A retrospective assessment of the accuracy of the paternity inference program CERVUS

CERVUS is a Windows-based software package written to infer paternity in natural populations. It offers advantages over exclusionary-based methods of paternity inference in that multiple nonexcluded males can be statistically distinguished, laboratory typing error is considered and statistical confidence is determined for assigned paternities through simulation. In this study we use a panel of 84 microsatellite markers to retrospectively determine the accuracy of statistical confidence when CERVUS was used to infer paternity in a population of red deer (Cervus elaphus). The actual confidence of CERVUS-assigned paternities was not significantly different from that predicted by simulation.     

Phylogenetic analyses of mode of larval development

Phylogenies based on morphological or molecular characters have been used to provide an evolutionary context for analysis of larval evolution. Studies of gastropods, bivalves, tunicates, sea stars, sea urchins, and polychaetes have revealed massive parallel evolution of similar larval forms. Some of these studies were designed to test, and have rejected, the species selection hypothesis for evolutionary trends in the frequency of derived larvae or life history traits. However, the lack of well supported models of larval character evolution leave some doubt about the quality of inferences of larval evolution from phylogenies of living taxa. Better models based on maximum likelihood methods and known prior probabilities of larval character state changes will improve our understanding of the history of larval evolution.     

Likelihood analysis of ongoing gene flow and historical association

Abstract.— We develop a Monte Carlo-based likelihood method for estimating migration rates and population divergence times from data at unlinked loci at which mutation rates are sufficiently low that, in the recent past, the effects of mutation can be ignored. The method is applicable to restriction fragment length polymorphisms (RFLPs) and single nucleotide polymorphisms (SNPs) sampled from a subdivided population. The method produces joint maximum-likelihood estimates of the migration rate and the time of population divergence, both scaled by population size, and provides a framework in which to test either for no ongoing gene flow or for population divergence in the distant past. We show the method performs well and provides reasonably accurate estimates of parameters even when the assumptions under which those estimates are obtained are not completely satisfied. Furthermore, we show that, provided that the number of polymorphic loci is sufficiently large, there is some power to distinguish between ongoing gene flow and historical association as causes of genetic similarity between pairs of populations.     

A diagnostic for Cox regression with discrete failure-time models

Changes in maximum likelihood parameter estimates due to deletion of individual observations are useful statistics, both for regression diagnostics and for computing robust estimates of covariance. For many likelihoods, including those in the exponential family, these delete-one statistics can be approximated analytically from a one-step Newton-Raphson iteration on the full maximum likelihood solution. But for general conditional likelihoods and the related Cox partial likelihood, the one-step method does not reduce to an analytic solution. For these likelihoods, an alternative analytic approximation that relies on an appropriately augmented design matrix has been proposed. In this paper, we extend the augmentation approach to explicitly deal with discrete failure-time models. In these models, an individual subject may contribute information at several time points, thereby appearing in multiple risk sets before eventually experiencing a failure or being censored. Our extension also allows the covariates to be time dependent. The new augmentation requires no additional computational resources while improving results.     

Estimation in a Cox proportional hazards cure model

Some failure time data come from a population that consists of some subjects who are susceptible to and others who are nonsusceptible to the event of interest. The data typically have heavy censoring at the end of the follow-up period, and a standard survival analysis would not always be appropriate. In such situations where there is good scientific or empirical evidence of a nonsusceptible population, the mixture or cure model can be used (Farewell, 1982, Biometrics 38, 1041-1046). It assumes a binary distribution to model the incidence probability and a parametric failure time distribution to model the latency. Kuk and Chen (1992, Biometrika 79, 531-541) extended the model by using Cox's proportional hazards regression for the latency. We develop maximum likelihood techniques for the joint estimation of the incidence and latency regression parameters in this model using the nonparametric form of the likelihood and an EM algorithm. A zero-tail constraint is used to reduce the near nonidentifiability of the problem. The inverse of the observed information matrix is used to compute the standard errors. A simulation study shows that the methods are competitive to the parametric methods under ideal conditions and are generally better when censoring from loss to follow-up is heavy. The methods are applied to a data set of tonsil cancer patients treated with radiation therapy.     

Survival analysis in clinical trials: past developments and future directions

The field of survival analysis emerged in the 20th century and experienced tremendous growth during the latter half of the century. The developments in this field that have had the most profound impact on clinical trials are the Kaplan-Meier (1958, Journal of the American Statistical Association 53, 457-481) method for estimating the survival function, the log-rank statistic (Mantel, 1966, Cancer Chemotherapy Report 50, 163-170) for comparing two survival distributions, and the Cox (1972, Journal of the Royal Statistical Society, Series B 34, 187-220) proportional hazards model for quantifying the effects of covariates on the survival time. The counting-process martingale theory pioneered by Aalen (1975, Statistical inference for a family of counting processes, Ph.D. dissertation, University of California, Berkeley) provides a unified framework for studying the small- and large-sample properties of survival analysis statistics. Significant progress has been achieved and further developments are expected in many other areas, including the accelerated failure time model, multivariate failure time data, interval-censored data, dependent censoring, dynamic treatment regimes and causal inference, joint modeling of failure time and longitudinal data, and Baysian methods.     

Applications of likelihood asymptotics for nonlinear regression in herbicide bioassays

Dose-response models are intensively used in herbicide bioassays. Despite recent advancements in the development of new herbicides, statistical analyses are commonly based on asymptotic approximations that are sometimes poor. This paper presents the use of recent results in higher order asymptotics for likelihood-based inference in nonlinear regression. The methods presented provide accurate approximation for the distribution of test statistics and for prediction limits. Analyses of the fit and measures of detection limits of the bioassays are considered, and the potential of the methods is illustrated by examples with real data.     

A linear mixed-effects model for multivariate censored data

We apply a linear mixed-effects model to multivariate failure time data. Computation of the regression parameters involves the Buckley-James method in an iterated Monte Carlo expectation-maximization algorithm, wherein the Monte Carlo E-step is implemented using the Metropolis-Hastings algorithm. From simulation studies, this approach compares favorably with the marginal independence approach, especially when there is a strong within-cluster correlation.     

Mitochondrial DNA phylogeography of the polytypic North American rat snake (Elaphe obsoleta): a critique of the subspecies concept

Subspecies have been considered artificial subdivisions of species, pattern classes, or incipient species. However, with more data and modern phylogenetic techniques, some subspecies may be found to represent true species. Mitochondrial DNA analysis of the polytypic snake, Elaphe obsoleta, yields well-supported clades that do not conform to any of the currently accepted subspecies. Complete nucleotide sequences of the cytochrome b gene and the mitochondrial control region produced robust maximum-parsimony and maximum-likelihood trees that do not differ statistically. Both trees were significantly shorter than a most parsimonious tree in which each subspecies was constrained to be monophyletic. Thus, the subspecies of E. obsoleta do not represent distinct genetic lineages. Instead, the evidence points to three well-supported mitochondrial DNA clades confined to particular geographic areas in the eastern United States. This research underscores the potential problems of recognizing subspecies based on one or a few characters.