Maximum likelihood estimation in random effects cure rate models with nonignorable missing covariates

We introduce a method of parameter estimation for a random effects cure rate model. We also propose a methodology that allows us to account for nonignorable missing covariates in this class of models. The proposed method corrects for possible bias introduced by complete case analysis when missing data are not missing completely at random and is motivated by data from a pair of melanoma studies conducted by the Eastern Cooperative Oncology Group in which clustering by cohort or time of study entry was suspected. In addition, these models allow estimation of cure rates, which is desirable when we do not wish to assume that all subjects remain at risk of death or relapse from disease after sufficient follow-up. We develop an EM algorithm for the model and provide an efficient Gibbs sampling scheme for carrying out the E-step of the algorithm.     

Maximum likelihood estimation of the heterogeneity of substitution rate among nucleotide sites

This paper presents a maximum likelihood approach to estimating the variation of substitution rate among nucleotide sites. We assume that the rate varies among sites according to an invariant+gamma distribution, which has two parameters: the gamma parameter alpha and the proportion of invariable sites theta. Theoretical treatments on three, four, and five sequences have been conducted, and computer program have been developed. It is shown that rho = (1 + theta alpha)/(1 + alpha) is a good measure for the rate heterogeneity among sites. Extensive simulations show that (1) if the proportion of invariable sites is negligible, i.e., theta = 0, the gamma parameter alpha can be satisfactorily estimated, even with three sequences; (2) if the proportion of invariable sites is not negligible, the heterogeneity rho can still be suitably estimated with four or more sequences; and (3) the distances estimated by the proposed method are almost unbiased and are robust against violation of the assumption of the invariant + gamma distribution.      

Maximum likelihood estimation of subsequence conservation

A statistical method is presented for comparing protein sequences by partitioning the polymers and estimating each subsegment's degree of conservation. Conservation is measured as a function of the number of transitions occurring in the underlying time homogeneous Markov process assumed to govern amino acid mutations. The Markovian assumption also permits estimation of the ancestral sequence. Partitioning and estimation are carried out via maximum likelihood. The method is contrasted with the commonly utilized percent homology measure. A moving likelihood ratio plot to aid in identifying regions of high conservation is suggested as an analogue to moving hydrophobicity plots. An application is presented which identifies highly conserved regions in thymidylate synthase from L. casei and E. coli.     

Maximum likelihood methods for cure rate models with missing covariates

We propose maximum likelihood methods for parameter estimation for a novel class of semiparametric survival models with a cure fraction, in which the covariates are allowed to be missing. We allow the covariates to be either categorical or continuous and specify a parametric distribution for the covariates that is written as a sequence of one-dimensional conditional distributions. We propose a novel EM algorithm for maximum likelihood estimation and derive standard errors by using Louis's formula (Louis, 1982, Journal of the Royal Statistical Society, Series B 44, 226-233). Computational techniques using the Monte Carlo EM algorithm are discussed and implemented. A real data set involving a melanoma cancer clinical trial is examined in detail to demonstrate the methodology.     

Maximum likelihood estimation of human craniometric heritabilities

This study presents univariate narrow-sense heritability estimates for 33 common craniometric dimensions, calculated using the maximum likelihood variance components method on a skeletal sample of 298 pedigreed individuals from Hallstatt, Austria. Quantitative genetic studies that use skeletal cranial measurements as a basis for inferring microevolutionary processes in human populations usually employ heritability estimates to represent the genetic variance of the population. The heritabilities used are often problematic: most come from studies of living humans, and/or they were calculated using statistical techniques or assumptions violated by human groups. Most bilateral breadth measures in the current study show low heritability estimates, while cranial length and height measures have heritability values ranging between 0.102-0.729. There appear to be differences between the heritabilities calculated from crania and those from anthropometric studies of living humans, suggesting that the use of the latter in quantitative genetic models of skeletal data may be inappropriate. The univariate skeletal heritability estimates seem to group into distinct regions of the cranium, based on their relative values. The most salient group of measurements is for the midfacial/orbital region, with a number of measures showing heritabilities less than 0.30. Several possible reasons behind this pattern are examined. Given the fact that heritabilities calculated on one population should not be applied to others, suggestions are made for the use of the data presented.     

Maximum likelihood estimation of oncogenetic tree models

We present a new approach for modelling the dependences between genetic changes in human tumours. In solid tumours, data on genetic alterations are usually only available at a single point in time, allowing no direct insight into the sequential order of genetic events. In our approach, genetic tumour development and progression is assumed to follow a probabilistic tree model. We show how maximum likelihood estimation can be used to reconstruct a tree model for the dependences between genetic alterations in a given tumour type. We illustrate the use of the proposed method by applying it to cytogenetic data from 173 cases of clear cell renal cell carcinoma, arriving at a model for the karyotypic evolution of this tumour.     

