Proportional hazards model with covariates subject to measurement error.

When covariates of a proportional hazards model are subject to measurement error, the maximum likelihood estimates of regression coefficients based on the partial likelihood are asymptotically biased. Prentice (1982, Biometrika 69, 331-342) presents an example of such bias and suggests a modified partial likelihood. This paper applies the corrected score function method (Nakamura, 1990, Biometrika 77, 127-137) to the proportional hazards model when measurement errors are additive and normally distributed. The result allows a simple correction to the ordinary partial likelihood that yields asymptotically unbiased estimates; the validity of the correction is confirmed via a limited simulation study.     

Catarrhine primate divergence dates estimated from complete mitochondrial genomes: concordance with fossil and nuclear DNA evidence

Accurate divergence date estimates improve scenarios of primate evolutionary history and aid in interpretation of the natural history of disease-causing agents. While molecule-based estimates of divergence dates of taxa within the superfamily Hominoidea (apes and humans) are common in the literature, few such estimates are available for the Cercopithecoidea (Old World monkeys), the sister taxon of the hominoids in the primate infraorder Catarrhini. To help fill this gap, we have sequenced the entire mitochondrial DNA (mtDNA) genomes from a representative of three cercopithecoid tribes, Cercopithecini (Chlorocebus aethiops), Colobini (Colobus guereza), and Presbytini (Trachypithecus obscurus), and analyzed these new data together with other catarrhine mtDNA genomes available in public databases. Molecular divergence date estimates are dependent on calibration points gleaned from the paleontological record. We defined criteria for the selection of good calibration points and identified three points meeting these criteria: Homo-Pan, 6.0 Ma; Pongo-hominines, 14.0 Ma; hominoid/cercopithecoid, 23.0 Ma. Because a uniform molecular clock does not fit the catarrhine mtDNA data, we estimated divergence dates using a penalized likelihood and a Bayesian method, both of which take into account the effects of rate differences on lineages, phylogenetic tree structure, and multiple calibration points. The penalized likelihood method applied to the coding regions of the mtDNA genome yielded the following divergence date estimates, with approximate 95% confidence intervals: cercopithecine-colobine, 16.2 (14.4-17.9) Ma; colobin-presbytin, 10.9 (9.6-12.3) Ma; cercopithecin-papionin, 11.6 (10.3-12.9) Ma; and Macaca-Papio, 9.8 (8.6-10.9) Ma. Within the hominoids, the following dates were inferred: hylobatid-hominid, 16.8 (15.0-18.5) Ma; Gorilla-Homo+Pan, 8.1 (7.1-9.0) Ma; Pongo pygmaeus pygmaeus-P. p. abelii, 4.1 (3.5-4.7) Ma; and Pan troglodytes-P. paniscus, 2.4 (2.0-2.7) Ma. These dates were similar to those found using penalized likelihood on other subsets of the data, but slightly younger than several of the Bayesian estimates.     

Estimation in the cox proportional hazards model with left-truncated and interval-censored data

We show that the nonparametric maximum likelihood estimate (NPMLE) of the regression coefficient from the joint likelihood (of the regression coefficient and the baseline survival) works well for the Cox proportional hazards model with left-truncated and interval-censored data, but the NPMLE may underestimate the baseline survival. Two alternatives are also considered: first, the marginal likelihood approach by extending Satten (1996, Biometrika 83, 355-370) to truncated data, where the baseline distribution is eliminated as a nuisance parameter; and second, the monotone maximum likelihood estimate that maximizes the joint likelihood by assuming that the baseline distribution has a nondecreasing hazard function, which was originally proposed to overcome the underestimation of the survival from the NPMLE for left-truncated data without covariates (Tsai, 1988, Biometrika 75, 319-324). The bootstrap is proposed to draw inference. Simulations were conducted to assess their performance. The methods are applied to the Massachusetts Health Care Panel Study data set to compare the probabilities of losing functional independence for male and female seniors.     

