Nonparametric estimation of cause-specific cross hazard ratio with bivariate competing risks data

We propose an alternative representation of the cause-specificcross hazard ratio for bivariate competing risks data. The representationleads to a simple plug-in estimator, unlike an existing ad hocprocedure. The large sample properties of the resulting inferencesare established. Simulations and a real data example demonstratethat the proposed methodology may substantially reduce the computationalburden of the existing procedure, while maintaining similarefficiency properties.     

Nonparametric estimation of bivariate failure time associations in the presence of a competing risk

Most research on the study of associations among paired failuretimes has either assumed time invariance or been based on complexmeasures or estimators. Little has accommodated competing risks.This paper targets the conditional cause-specific hazard ratio,henceforth called the cause-specific cross ratio, a recent modificationof the conditional hazard ratio designed to accommodate competingrisks data. Estimation is accomplished by an intuitive, nonparametricmethod that localizes Kendall's tau. Time variance is accommodatedthrough a partitioning of space into ‘bins’ betweenwhich the strength of association may differ. Inferential proceduresare developed, small-sample performance is evaluated, and themethods are applied to the investigation of familial associationin dementia onset.     

Statistical analysis of nonlinear parameter estimation for Monod biodegradation kinetics using bivariate data

A nonlinear regression technique for estimating the Monod parameters describing biodegradation kinetics is presented and analyzed. Two model data sets were taken from a study of aerobic biodegradation of the polycyclic aromatic hydrocarbons (PAHs), naphthalene and 2-methylnaphthalene, as the growth-limiting substrates, where substrate and biomass concentrations were measured with time. For each PAH, the parameters estimated were: q(max), the maximum substrate utilization rate per unit biomass; K(S), the half-saturation coefficient; and Y, the stoichiometric yield coefficient. Estimating parameters when measurements have been made for two variables with different error structures requires a technique more rigorous than least squares regression. An optimization function is derived from the maximumlikelihood equation assuming an unknown, nondiagonal covariance matrix for the measured variables. Because the derivation is based on an assumption of normally distributed errors in the observations, the error structures of the regression variables were examined. Through residual analysis, the errors in the substrate concentration data were found to be distributed log-normally, demonstrating a need for log transformation of this variable. The covariance between ln C and X was found to be small but significantly nonzero at the 67% confidence level for NPH and at the 94% confidence level for 2MN. The nonlinear parameter estimation yielded unique values for q(max), K(S), and Y for naphthalene. Thus, despite the low concentrations of this sparingly soluble compound, the data contained sufficient information for parameter estimation. For 2-methylnaphthalene, the values of q(max) and K(S) could not be estimated uniquely; however, q(max)/K(S) was estimated. To assess the value of including the relatively imprecise biomass concentration data, the results from the bivariate method were compared with a univariate method using only the substrate concentration data. The results demonstrated that the bivariate data yielded a better confidence in the estimates and provided additional information about the model fit and model adequacy. The combination of the value of the bivariate data set and their nonzero covariance justifies the need for maximum likelihood estimation over the simpler nonlinear least squares regression.     

Parameter estimation for the distribution of single cell lag times

In Quantitative Microbial Risk Assessment, it is vital to understand how lag times of individual cells are distributed over a bacterial population. Such identified distributions can be used to predict the time by which, in a growth-supporting environment, a few pathogenic cells can multiply to a poisoning concentration level.We model the lag time of a single cell, inoculated into a new environment, by the delay of the growth function characterizing the generated subpopulation. We introduce an easy-to-implement procedure, based on the method of moments, to estimate the parameters of the distribution of single cell lag times. The advantage of the method is especially apparent for cases where the initial number of cells is small and random, and the culture is detectable only in the exponential growth phase.     

Maximum-likelihood estimation of coalescence times in genealogical trees

We develop a method for maximum-likelihood estimation of coalescence times in genealogical trees, based on population genetics data. For this purpose, a Viterbi-type algorithm is constructed to maximize the joint likelihood of the coalescence times. Marginal confidence intervals for the coalescence times based on the profile likelihoods are also computed. Our method of finding MLEs and calculating C.I.'s appears to be more accurate than alternative numerical maximization methods, and maximum-likelihood inference appears to be more accurate than other existing model-free approaches to estimating coalescent times. We demonstrate the method on two different data sets: human Y chromosome DNA data and fungus DNA data.     