Maximum likelihood estimation of ordered multinomial parameters

The pool adjacent violator algorithm Ayer et al. (1955, The Annals of Mathematical Statistics, 26, 641-647) has long been known to give the maximum likelihood estimator of a series of ordered binomial parameters, based on an independent observation from each distribution (see Barlow et al., 1972, Statistical Inference under Order Restrictions, Wiley, New York). This result has immediate application to estimation of a survival distribution based on current survival status at a set of monitoring times. This paper considers an extended problem of maximum likelihood estimation of a series of 'ordered' multinomial parameters p(i)= (p(1i),p(2i),.,p(mi)) for 1 相似文献   

Maximum likelihood estimation in dynamical models of HIV

The study of dynamical models of HIV infection, based on a system of nonlinear ordinary differential equations (ODE), has considerably improved the knowledge of its pathogenesis. While the first models used simplified ODE systems and analyzed each patient separately, recent works dealt with inference in non-simplified models borrowing strength from the whole sample. The complexity of these models leads to great difficulties for inference and only the Bayesian approach has been attempted by now. We propose a full likelihood inference, adapting a Newton-like algorithm for these particular models. We consider a relatively complex ODE model for HIV infection and a model for the observations including the issue of detection limits. We apply this approach to the analysis of a clinical trial of antiretroviral therapy (ALBI ANRS 070) and we show that the whole algorithm works well in a simulation study.     

Maximum likelihood estimation in the additive hazards model

The additive hazards model specifies the effect of covariates on the hazard in an additive way, in contrast to the popular Cox model, in which it is multiplicative. As the non-parametric model, additive hazards offer a very flexible way of modeling time-varying covariate effects. It is most commonly estimated by ordinary least squares. In this paper, we consider the case where covariates are bounded, and derive the maximum likelihood estimator under the constraint that the hazard is non-negative for all covariate values in their domain. We show that the maximum likelihood estimator may be obtained by separately maximizing the log-likelihood contribution of each event time point, and we show that the maximizing problem is equivalent to fitting a series of Poisson regression models with an identity link under non-negativity constraints. We derive an analytic solution to the maximum likelihood estimator. We contrast the maximum likelihood estimator with the ordinary least-squares estimator in a simulation study and show that the maximum likelihood estimator has smaller mean squared error than the ordinary least-squares estimator. An illustration with data on patients with carcinoma of the oropharynx is provided.     

Maximum likelihood estimation of the kinetics of receptor-mediated adhesion

Adhesion flow assays are commonly employed to characterize the kinetics and force-dependence of receptor-ligand interactions. As transient cellular adhesion events are often mediated by a small number of receptor-ligand complexes (tether bonds) their durations are highly variable, which in turn presents obstacles to standard methods of analysis. In this paper, we employ the stochastic approach to chemical kinetics to construct the pause time distribution. Using this distribution, we develop a robust maximum likelihood (ML) approach to the robust estimation of rate constants associated with receptor-mediated transient adhesion and their confidence intervals. We then formulate robust estimators of the parameters of models for the force-dependence of the off-rate. Lastly, we develop a robust method of elucidation of the force-dependence of the off-rate using Akaike's information criterion (AIC). Our findings conclusively demonstrate that ML estimators of adhesion kinetics are substantial improvements over more conventional approaches, and when combined with Fisher information, they may be used to objectively and reproducibly distinguish the kinetics of different receptor-ligand complexes. Software for the implementation of these methods with experimental data is publicly available as for download at http://www.laurenzi.net.     

Catch estimation in the presence of declining catch rate due to gear saturation

One strategy for estimating total catch is to employ two separate surveys that independently estimate total fishing effort and catch rate with the estimator for total catch formed by their product. Survey designs for estimating catch rate often involve interviewing the fishermen during their fishing episodes. Such roving designs result in incomplete episode data and characteristically have employed a model in which the catch rate is assumed to be constant over time. This article extends the problem to that of estimating total catch in the presence of a declining catch rate due, e.g., to gear saturation. Using a gill net fishery as an example, a mean-of-ratios type of estimator for the catch rate together with its variance estimator are developed. Their performance is examined using simulations, with special attention given to effects of restrictions on the roving survey window. Finally, data from a Fraser River gill net fishery are used to illustrate the use of the proposed estimator and to compare results with those from an estimator based on a constant catch rate.     

Maximum likelihood estimation of linkage disequilibrium in half-sib families

Maximum likelihood methods for the estimation of linkage disequilibrium between biallelic DNA-markers in half-sib families (half-sib method) are developed for single and multifamily situations. Monte Carlo computer simulations were carried out for a variety of scenarios regarding sire genotypes, linkage disequilibrium, recombination fraction, family size, and number of families. A double heterozygote sire was simulated with recombination fraction of 0.00, linkage disequilibrium among dams of δ=0.10, and alleles at both markers segregating at intermediate frequencies for a family size of 500. The average estimates of δ were 0.17, 0.25, and 0.10 for Excoffier and Slatkin (1995), maternal informative haplotypes, and the half-sib method, respectively. A multifamily EM algorithm was tested at intermediate frequencies by computer simulation. The range of the absolute difference between estimated and simulated δ was between 0.000 and 0.008. A cattle half-sib family was genotyped with the Illumina 50K BeadChip. There were 314,730 SNP pairs for which the sire was a homo-heterozygote with average estimates of r2 of 0.115, 0.067, and 0.111 for half-sib, Excoffier and Slatkin (1995), and maternal informative haplotypes methods, respectively. There were 208,872 SNP pairs for which the sire was double heterozygote with average estimates of r2 across the genome of 0.100, 0.267, and 0.925 for half-sib, Excoffier and Slatkin (1995), and maternal informative haplotypes methods, respectively. Genome analyses for all possible sire genotypes with 829,042 tests showed that ignoring half-sib family structure leads to upward biased estimates of linkage disequilibrium. Published inferences on population structure and evolution of cattle should be revisited after accommodating existing half-sib family structure in the estimation of linkage disequilibrium.