A Monte Carlo maximum likelihood method for estimating uncertainty arising from shared errors in exposures in epidemiological studies of nuclear workers

Errors in the estimation of exposures or doses are a major source of uncertainty in epidemiological studies of cancer among nuclear workers. This paper presents a Monte Carlo maximum likelihood method that can be used for estimating a confidence interval that reflects both statistical sampling error and uncertainty in the measurement of exposures. The method is illustrated by application to an analysis of all cancer (excluding leukemia) mortality in a study of nuclear workers at the Oak Ridge National Laboratory (ORNL). Monte Carlo methods were used to generate 10,000 data sets with a simulated corrected dose estimate for each member of the cohort based on the estimated distribution of errors in doses. A Cox proportional hazards model was applied to each of these simulated data sets. A partial likelihood, averaged over all of the simulations, was generated; the central risk estimate and confidence interval were estimated from this partial likelihood. The conventional unsimulated analysis of the ORNL study yielded an excess relative risk (ERR) of 5.38 per Sv (90% confidence interval 0.54-12.58). The Monte Carlo maximum likelihood method yielded a slightly lower ERR (4.82 per Sv) and wider confidence interval (0.41-13.31).     

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   

Nonparametric estimation and testing in a cure model.

Nonparametric generalized maximum likelihood product limit point estimators and confidence intervals are given for a cure model with random censorship. One-, two-, and K-sample likelihood ratio tests for inference on the cure rates are developed. In the two-sample case its power is compared to the power of several alternatives, including the log-rank and Gray and Tsiatis (1989, Biometrics 45, 899-904) tests. Implications for the use of the likelihood ratio test in a clinical trial designed to compare cure rates are discussed.     

Diagnostic Value of Multiple Tumor Markers for Patients with Esophageal Carcinoma

BackgroundVarious studies assessing the diagnostic value of serum tumor markers in patients with esophageal cancer remain controversial. This study aims to comprehensively and quantitatively summarize the potential diagnostic value of 5 serum tumour markers in esophageal cancer.MethodsWe systematically searched PubMed, Embase, Chinese National Knowledge Infrastructure (CNKI) and Chinese Biomedical Database (CBM), through February 28, 2013, without language restriction. Studies were assessed for quality using QUADAS (quality assessment of studies of diagnostic accuracy). The positive likelihood ratio (PLR) and negative likelihood ratio (NLR) were pooled separately and compared with overall accuracy measures using diagnostic odds ratios (DORs) and symmetric summary receiver operating characteristic (SROC) curves.ResultsOf 4391 studies initially identified, 44 eligible studies including five tumor markers met the inclusion criteria for the meta-analysis, while meta-analysis could not be conducted for 12 other tumor markers. Approximately 79.55% (35/44) of the included studies were of relatively high quality (QUADAS score≥7). The summary estimates of the positive likelihood ratio (PLR), negative likelihood ratio (NLR) and diagnostic odds ratio (DOR) for diagnosing EC were as follows: CEA, 5.94/0.76/9.26; Cyfra21-1, 12.110.59/22.27; p53 antibody, 6.71/0.75/9.60; SCC-Ag, 7.66/0.68/12.41; and VEGF-C, 0.74/0.37/8.12. The estimated summary receiver operating characteristic curves showed that the performance of all five tumor markers was reasonable.ConclusionsThe current evidence suggests that CEA, Cyfra21-1, p53, SCC-Ag and VEGF-C have a potential diagnostic value for esophageal carcinoma.     

Failed refutations: further comments on parsimony and likelihood methods and their relationship to Popper's degree of corroboration