Approximate likelihood calculation on a phylogeny for Bayesian estimation of divergence times

The molecular clock provides a powerful way to estimate species divergence times. If information on some species divergence times is available from the fossil or geological record, it can be used to calibrate a phylogeny and estimate divergence times for all nodes in the tree. The Bayesian method provides a natural framework to incorporate different sources of information concerning divergence times, such as information in the fossil and molecular data. Current models of sequence evolution are intractable in a Bayesian setting, and Markov chain Monte Carlo (MCMC) is used to generate the posterior distribution of divergence times and evolutionary rates. This method is computationally expensive, as it involves the repeated calculation of the likelihood function. Here, we explore the use of Taylor expansion to approximate the likelihood during MCMC iteration. The approximation is much faster than conventional likelihood calculation. However, the approximation is expected to be poor when the proposed parameters are far from the likelihood peak. We explore the use of parameter transforms (square root, logarithm, and arcsine) to improve the approximation to the likelihood curve. We found that the new methods, particularly the arcsine-based transform, provided very good approximations under relaxed clock models and also under the global clock model when the global clock is not seriously violated. The approximation is poorer for analysis under the global clock when the global clock is seriously wrong and should thus not be used. The results suggest that the approximate method may be useful for Bayesian dating analysis using large data sets.     

Model-based multi-locus estimation of decapod phylogeny and divergence times

Phylogenetic relationships among all of the major decapod infraorders have never been estimated using molecular data, while morphological studies produce conflicting results. In the present study, the phylogenetic relationships among the decapod basal suborder Dendrobranchiata and all of the currently recognized decapod infraorders within the suborder Pleocyemata (Caridea, Stenopodidea, Achelata, Astacidea, Thalassinidea, Anomala, and Brachyura) were inferred using 16S mtDNA, 18S and 28S rRNA, and the histone H3 gene. Phylogenies were reconstructed using the model-based methods of maximum likelihood and Bayesian methods coupled with Markov Chain Monte Carlo inference. The phylogenies revealed that the seven infraorders are monophyletic, with high clade support values (bp>70; pP>0.95) under both methods. The two suborders also were recovered as monophyletic, but with weaker support (bp=70; pP=0.74). Although the nodal support values for infraordinal relationships were low (bp<50; pP<0.77) the Anomala and Brachyura were basal to the rest of the 'Reptantia' in both reconstructions and using Bayesian tree topology tests alternate morphology-based hypotheses were rejected (P<0.01). Newly developed multi-locus Bayesian and likelihood heuristic rate-smoothing methods to estimate divergence times were compared using eight fossil and geological calibrations. Estimated times revealed that the Decapoda originated earlier than 437MYA and that the radiation within the group occurred rapidly, with all of the major lineages present by 325MYA. Node time estimation under both approaches is severely affected by the number and phylogenetic distribution of the fossil calibrations chosen. For analyses incorporating fossils as fixed ages, more consistent results were obtained by using both shallow and deep or clade-related calibration points. Divergence time estimation using fossils as lower and upper limits performed well with as few as one upper limit and a single deep fossil lower limit calibration.     

Bayesian relaxed clock estimation of divergence times in foraminifera

Accurate and precise estimation of divergence times during the Neo-Proterozoic is necessary to understand the speciation dynamic of early Eukaryotes. However such deep divergences are difficult to date, as the molecular clock is seriously violated. Recent improvements in Bayesian molecular dating techniques allow the relaxation of the molecular clock hypothesis as well as incorporation of multiple and flexible fossil calibrations. Divergence times can then be estimated even when the evolutionary rate varies among lineages and even when the fossil calibrations involve substantial uncertainties. In this paper, we used a Bayesian method to estimate divergence times in Foraminifera, a group of unicellular eukaryotes, known for their excellent fossil record but also for the high evolutionary rates of their genomes. Based on multigene data we reconstructed the phylogeny of Foraminifera and dated their origin and the major radiation events. Our estimates suggest that Foraminifera emerged during the Cryogenian (650-920 Ma, Neo-Proterozoic), with a mean time around 770 Ma, about 220 Myr before the first appearance of reliable foraminiferal fossils in sediments (545 Ma). Most dates are in agreement with the fossil record, but in general our results suggest earlier origins of foraminiferal orders. We found that the posterior time estimates were robust to specifications of the prior. Our results highlight inter-species variations of evolutionary rates in Foraminifera. Their effect was partially overcome by using the partitioned Bayesian analysis to accommodate rate heterogeneity among data partitions and using the relaxed molecular clock to account for changing evolutionary rates. However, more coding genes appear necessary to obtain more precise estimates of divergence times and to resolve the conflicts between fossil and molecular date estimates.     

Improved estimation of potency in slope ratio assays

Regression coefficients are regarded as stochastic variables in order to account for this kind of variability. This is needed, because differences in responses at successive doses vary generally and thus the assumption of constancy of regression coefficients is violated.     

Two auxiliary variates in ratio method of estimation

A ratio type estimator using two auxiliary variates has been proposed and conditions are obtained to choose between proposed estimator and OLKIN'S (1958) estimator using two auxiliary variates.