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PubMed2005

Effect of attenuation correction on lesion detection using a hybrid PET system.

OBJECTIVE: The purpose of this study was to investigate the effect of attenuation correction (AC) on lesion detection for a hybrid PET system. MATERIAL AND METHOD: Experimental list-mode data were acquired from hot spheres inside a uniform cylindrical phantom with an elliptical cross-section using a Siemens E. CAM+ dual-camera hybrid PET system. Spheres with inner diameters of 0.8- and 1-cm and the cylindrical phantom were filled with F-18 to simulate lesions with lesion-to-background (L/B) ratios of 14:1 and 8:1, respectively, found in clinical PET studies. The list-mode data of each sphere size were regrouped into sinograms with peak-to-peak energy window settings at 30% and 20% for the 0.8- and 1-cm diameter lesion, respectively. They were then rebinned using the single slice rebinning method. Attenuation correction was applied assuming uniform attenuation. The sinograms with and without AC were reconstructed using 5 iterations of OS-EM algorithm with 8 angles/ subset and postfiltered with a Butterworth filter with n = 5 and fc = 0.52 cycles/cm. Human observer performance study and localization receiver operating characteristic (LROC) analysis were used to evaluate the reconstructed images for maximum lesion detection. Average areas under the LROC curves (A(LROC)) across 8 observers obtained with and without AC were determined. The null hypothesis that there was no difference between with AC and without AC was tested using a two-tailed t-test with 95% confidence interval. RESULTS: The results indicated that for the 0. 8-cm lesion with 14:1 L/B ratio, the A(LROC) decreases from 0.66 to 0.62 when AC is applied as compared to without AC andfrom 0.69 to 0.63 for the 1.0-cm lesion with 8:1 L/ B ratio, but no statistical significant difference (p > 0. 05). CONCLUSION: The authors conclude that for a phantom with hot lesions embedded in a uniform background, AC decreases lesion detectability compared to without AC using a hybrid PET system for small lesion sizes.

Humans↗

PubMed2005

[Analysis and application of SNP and haplotype in the human genome].

Single nucleotide polymorphism (SNP) is the most common type of genetic variant in human genome. Haplotype, defined as a specific set of alleles observed on a single chromosome, or a part of a chromosome,has been an integral part of human genetics for decades. The goal of the international HapMap project is to determine the common patterns of DNA sequence variation and find the Tag SNPs representing all SNPs in the human genome. Some studies demonstrated that the analyses of haplotype defined by the grouping and interaction of several variants rather than any individual SNP correlated with complex phenotypes. Here, we describe the definitions of SNPs, genotype, haplotype and some information of the HapMap project. In this review, we summarize the current three haplotype-inference methods, including Clark' method, EM algorithm and Byes approach, and the different defining methods for haplotype block, as well as the methods for choosing tag SNPs and association studies of complex diseases using haplotype. The major public SNP databases and applications of SNPs and haplotype in common complex diseases and drug response are also introduced in the paper.

Algorithms↗

PubMed1992

The effect of diagnostic misclassification on non-cancer and cancer mortality dose response in A-bomb survivors.

We used the EM algorithm in the context of a joint Poisson regression analysis of cancer and non-cancer mortality in the Radiation Effects Research Foundation (RERF) Life Span Study (LSS) to assess whether the observed increased risk of non-cancer death due to radiation exposure (Shimizu et al., RERF Technical Report 02-91, 1991) can be attributed solely to misclassification of cancer as non-cancer on death certificates. We show that greater levels of dose-independent misclassification than are indicated by a series of autopsies conducted on a subset of LSS members would be required to explain the non-cancer dose response, but that a relatively small amount of dose-dependence in the misclassification of cancer would explain the result. The adjustment for misclassification also results in higher risk estimates for cancer mortality. We review applications of similar statistical methods in other contexts and discuss extensions of the methods to more than two causes of death.

Age Factors↗

PubMed2003

LOGOS: a modular Bayesian model for de novo motif detection.