Kluge's (2001, Syst. Biol. 50:322-330) continued arguments that phylogenetic methods based on the statistical principle of likelihood are incompatible with the philosophy of science described by Karl Popper are based on false premises related to Kluge's misrepresentations of Popper's philosophy. Contrary to Kluge's conjectures, likelihood methods are not inherently verificationist; they do not treat every instance of a hypothesis as confirmation of that hypothesis. The historical nature of phylogeny does not preclude phylogenetic hypotheses from being evaluated using the probability of evidence. The low absolute probabilities of hypotheses are irrelevant to the correct interpretation of Popper's concept termed degree of corroboration, which is defined entirely in terms of relative probabilities. Popper did not advocate minimizing background knowledge; in any case, the background knowledge of both parsimony and likelihood methods consists of the general assumption of descent with modification and additional assumptions that are deterministic, concerning which tree is considered most highly corroborated. Although parsimony methods do not assume (in the sense of entailing) that homoplasy is rare, they do assume (in the sense of requiring to obtain a correct phylogenetic inference) certain things about patterns of homoplasy. Both parsimony and likelihood methods assume (in the sense of implying by the manner in which they operate) various things about evolutionary processes, although violation of those assumptions does not always cause the methods to yield incorrect phylogenetic inferences. Test severity is increased by sampling additional relevant characters rather than by character reanalysis, although either interpretation is compatible with the use of phylogenetic likelihood methods. Neither parsimony nor likelihood methods assess test severity (critical evidence) when used to identify a most highly corroborated tree(s) based on a single method or model and a single body of data; however, both classes of methods can be used to perform severe tests. The assumption of descent with modification is insufficient background knowledge to justify cladistic parsimony as a method for assessing degree of corroboration. Invoking equivalency between parsimony methods and likelihood models that assume no common mechanism emphasizes the necessity of additional assumptions, at least some of which are probabilistic in nature. Incongruent characters do not qualify as falsifiers of phylogenetic hypotheses except under extremely unrealistic evolutionary models; therefore, justifications of parsimony methods as falsificationist based on the idea that they minimize the ad hoc dismissal of falsifiers are questionable. Probabilistic concepts such as degree of corroboration and likelihood provide a more appropriate framework for understanding how phylogenetics conforms with Popper's philosophy of science. Likelihood ratio tests do not assume what is at issue but instead are methods for testing hypotheses according to an accepted standard of statistical significance and for incorporating considerations about test severity. These tests are fundamentally similar to Popper's degree of corroboration in being based on the relationship between the probability of the evidence e in the presence versus absence of the hypothesis h, i.e., between p(e|hb) and p(e|b), where b is the background knowledge. Both parsimony and likelihood methods are inductive in that their inferences (particular trees) contain more information than (and therefore do not follow necessarily from) the observations upon which they are based; however, both are deductive in that their conclusions (tree lengths and likelihoods) follow necessarily from their premises (particular trees, observed character state distributions, and evolutionary models). For these and other reasons, phylogenetic likelihood methods are highly compatible with Karl Popper's philosophy of science and offer several advantages over parsimony methods in this context.     

A multigene framework for polychaete phylogenetic studies

Producing a robust phylogenetic reconstruction for Polychaeta using either morphological or molecular data sets has proven very difficult. There remain many conflicts between morphological analyses and hypotheses based on DNA data, the latter principally derived from 18S rRNA sequences. For the present study a data set covering a broad range of polychaete diversity was assembled, including 38 new sequences from 21 species. Besides available 18S rRNA data, five additional gene segments were examined: the D1 and D9-10 expansion regions of 28S rRNA, histone H3, snU2 RNA and cytochrome c oxidase subunit I. Maximum parsimony, maximum likelihood and Bayesian analyses were conducted.Annelida and Mollusca were reciprocally monophyletic in maximum likelihood analyses, but Polychaeta included a cephalopod in maximum parsimony analyses, and a patellogastropod in Bayesian analyses. When rooted on the Mollusca, optimal topologies from maximum likelihood analyses showed a recognisable basal group of taxa, including Oweniidae, Chaetopteridae and Amphinomidae. The six studied phyllodocidan families plus Orbiniidae (as the sister group of the scale-worms) formed the next most basal group. All analyses support the inclusion of Echiura, Clitellata and Siboglinidae within polychaetes. Bayesian analyses show Echiura as the sister group of Capitellidae, in agreement with previous 18S rRNA results, In contrast, Echiura formed the sister group to Trichobranchidae in maximum likelihood and maximum parsimony analyses.Supra-familial groupings consistently recovered within Polychaeta in the analyses are: (i) Terebellida without Ampharetidae; (ii) Scolecida (excepting Orbiniidae); (iii) Eunicidae, Lumbrineridae and Clitellata; and (iv) “Cirratuliformia” (including Sternaspidae) plus Sabellidae, Serpulidae and Spionidae.     

