Multivariate linear mixed models with censored and nonignorable missing outcomes, with application to AIDS studies.

The analysis of multivariate longitudinal data could encounter some complications due to censorship induced by detection limits of the assay and nonresponse occurring when participants missed scheduled visits intermittently or discontinued participation. This paper establishes a generalization of the multivariate linear mixed model that can accommodate censored responses and nonignorable missing outcomes simultaneously. To account for the nonignorable missingness, the selection approach which decomposes the joint distribution as a marginal distribution for the primary outcome variables and a model describing the missing process conditional on the hypothetical complete data is used. A computationally feasible Monte Carlo expectation conditional maximization algorithm is developed for parameter estimation with the maximum likelihood (ML) method. Furthermore, a general information-based approach is presented to assess the variability of ML estimators. The techniques for the prediction of censored responses and imputation of missing outcomes are also discussed. The methodology is motivated and exemplified by a real dataset concerning HIV-AIDS clinical trials. A simulation study is conducted to examine the performance of the proposed method compared with other traditional approaches.

Multivariate-$t$ nonlinear mixed models with application to censored multi-outcome AIDS studies.

In multivariate longitudinal HIV/AIDS studies, multi-outcome repeated measures on each patient over time may contain outliers, and the viral loads are often subject to a upper or lower limit of detection depending on the quantification assays. In this article, we consider an extension of the multivariate nonlinear mixed-effects model by adopting a joint multivariate-$t$ distribution for random effects and within-subject errors and taking the censoring information of multiple responses into account. The proposed model is called the multivariate-$t$ nonlinear mixed-effects model with censored responses (MtNLMMC), allowing for analyzing multi-outcome longitudinal data exhibiting nonlinear growth patterns with censorship and fat-tailed behavior. Utilizing the Taylor-series linearization method, a pseudo-data version of expectation conditional maximization either (ECME) algorithm is developed for iteratively carrying out maximum likelihood estimation. We illustrate our techniques with two data examples from HIV/AIDS studies. Experimental results signify that the MtNLMMC performs favorably compared to its Gaussian analogue and some existing approaches.

Multivariate longitudinal data analysis with censored and intermittent missing responses.

The multivariate linear mixed model (MLMM) has emerged as an important analytical tool for longitudinal data with multiple outcomes. However, the analysis of multivariate longitudinal data could be complicated by the presence of censored measurements because of a detection limit of the assay in combination with unavoidable missing values arising when subjects miss some of their scheduled visits intermittently. This paper presents a generalization of the MLMM approach, called the MLMM-CM, for a joint analysis of the multivariate longitudinal data with censored and intermittent missing responses. A computationally feasible expectation maximization-based procedure is developed to carry out maximum likelihood estimation within the MLMM-CM framework. Moreover, the asymptotic standard errors of fixed effects are explicitly obtained via the information-based method. We illustrate our methodology by using simulated data and a case study from an AIDS clinical trial. Experimental results reveal that the proposed method is able to provide more satisfactory performance as compared with the traditional MLMM approach.

Multivariate t nonlinear mixed-effects models for multi-outcome longitudinal data with missing values.

The multivariate nonlinear mixed-effects model (MNLMM) has emerged as an effective tool for modeling multi-outcome longitudinal data following nonlinear growth patterns. In the framework of MNLMM, the random effects and within-subject errors are assumed to be normally distributed for mathematical tractability and computational simplicity. However, a serious departure from normality may cause lack of robustness and subsequently make invalid inference. This paper presents a robust extension of the MNLMM by considering a joint multivariate t distribution for the random effects and within-subject errors, called the multivariate t nonlinear mixed-effects model. Moreover, a damped exponential correlation structure is employed to capture the extra serial correlation among irregularly observed multiple repeated measures. An efficient expectation conditional maximization algorithm coupled with the first-order Taylor approximation is developed for maximizing the complete pseudo-data likelihood function. The techniques for the estimation of random effects, imputation of missing responses and identification of potential outliers are also investigated. The methodology is motivated by a real data example on 161 pregnant women coming from a study in a private fertilization obstetrics clinic in Santiago, Chile and used to analyze these data.

