CAMCR: Computer assisted mixture model analysis for capture-recapture count data

Population size estimation with discrete or nonparametric mixture models is considered, and reliable ways of construction of the nonparametric mixture model estimator are reviewed and set into perspective. Construction of the maximum likelihood estimator of the mixing distribution is done for any number of components up to the global nonparametric maximum likelihood bound using the EM algorithm. In addition, the estimators of Chao and Zelterman are considered with some generalisations of Zelterman’s estimator. All computations are done with CAMCR, a special software developed for population size estimation with mixture models. Several examples and data sets are discussed and the estimators illustrated. Problems using the mixture model-based estimators are highlighted.

CAMCR: Computer-Assisted Mixture model analysis for Capture–Recapture count data

Population size estimation with discrete or nonparametric mixture models is considered, and reliable ways of construction of the nonparametric mixture model estimator are reviewed and set into perspective. Construction of the maximum likelihood estimator of the mixing distribution is done for any number of components up to the global nonparametric maximum likelihood bound using the EM algorithm. In addition, the estimators of Chao and Zelterman are considered with some generalisations of Zelterman’s estimator. All computations are done with CAMCR, a special software developed for population size estimation with mixture models. Several examples and data sets are discussed and the estimators illustrated. Problems using the mixture model-based estimators are highlighted.

Additive Hazards Models with Latent Treatment Effectiveness Lag Time

In many clinical trials to evaluate treatment efficacy, it is believed that there may exist latent treatment effectiveness lag times after which medical procedure or chemical compound would be in full effect. In this article, semiparametric regression models are proposed and studied to estimate the treatment effect accounting for such latent lag times. The new models take advantage of the invariance property of the additive hazards model in marginalizing over random effects, so parameters in the models are easy to be estimated and interpreted, while the flexibility without specifying baseline hazard function is kept. Monte Carlo simulation studies demonstrate the appropriateness of the proposed semiparametric estimation procedure. Data collected in the actual randomized clinical trial, which evaluates the effectiveness of biodegradable carmustine polymers for treatment of recurrent brain tumors, are analyzed.

Mixture modeling for joint analysis of survival, discrete, and continuous data

Mixture modeling is commonly used to model categorical latent variables that represent subpopulations in which population membership is unknown but can be inferred from the data. In relatively recent years, the potential of finite mixture models has been applied in time-to-event data. However, the commonly used survival mixture model assumes that the effects of the covariates involved in failure times differ across latent classes, but the covariate distribution is homogeneous. The aim of this dissertation is to develop a method to examine time-to-event data in the presence of unobserved heterogeneity under a framework of mixture modeling. A joint model is developed to incorporate the latent survival trajectory along with the observed information for the joint analysis of a time-to-event variable, its discrete and continuous covariates, and a latent class variable. It is assumed that the effects of covariates on survival times and the distribution of covariates vary across different latent classes. The unobservable survival trajectories are identified through estimating the probability that a subject belongs to a particular class based on observed information. We applied this method to a Hodgkin lymphoma study with long-term follow-up and observed four distinct latent classes in terms of long-term survival and distributions of prognostic factors. Our results from simulation studies and from the Hodgkin lymphoma study demonstrated the superiority of our joint model compared with the conventional survival model. This flexible inference method provides more accurate estimation and accommodates unobservable heterogeneity among individuals while taking involved interactions between covariates into consideration.^

On a resampling approach for tests on the number of clusters with mixture model-based clustering of tissue samples

We consider the problem of assessing the number of clusters in a limited number of tissue samples containing gene expressions for possibly several thousands of genes. It is proposed to use a normal mixture model-based approach to the clustering of the tissue samples. One advantage of this approach is that the question on the number of clusters in the data can be formulated in terms of a test on the smallest number of components in the mixture model compatible with the data. This test can be carried out on the basis of the likelihood ratio test statistic, using resampling to assess its null distribution. The effectiveness of this approach is demonstrated on simulated data and on some microarray datasets, as considered previously in the bioinformatics literature. (C) 2004 Elsevier Inc. All rights reserved.

Speeding up the EM algorithm for mixture model-based segmentation of magnetic resonance images

Mixture models implemented via the expectation-maximization (EM) algorithm are being increasingly used in a wide range of problems in pattern recognition such as image segmentation. However, the EM algorithm requires considerable computational time in its application to huge data sets such as a three-dimensional magnetic resonance (MR) image of over 10 million voxels. Recently, it was shown that a sparse, incremental version of the EM algorithm could improve its rate of convergence. In this paper, we show how this modified EM algorithm can be speeded up further by adopting a multiresolution kd-tree structure in performing the E-step. The proposed algorithm outperforms some other variants of the EM algorithm for segmenting MR images of the human brain. (C) 2004 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.

A Bayesian Spatial Mixture Model for FMRI Analysis

We develop, implement and study a new Bayesian spatial mixture model (BSMM). The proposed BSMM allows for spatial structure in the binary activation indicators through a latent thresholded Gaussian Markov random field. We develop a Gibbs (MCMC) sampler to perform posterior inference on the model parameters, which then allows us to assess the posterior probabilities of activation for each voxel. One purpose of this article is to compare the HJ model and the BSMM in terms of receiver operating characteristics (ROC) curves. Also we consider the accuracy of the spatial mixture model and the BSMM for estimation of the size of the activation region in terms of bias, variance and mean squared error. We perform a simulation study to examine the aforementioned characteristics under a variety of configurations of spatial mixture model and BSMM both as the size of the region changes and as the magnitude of activation changes.