Fundamental differences between the methods of maximum likelihood and maximum posterior probability in phylogenetics

Using a four-taxon example under a simple model of evolution, we show that the methods of maximum likelihood and maximum posterior probability (which is a Bayesian method of inference) may not arrive at the same optimal tree topology. Some patterns that are separately uninformative under the maximum likelihood method are separately informative under the Bayesian method. We also show that this difference has impact on the bootstrap frequencies and the posterior probabilities of topologies, which therefore are not necessarily approximately equal. Efron et al. (Proc. Natl. Acad. Sci. USA 93:13429-13434, 1996) stated that bootstrap frequencies can, under certain circumstances, be interpreted as posterior probabilities. This is true only if one includes a non-informative prior distribution of the possible data patterns, and most often the prior distributions are instead specified in terms of topology and branch lengths. [Bayesian inference; maximum likelihood method; Phylogeny; support.].     

Semiparametric regression analysis of interval-censored data

We propose a semiparametric approach to the proportional hazards regression analysis of interval-censored data. An EM algorithm based on an approximate likelihood leads to an M-step that involves maximizing a standard Cox partial likelihood to estimate regression coefficients and then using the Breslow estimator for the unknown baseline hazards. The E-step takes a particularly simple form because all incomplete data appear as linear terms in the complete-data log likelihood. The algorithm of Turnbull (1976, Journal of the Royal Statistical Society, Series B 38, 290-295) is used to determine times at which the hazard can take positive mass. We found multiple imputation to yield an easily computed variance estimate that appears to be more reliable than asymptotic methods with small to moderately sized data sets. In the right-censored survival setting, the approach reduces to the standard Cox proportional hazards analysis, while the algorithm reduces to the one suggested by Clayton and Cuzick (1985, Applied Statistics 34, 148-156). The method is illustrated on data from the breast cancer cosmetics trial, previously analyzed by Finkelstein (1986, Biometrics 42, 845-854) and several subsequent authors.     

The “Buruli Score”: Development of a Multivariable Prediction Model for Diagnosis of Mycobacterium ulcerans Infection in Individuals with Ulcerative Skin Lesions,Akonolinga, Cameroon

Background

Access to laboratory diagnosis can be a challenge for individuals suspected of Buruli Ulcer (BU). Our objective was to develop a clinical score to assist clinicians working in resource-limited settings for BU diagnosis.

Methododology/Principal Findings

Between 2011 and 2013, individuals presenting at Akonolinga District Hospital, Cameroon, were enrolled consecutively. Clinical data were collected prospectively. Based on a latent class model using laboratory test results (ZN, PCR, culture), patients were categorized into high, or low BU likelihood. Variables associated with a high BU likelihood in a multivariate logistic model were included in the Buruli score. Score cut-offs were chosen based on calculated predictive values. Of 325 patients with an ulcerative lesion, 51 (15.7%) had a high BU likelihood. The variables identified for the Buruli score were: characteristic smell (+3 points), yellow color (+2), female gender (+2), undermining (+1), green color (+1), lesion hyposensitivity (+1), pain at rest (-1), size >5cm (-1), locoregional adenopathy (-2), age above 20 up to 40 years (-3), or above 40 (-5). This score had AUC of 0.86 (95%CI 0.82–0.89), indicating good discrimination between infected and non-infected individuals. The cut-off to reasonably exclude BU was set at scores <0 (NPV 96.5%; 95%CI 93.0–98.6). The treatment threshold was set at a cut-off ≥4 (PPV 69.0%; 95%CI 49.2–84.7). Patients with intermediate BU probability needed to be tested by PCR.

Conclusions/Significance

We developed a decisional algorithm based on a clinical score assessing BU probability. The Buruli score still requires further validation before it can be recommended for wide use.     