Mixtures of t $$ t $$ factor analysers with censored responses and external covariates: An application to educational data from Peru.

Analysing data from educational tests allows governments to make decisions for improving the quality of life of individuals in a society. One of the key responsibilities of statisticians is to develop models that provide decision-makers with pertinent information about the latent process that educational tests seek to represent. Mixtures of t $$ t $$ factor analysers (MtFA) have emerged as a powerful device for model-based clustering and classification of high-dimensional data containing one or several groups of observations with fatter tails or anomalous outliers. This paper considers an extension of MtFA for robust clustering of censored data, referred to as the MtFAC model, by incorporating external covariates. The enhanced flexibility of including covariates in MtFAC enables cluster-specific multivariate regression analysis of dependent variables with censored responses arising from upper and/or lower detection limits of experimental equipment. An alternating expectation conditional maximization (AECM) algorithm is developed for maximum likelihood estimation of the proposed model. Two simulation experiments are conducted to examine the effectiveness of the techniques presented. Furthermore, the proposed methodology is applied to Peruvian data from the 2007 Early Grade Reading Assessment, and the results obtained from the analysis provide new insights regarding the reading skills of Peruvian students.

Flexible modeling of multiple nonlinear longitudinal trajectories with censored and non-ignorable missing outcomes.

Multivariate nonlinear mixed-effects models (MNLMMs) have become a promising tool for analyzing multi-outcome longitudinal data following nonlinear trajectory patterns. However, such a classical analysis can be challenging due to censorship induced by detection limits of the quantification assay or non-response occurring when participants missed scheduled visits intermittently or discontinued participation. This article proposes an extension of the MNLMM approach, called the MNLMM-CM, by taking the censored and non-ignorable missing responses into account simultaneously. The non-ignorable missingness is described by the selection-modeling factorization to tackle the missing not at random mechanism. A Monte Carlo expectation conditional maximization algorithm coupled with the first-order Taylor approximation is developed for parameter estimation. The techniques for the calculation of standard errors of fixed effects, estimation of unobservable random effects, imputation of censored and missing responses and prediction of future values are also provided. The proposed methodology is motivated and illustrated by the analysis of a clinical HIV/AIDS dataset with censored RNA viral loads and the presence of missing CD4 and CD8 cell counts. The superiority of our method on the provision of more adequate estimation is validated by a simulation study.

Parametric modeling of cellular state transitions as measured with flow cytometry.

BACKGROUND: Gradual or sudden transitions among different states as exhibited by cell populations in a biological sample under particular conditions or stimuli can be detected and profiled by flow cytometric time course data. Often such temporal profiles contain features due to transient states that present unique modeling challenges. These could range from asymmetric non-Gaussian distributions to outliers and tail subpopulations, which need to be modeled with precision and rigor. RESULTS: To ensure precision and rigor, we propose a parametric modeling framework StateProfiler based on finite mixtures of skew t-Normal distributions that are robust against non-Gaussian features caused by asymmetry and outliers in data. Further, we present in StateProfiler a new greedy EM algorithm for fast and optimal model selection. The parsimonious approach of our greedy algorithm allows us to detect the genuine dynamic variation in the key features as and when they appear in time course data. We also present a procedure to construct a well-fitted profile by merging any redundant model components in a way that minimizes change in entropy of the resulting model. This allows precise profiling of unusually shaped distributions and less well-separated features that may appear due to cellular heterogeneity even within clonal populations. CONCLUSIONS: By modeling flow cytometric data measured over time course and marker space with StateProfiler, specific parametric characteristics of cellular states can be identified. The parameters are then tested statistically for learning global and local patterns of spatio-temporal change. We applied StateProfiler to identify the temporal features of yeast cell cycle progression based on knockout of S-phase triggering cyclins Clb5 and Clb6, and then compared the S-phase delay phenotypes due to differential regulation of the two cyclins. We also used StateProfiler to construct the temporal profile of clonal divergence underlying lineage selection in mammalian hematopoietic progenitor cells.