Influence of patient age and implantation technique on the probability of re-replacement of the homograft aortic valve

Background and aim of the study: Results of valve re-replacement (reoperation) in 898 patients undergoing aortic valve replacement with cryopreserved homograft valves between 1975 and 1998 are reported. The study aim was to provide estimates of unconditional probability of valve reoperation and cumulative incidence function (actual risk) of reoperation. Methods: Valves were implanted by subcoronary insertion (n = 500), inclusion cylinder (n = 46), and aortic root replacement (n = 352). Probability of reoperation was estimated by adopting a mixture model framework within which estimates were adjusted for two risk factors: patient age at initial replacement, and implantation technique. Results: For a patient aged 50 years, the probability of reoperation in his/her lifetime was estimated as 44% and 56% for non-root and root replacement techniques, respectively. For a patient aged 70 years, estimated probability of reoperation was 16% and 25%, respectively. Given that a reoperation is required, patients with non-root replacement have a higher hazard rate than those with root replacement (hazards ratio = 1.4), indicating that non-root replacement patients tend to undergo reoperation earlier before death than root replacement patients. Conclusion: Younger patient age and root versus non-root replacement are risk factors for reoperation. Valve durability is much less in younger patients, while root replacement patients appear more likely to live longer and hence are more likely to require reoperation.

Standard errors of fitted component means of normal mixtures

In this paper use consider the problem of providing standard errors of the component means in normal mixture models fitted to univariate or multivariate data by maximum likelihood via the EM algorithm. Two methods of estimation of the standard errors are considered: the standard information-based method and the computationally-intensive bootstrap method. They are compared empirically by their application to three real data sets and by a small-scale Monte Carlo experiment.

A general hazard model for lifetime data in the presence of cure rate

Historically, the cure rate model has been used for modeling time-to-event data within which a significant proportion of patients are assumed to be cured of illnesses, including breast cancer, non-Hodgkin lymphoma, leukemia, prostate cancer, melanoma, and head and neck cancer. Perhaps the most popular type of cure rate model is the mixture model introduced by Berkson and Gage [1]. In this model, it is assumed that a certain proportion of the patients are cured, in the sense that they do not present the event of interest during a long period of time and can found to be immune to the cause of failure under study. In this paper, we propose a general hazard model which accommodates comprehensive families of cure rate models as particular cases, including the model proposed by Berkson and Gage. The maximum-likelihood-estimation procedure is discussed. A simulation study analyzes the coverage probabilities of the asymptotic confidence intervals for the parameters. A real data set on children exposed to HIV by vertical transmission illustrates the methodology.

Fitting mixtures of Kent distributions to aid in joint set identification

When examining a rock mass, joint sets and their orientations can play a significant role with regard to how the rock mass will behave. To identify joint sets present in the rock mass, the orientation of individual fracture planer can be measured on exposed rock faces and the resulting data can be examined for heterogeneity. In this article, the expectation-maximization algorithm is used to lit mixtures of Kent component distributions to the fracture data to aid in the identification of joint sets. An additional uniform component is also included in the model to accommodate the noise present in the data.

Enhancing the selection of a model-based clustering with external categorical variables

In cluster analysis, it can be useful to interpret the partition built from the data in the light of external categorical variables which are not directly involved to cluster the data. An approach is proposed in the model-based clustering context to select a number of clusters which both fits the data well and takes advantage of the potential illustrative ability of the external variables. This approach makes use of the integrated joint likelihood of the data and the partitions at hand, namely the model-based partition and the partitions associated to the external variables. It is noteworthy that each mixture model is fitted by the maximum likelihood methodology to the data, excluding the external variables which are used to select a relevant mixture model only. Numerical experiments illustrate the promising behaviour of the derived criterion. © 2014 Springer-Verlag Berlin Heidelberg.

Enhancing the selection of a model-based clustering with external categorical variables

In cluster analysis, it can be useful to interpret the partition built from the data in the light of external categorical variables which are not directly involved to cluster the data. An approach is proposed in the model-based clustering context to select a number of clusters which both fits the data well and takes advantage of the potential illustrative ability of the external variables. This approach makes use of the integrated joint likelihood of the data and the partitions at hand, namely the model-based partition and the partitions associated to the external variables. It is noteworthy that each mixture model is fitted by the maximum likelihood methodology to the data, excluding the external variables which are used to select a relevant mixture model only. Numerical experiments illustrate the promising behaviour of the derived criterion.

Modelling HIV/AIDS length of stay in Portugal

Tese apresentada como requisito parcial para obtenção do grau de Doutor em Estatística e Gestão de Informação pelo Instituto Superior de Estatística e Gestão de Informação da Universidade Nova de Lisboa

Modeling usage of medical care services: the medical expenditure panel survey data, 1996-2000

We explore the determinants of usage of six different types of health care services, using the Medical Expenditure Panel Survey data, years 1996-2000. We apply a number of models for univariate count data, including semiparametric, semi-nonparametric and finite mixture models. We find that the complexity of the model that is required to fit the data well depends upon the way in which the data is pooled across sexes and over time, and upon the characteristics of the usage measure. Pooling across time and sexes is almost always favored, but when more heterogeneous data is pooled it is often the case that a more complex statistical model is required.