A solution to the problem of monotone likelihood in Cox regression

The phenomenon of monotone likelihood is observed in the fitting process of a Cox model if the likelihood converges to a finite value while at least one parameter estimate diverges to +/- infinity. Monotone likelihood primarily occurs in small samples with substantial censoring of survival times and several highly predictive covariates. Previous options to deal with monotone likelihood have been unsatisfactory. The solution we suggest is an adaptation of a procedure by Firth (1993, Biometrika 80, 27-38) originally developed to reduce the bias of maximum likelihood estimates. This procedure produces finite parameter estimates by means of penalized maximum likelihood estimation. Corresponding Wald-type tests and confidence intervals are available, but it is shown that penalized likelihood ratio tests and profile penalized likelihood confidence intervals are often preferable. An empirical study of the suggested procedures confirms satisfactory performance of both estimation and inference. The advantage of the procedure over previous options of analysis is finally exemplified in the analysis of a breast cancer study.     

Long term prognosis in preschool children with wheeze: longitudinal postal questionnaire study 1993-2004

Objectives To follow a population of preschool children with and without parent reported wheeze over a period of 6-11 years to determine prognosis and its important predictive factors.Design Longitudinal series of five postal surveys based on the international study of asthma and allergies in childhood questionnaire carried out between 1993 and 2004.Setting Two general practice populations, south Manchester.Participants 628 children aged less than 5 years at recruitment and those with at least six years’ follow-up data.Main outcome measures Parent completed questionnaire data for respiratory symptoms and associated features.Results Of 628 children included in the study, 201 (32%) had parent reported wheeze at the first observation (baseline), of whom 27% also reported the symptom on the second occasion (persistent asthma). The only important baseline predictors of persistent asthma were exercise induced wheeze (odds ratio 3.94, 95% confidence interval 1.72 to 9.00) and a history of atopic disorders (4.44, 1.94 to 10.13). The presence of both predictors indicated a likelihood of 53.2% of developing asthma; if only one feature was present this decreased to 17.2%, whereas if neither was present the likelihood was 10.9%. Family history of asthma was not predictive of persistent asthma among children with preschool wheeze.Conclusion Using two simple predictive factors (baseline parent reported exercise induced wheeze and a history of atopic disorders), it is possible to estimate the likelihood of future asthma in children presenting with preschool wheeze. The absence of baseline exercise induced wheeze and a history of atopic disorders reduces the likelihood of subsequent asthma by a factor of five.     

The Value of BISAP Score for Predicting Mortality and Severity in Acute Pancreatitis: A Systematic Review and Meta-Analysis

Purpose

The Bedside Index for Severity in Acute Pancreatitis (BISAP) score has been developed to identify patients at high risk for mortality or severe disease early during the course of acute pancreatitis. We aimed to undertake a meta-analysis to quantify the accuracy of BISAP score for predicting mortality and severe acute pancreatitis (SAP).

Materials and Methods

We searched the databases of Pubmed, Embase, and the Cochrane Library to identify studies using the BISAP score to predict mortality or SAP. The pooled sensitivity, specificity, likelihood ratios, and diagnostic odds ratio (DOR) were calculated from each study and were compared with the traditional scoring systems.

Results

Twelve cohorts from 10 studies were included. The overall sensitivity of a BISAP score of ≥3 for mortality was 56% (95% CI, 53%-60%), with a specificity of 91% (95% CI, 90%-91%). The positive and negative likelihood ratios were 5.65 (95% CI, 4.23-7.55) and 0.48 (95% CI, 0.41-0.56), respectively. Regarding the outcome of SAP, the pooled sensitivity was 51% (43%-60%), and the specificity was 91% (89%-92%). The pooled positive and negative likelihood ratios were 7.23 (4.21-12.42) and 0.56 (0.44-0.71), respectively. Compared with BISAP score, the Ranson criteria and APACHEⅡscore showed higher sensitivity and lower specificity for both outcomes.

Conclusions

The BISAP score was a reliable tool to identify AP patients at high risk for unfavorable outcomes. Compared with the Ranson criteria and APACHEⅡscore, BISAP score outperformed in specificity, but having a suboptimal sensitivity for mortality as well as SAP.     