The complexity of the global organization and internal structures of motifs in higher eukaryotic organisms raises significant challenges for motif detection techniques. To achieve successful de novo motif detection it is necessary to model the complex dependencies within and among motifs and incorporate biological prior knowledge. In this paper, we present LOGOS, an integrated LOcal and GlObal motif Sequence model for biopolymer sequences, which provides a principled framework for developing, modularizing, extending and computing expressive motif models for complex biopolymer sequence analysis. LOGOS consists of two interacting submodels: HMDM, a local alignment model capturing biological prior knowledge and positional dependence within the motif local structure; and HMM, a global motif distribution model modeling frequencies and dependencies of motif occurrences. Model parameters can be fit using training motifs within an empirical Bayesian framework. A variational EM algorithm is developed for de novo motif detection. LOGOS improves over existing models that ignore biological priors and dependencies in motif structures and motif occurrences, and demonstrates superior performance on both semi-realistic test data and cis-regulatory sequences from yeast and Drosophila sequences with regard to sensitivity, specificity, flexibility and extensibility.

Algorithms↗

PubMed2006

[Haplotypes of four single nucleotide polymorphisms in caspase-8, -10 genes in Han nationality of Zhejiang province in China].

OBJECTIVE: To investigate single nucleotide polymorphisms (SNPs) and the distribution of their haplotypes in caspase-8, -10 genes in Zhejiang Han nationality in China. METHODS: PCR, denaturing high-performance liquid chromatography (DHPLC) and DNA sequencing were used to detect the SNPs in the 2nd-5th exons of caspase-10 gene, the 8th-10th exons of caspase-8 and their flanking sequences. Expectation Maximization (EM) algorithm was used for haplotype frequencies analysis and pairwise linkage disequilibrium (LD) test. RESULTS: (1) Two SNPs, A2823G and A12799G, were identified in caspase-10 gene, located in exon 2 and exon 5 respectively. A12799G was newly found with low informativeness. Three SNPs were identified in caspase-8 gene; A43466G, G51484A and G52951A were located in exon 8, exon 9 and intron 9, respectively. They do not change the primary structure of the encoded protein. (2) Linkage equilibrium was observed between A2823G in caspase-10 gene and the three sites in caspase-8 gene. A43466G and G52951A, and G51484A and G52951A in caspase-8 gene were also in linkage equilibrium. Their coefficients of disequilibrium were near 0. Whereas strong linkage disequilibrium was observed between A43466G and G51484A, because its coefficient of disequilibrium was near 1. (3) A total of 11 haplotypes were estimated within A2823G in caspase-10 gene and three sites in caspase-8 gene. A-2823/A-43466/G-51484/G-52951 was the main haplotype with a frequency of 0.3811. A-2823/A-43466/G-51484/A-52951 was the second haplotype with a frequency of 0.2536. The polymorphism information content of their haplotypes was 0.7106. CONCLUSION: The SNPs of caspase-8, -10 genes in Han Chinese of Zhejiang could be parsed into at least three different haplotype blocks. The polymorphism information content can be improved by using haplotype analysis of several SNPs.

Alleles↗

PubMed1991

Fitting mixture models to birth weight data: a case study.

Birth weights by gestational age are compared in two birth cohorts from Northern Finland, the first from 1966 and the second from 1985-1986. A curious fact in the data is that mean birth weight before the 39th week was lower in the latter series although the mean birth weight for the total series was higher. Similar findings have been reported in other series. A mixture model with the nonparametric regression function is proposed for studying the hypothesis that the difference was caused by more frequent gross errors in gestational assessment in the earlier cohort. The probability of an error in gestational assessment then greatly depends on the observed gestational age, which makes the mixture model nonstandard. Maximum likelihood solutions to the parameters in the proposed model were computed employing the general expectation-maximization (EM) algorithm. A technique for studying the effect of errors on the intrauterine weight gain curve is proposed and applied to our two birth cohorts. The risk of underestimation of gestational age seems to be larger in the previous series and the differences between the growth curves almost totally vanish when "corrected" by means of the mixture model.

Algorithms↗

PubMed1991

Nonparametric estimation of the size-metastasis relationship in solid cancers.

This paper is concerned with the relationship between the occurrence of metastases and the size of primary cancers. We consider two probabilistic characterizations of this relationship. First is the distribution function of tumor sizes at the point of metastatic transition; second is the probability that detectable metastases are present when the cancer comes to medical attention. The equation relating these two functions is developed and conditions for their being identical are explored. Since the tumor size at the point of metastasis is not usually observable, estimation of the first distribution requires the use of the EM algorithm. Nonparametric methods of estimating both functions are explored, with attention to the fact that tumors often fail to be measured, particularly those that are known to be metastatic. The methods are applied to the estimation of primary tumor size at the point of distant metastasis in lung cancer (epidermoid and adenocarcinoma) and colorectal cancer and at the point of nodal metastasis in breast cancer. Monte Carlo experiments confirm that the bias inherent in the methodology is acceptably small.

