residues.     

ESTIMATING THE MATING BEHAVIOR OF A PAIR OF HYBRIDIZING HELICONIUS SPECIES IN THE WILD

Premating isolation between incipient species is rarely studied in nature, even though mating tests in captivity may give an inaccurate picture of natural hybridization. We studied premating barriers between the warningly colored butterflies Heliconius erato and H. himera (Lepidoptera) in a narrow contact zone in Ecuador, where hybrids are found at low frequency. Eggs obtained from wild-mated females, supplemented with eggs and young larvae collected from the wild, were reared to adulthood. Adult color patterns of these progeny were then used to infer how their parents must have mated. Likelihood was used to estimate both the frequencies of potential parental genotypes from adult phenotypes collected in the wild, and the degree of assortative mating from the inferred parents. The frequencies of parental genotypes varied across the hybrid zone, but our statistical method allowed estimates of hybrid deficit and assortative mating to be integrated across all sites sampled. The best estimate of the frequency of F₁ and backcross hybrid adults in the center of the hybrid zone was 10%, with support limits (7.1%, 13.0%; support limits are asymptotically equivalent to 95% confidence limits). Mating was highly assortative: in the center of the hybrid zone the cross-mating probability between H. erato and H. himera was only 5% (0.3%, 21.4%). Wild hybrids themselves mated with both pure forms, and the probabilities that they mated in any direction were not significantly lower than those among conspecifics. These results are consistent with earlier laboratory studies on mate choice, and suggest that selection against hybrids must be strong to prevent formation of a hybrid swarm. Unfortunately, the wide support limits on mating behavior precluded a measure of the strength of selection from these data alone. Our statistical approach provides a useful general method for estimating mate choice in the wild.     

Property and efficiency of the maximum likelihood method for molecular phylogeny

Summary The maximum likelihood (ML) method for constructing phylogenetic trees (both rooted and unrooted trees) from DNA sequence data was studied. Although there is some theoretical problem in the comparison of ML values conditional for each topology, it is possible to make a heuristic argument to justify the method. Based on this argument, a new algorithm for estimating the ML tree is presented. It is shown that under the assumption of a constant rate of evolution, the ML method and UPGMA always give the same rooted tree for the case of three operational taxonomic units (OTUs). This also seems to hold approximately for the case with four OTUs. When we consider unrooted trees with the assumption of a varying rate of nucleotide substitution, the efficiency of the ML method in obtaining the correct tree is similar to those of the maximum parsimony method and distance methods. The ML method was applied to Brown et al.'s data, and the tree topology obtained was the same as that found by the maximum parsimony method, but it was different from those obtained by distance methods.