Estimation of offspring production from a limited number of stage-structured censuses

We propose a procedure for maximum likelihood estimation of the number of animals or offspring in a closed population where the individuals counted go through stages or age-groups. Application of the procedure requires knowledge of the distributions of the stage durations. A procedure for maximum likelihood estimation of those based on marked animals is also given. The procedures are illustrated by applying them to gray seal (Halichoerus grypus) data from Froan Nature Reserve, Central Norway, from the breeding seasons 1990-1999.     

Primate phylogeny, evolutionary rate variations, and divergence times: a contribution from the nuclear gene IRBP

The first third (ca. 1200 bp) of exon 1 of the nuclear gene encoding the interstitial retinoid-binding protein (IRBP) has been sequenced for 12 representative primates belonging to Lemuriformes, Lorisiformes, Tarsiiformes, Platyrrhini, and Catarrhini, and combined with available data (13 other primates, 11 nonprimate placentals, and 2 marsupials). Phylogenetic analyses using maximum likelihood on nucleotides and amino acids robustly support the monophyly of primates, Strepsirrhini, Lemuriformes, Lorisiformes, Anthropoidea, Catarrhini, and Platyrrhini. It is interesting to note that 1) Tarsiidae grouped with Anthropoidea, and the support for this node depends on the molecular characters considered; 2) Cheirogaleidae grouped within Lemuriformes; and 3) Daubentonia was the sister group of all other Lemuriformes. Study of the IRBP evolutionary rate shows a high heterogeneity within placentals and also within primates. Maximum likelihood local molecular clocks were assigned to three clades displaying significantly contrasted evolutionary rates. Paenungulata were shown to evolve 2.5-3 times faster than Perissodactyla and Lemuriformes. Six independent calibration points were used to estimate splitting ages of the main primate clades, and their compatibility was evaluated. Divergence ages were obtained for the following crown groups: 13.8-14.2 MY for Lorisiformes, 26.5-27.2 MY for Lemuroidea, 39.6-40.7 MY for Lemuriformes, 45.4-46.7 MY for Strepsirrhini, and 56.7-58.4 MY for Haplorrhini. The incompatibility between some paleontological and molecular estimates may reflect the incompleteness of the placental fossil record, and/or indicate that the variable IRBP evolutionary rates are not fully accommodated by local molecular clocks.     

Estimating Effective Population Size and Mutation Rate from Sequence Data Using Metropolis-Hastings Sampling

We present a new way to make a maximum likelihood estimate of the parameter 4N(e)μ (effective population size times mutation rate per site, or θ) based on a population sample of molecular sequences. We use a Metropolis-Hastings Markov chain Monte Carlo method to sample genealogies in proportion to the product of their likelihood with respect to the data and their prior probability with respect to a coalescent distribution. A specific value of θ must be chosen to generate the coalescent distribution, but the resulting trees can be used to evaluate the likelihood at other values of θ, generating a likelihood curve. This procedure concentrates sampling on those genealogies that contribute most of the likelihood, allowing estimation of meaningful likelihood curves based on relatively small samples. The method can potentially be extended to cases involving varying population size, recombination, and migration.     

An alternative derivation of Harville's restricted log likelihood function for variance component estimation

Estimation of variance components in linear mixed models is important in clinical trial and longitudinal data analysis. It is also important in animal and plant breeding for accurately partitioning total phenotypic variance into genetic and environmental variances. Restricted maximum likelihood (REML) method is often preferred over the maximum likelihood (ML) method for variance component estimation because REML takes into account the lost degree of freedom resulting from estimating the fixed effects. The original restricted likelihood function involves a linear transformation of the original response variable (a collection of error contrasts). Harville's final form of the restricted likelihood function does not involve the transformation and thus is much easier to manipulate than the original restricted likelihood function. There are several different ways to show that the two forms of the restricted likelihood are equivalent. In this study, I present a much simpler way to derive Harville's restricted likelihood function. I first treat the fixed effects as random effects and call such a mixed model a pseudo random model (PDRM). I then construct a likelihood function for the PDRM. Finally, I let the variance of the pseudo random effects be infinity and show that the limit of the likelihood function of the PDRM is the restricted likelihood function.