Adenocarcinoma↗

PubMed1991

A two-state Markov mixture model for a time series of epileptic seizure counts.

This paper discusses a model for a time series of epileptic seizure counts in which the mean of a Poisson distribution changes according to an underlying two-state Markov chain. The EM algorithm (Dempster, Laird, and Rubin, 1977, Journal of the Royal Statistical Society, Series B 39, 1-38) is used to compute maximum likelihood estimators for the parameters of this two-state mixture model and extensions are made allowing for nonstationarity. The model is illustrated using daily seizure counts for patients with intractable epilepsy and results are compared with a simple Poisson distribution and Poisson regressions. Some simulation results are also presented to demonstrate the feasibility of this model.

Biometry↗

PubMed1991

Mixture models for continuous data in dose-response studies when some animals are unaffected by treatment.

A mixture model is described for dose-response studies where measurements on a continuous variable suggest that some animals are not affected by treatment. The model combines a logistic regression on dose for the probability an animal will "respond" to treatment with a linear regression on dose for the mean of the responders. Maximum likelihood estimation via the EM algorithm is described and likelihood ratio tests are used to distinguish between the full model and meaningful reduced-parameter versions. Use of the model is illustrated with three real-data examples.

Algorithms↗

PubMed1991

Fitting mixture distributions to phenylthiocarbamide (PTC) sensitivity.

A technique for fitting mixture distributions to phenylthiocarbamide (PTC) sensitivity is described. Under the assumptions of Hardy-Weinberg equilibrium, a mixture of three normal components is postulated for the observed distribution, with the mixing parameters corresponding to the proportions of the three genotypes associated with two alleles A and a acting at a single locus. The corresponding genotypes AA, Aa, and aa are then considered to have separate means and variances. This paper is concerned with estimating the parameters of the model, and their standard errors, by using an application of the EM algorithm. This technique also caters for the fact that the sensitivity measurements are only known to lie between the endpoints of certain intervals and that the exact measurement of the attribute is not possible.

Algorithms↗

PubMed1979

Log-linear models in the analysis of disease prevalence data from survival/sacrifice experiments.

This paper considers the problem of analyzing disease prevalence data from survival experiments in which there may also be some serial sacrifice. The assumptions needed for "standard" analyses are reviewed in the context of a general model recently proposed by the authors. This model is then reparametrized in log-linear form, and a generalized EM algorithm is utilized to obtain maximum likelihood estimates of the parameters for a broad class of unsaturated models. Tests based on the relative likelihood are proposed to investigate the effects of treatment, time, and the presence of other diseases on the prevalences and lethalities of specific diseases of interest. An example is given, using data from a large experiment to investigate the effects of low-level radiation on laboratory mice. Finally, some possible directions for future research are indicated.

Animals↗

PubMed1987

Mixed-model analysis of a censored normal distribution with reference to animal breeding.

A mixed-model procedure for analysis of censored data assuming a multivariate normal distribution is described. A Bayesian framework is adopted which allows for estimation of fixed effects and variance components and prediction of random effects when records are left-censored. The procedure can be extended to right- and two-tailed censoring. The model employed is a generalized linear model, and the estimation equations resemble those arising in analysis of multivariate normal or categorical data with threshold models. Estimates of variance components are obtained using expressions similar to those employed in the EM algorithm for restricted maximum likelihood (REML) estimation under normality.

Analysis of Variance↗

PubMed1986

The beta-geometric distribution applied to comparative fecundability studies.

A convenient measure of fecundability is time (number of menstrual cycles) required to achieve pregnancy. Couples attempting pregnancy are heterogeneous in their per-cycle probability of success. If success probabilities vary among couples according to a beta distribution, then cycles to pregnancy will have a beta-geometric distribution. Under this model, the inverse of the cycle-specific conception rate is a linear function of time. Data on cycles to pregnancy can be used to estimate the beta parameters by maximum likelihood in a straightforward manner with a package such as GLIM. The likelihood ratio test can thus be employed in studies of exposures that may impair fecundability. Covariates are incorporated in a natural way. The model is illustrated by applying it to data on cycles to pregnancy in smokers and nonsmokers, with adjustment for covariates. For a cross-sectional study, when length-biased sampling is taken into account, the pre-interview attempt time is shown to follow a beta-geometric distribution, so that the same methods of analysis can be applied even though all of the available data are right-censored. For a cohort followed prospectively, there will be some couples enrolled whose fecundability is effectively 0, and for such applications, the beta could be considered to be contaminated by a distribution degenerate at 0. The mixing parameter (proportion sterile) can be estimated by application of the expectation-maximization (EM) algorithm. This, too, can be carried out using GLIM.

Biometry↗

PubMed1986

An approximate likelihood procedure for censored data.

An approximate likelihood procedure is suggested for the estimation of the parameters of the density of a single homogeneous sample subject to right censoring. Two examples are given involving the gamma distribution. The method is typically consistent and although it is always inefficient, the efficiency loss is second-order in the degree of censoring when this is small. The relation of the techniques to the results of Reid (1981, Annals of Statistics 9, 78-92) on influence functions for censored data, to the EM algorithm, and to the nonparametric regression techniques of Miller (1976, Biometrika 63, 449-464) and Buckley and James (1979, Biometrika 66, 429-436) are indicated. Simple estimates of standard error are obtained.

Animals↗

PubMed1985

A Bayesian approach to nonlinear random effects models.

Nonlinear random effects models are considered from the Bayesian point of view. The method of analysis follows closely that of Lindley and Smith (1972, Journal of the Royal Statistical Society, Series B 34, 1-42). The numerical method is related to the EM algorithm.

Analysis of Variance↗

PubMed1984

Mixture distributions in psychiatric research.

This paper describes the application of Gaussian mixture distributions to biological marker research in psychiatry. Mixtures of univariate and multivariate normal distributions can be used to determine if diagnostically similar psychiatric patients belong to biologically distinct subpopulations. The resulting biological subtypes may be important in understanding the etiology of psychiatric disorders. The general model and estimation procedure are described (EM algorithm; Dempster, Laird and Rubin 1977). The method is illustrated using two examples of biological data: (1) red cell membranes and monoamine oxidase activity data in normal individuals having no family history of psychiatric illness, the first-degree relatives of bipolar depressed patients and a heterogeneous patient population; and (2) smooth pursuit eye movements that classify relatives of schizophrenics, nonschizophrenics and normal controls into biologically distinct populations.

Bipolar Disorder↗

PubMed1984

Random-effects models for serial observations with binary response.

This paper presents a general mixed model for the analysis of serial dichotomous responses provided by a panel of study participants. Each subject's serial responses are assumed to arise from a logistic model, but with regression coefficients that vary between subjects. The logistic regression parameters are assumed to be normally distributed in the population. Inference is based upon maximum likelihood estimation of fixed effects and variance components, and empirical Bayes estimation of random effects. Exact solutions are analytically and computationally infeasible, but an approximation based on the mode of the posterior distribution of the random parameters is proposed, and is implemented by means of the EM algorithm. This approximate method is compared with a simpler two-step method proposed by Korn and Whittemore (1979, Biometrics 35, 795-804), using data from a panel study of asthmatics originally described in that paper. One advantage of the estimation strategy described here is the ability to use all of the data, including that from subjects with insufficient data to permit fitting of a separate logistic regression model, as required by the Korn and Whittemore method. However, the new method is computationally intensive.

Air Pollution↗

PubMed1984

Nonparametric estimation of the distribution of time to onset for specific diseases in survival/sacrifice experiments.

This paper concerns the analysis of an animal survival/sacrifice experiment designed to investigate the incidence of a particular disease of interest. The disease is assumed to be irreversible, and detectable only at death, for example by a necropsy. Each observation can be of one of three types: (i) death caused by the disease, (ii) death from a competing cause such as sacrifice, with the disease present, or (iii) death with the disease absent. A two-dimensional EM algorithm is proposed for the nonparametric maximum likelihood estimation of the distributions of the time to onset and of the time to death from the disease. These can be compared with nonparametric estimators recently proposed by Kodell , Shaw and Johnson (1982, Biometrics 38, 43-58) and by Dinse and Lagakos (1982, Biometrics 38, 921-932). A slight modification of the algorithm permits the construction of likelihood-based interval estimates of quantiles of the distributions. Some extensions and generalizations are indicated.

Age Factors↗