A framework for analytical characterization of monoclonal antibodies based on reactivity profiles in different tissues.

MOTIVATION: Monoclonal antibodies (mAbs) are among the most powerful and important tools in biology and medicine. MAb development is of great significance to many research and clinical applications. Therefore, objective mAb classification is essential for categorizing and comparing mAb panels based on their reactivity patterns in different cellular species. However, typical flow cytometric mAb profiles present unique modeling challenges with their non-Gaussian features and intersample variations. It makes accurate mAb classification difficult to do with the currently used kernel-based or hierarchical clustering techniques. RESULTS: To address these challenges, in the present study we developed a formal two-step framework called mAbprofiler for systematic, parametric characterization of mAb profiles. Further, we measured the reactivity of hundreds of new antibodies in diverse tissues using flow cytometry, which we successfully classified using mAbprofiler. First, mAbprofiler fits a mAb's flow cytometric histogram with a finite mixture model of skew t distributions that is robust against non-Gaussian features, and constructs a precise, smooth and mathematically rigorous profile. Then it performs novel curve clustering of the fitted mAb profiles using a skew t mixture of non-linear regression model that can handle intersample variation. Thus, mAbprofiler provides a new framework for identifying robust mAb classes, all well defined by distinct parametric templates, which can be used for classifying new mAb samples. We validated our classification results both computationally and empirically using mAb profiles of known classification. AVAILABILITY AND IMPLEMENTATION: A demonstration code in R is available at the journal website. The R code implementing the full framework is available from the author website - http://amath.nchu.edu.tw/www/teacher/tilin/software CONTACT: saumyadipta_pyne@dfci.harvard.edu SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Automated high-dimensional flow cytometric data analysis.

Flow cytometric analysis allows rapid single cell interrogation of surface and intracellular determinants by measuring fluorescence intensity of fluorophore-conjugated reagents. The availability of new platforms, allowing detection of increasing numbers of cell surface markers, has challenged the traditional technique of identifying cell populations by manual gating and resulted in a growing need for the development of automated, high-dimensional analytical methods. We present a direct multivariate finite mixture modeling approach, using skew and heavy-tailed distributions, to address the complexities of flow cytometric analysis and to deal with high-dimensional cytometric data without the need for projection or transformation. We demonstrate its ability to detect rare populations, to model robustly in the presence of outliers and skew, and to perform the critical task of matching cell populations across samples that enables downstream analysis. This advance will facilitate the application of flow cytometry to new, complex biological and clinical problems.

Robust linear mixed models using the skew t distribution with application to schizophrenia data.

We consider an extension of linear mixed models by assuming a multivariate skew t distribution for the random effects and a multivariate t distribution for the error terms. The proposed model provides flexibility in capturing the effects of skewness and heavy tails simultaneously among continuous longitudinal data. We present an efficient alternating expectation-conditional maximization (AECM) algorithm for the computation of maximum likelihood estimates of parameters on the basis of two convenient hierarchical formulations. The techniques for the prediction of random effects and intermittent missing values under this model are also investigated. Our methodologies are illustrated through an application to schizophrenia data.

Multivariate-t linear mixed models with censored responses, intermittent missing values and heavy tails.

Multivariate longitudinal data arisen in medical studies often exhibit complex features such as censored responses, intermittent missing values, and atypical or outlying observations. The multivariate-t linear mixed model (MtLMM) has been recognized as a powerful tool for robust modeling of multivariate longitudinal data in the presence of potential outliers or fat-tailed noises. This paper presents a generalization of MtLMM, called the MtLMM-CM, to properly adjust for censorship due to detection limits of the assay and missingness embodied within multiple outcome variables recorded at irregular occasions. An expectation conditional maximization either (ECME) algorithm is developed to compute parameter estimates using the maximum likelihood (ML) approach. The asymptotic standard errors of the ML estimators of fixed effects are obtained by inverting the empirical information matrix according to Louis' method. The techniques for the estimation of random effects and imputation of missing responses are also investigated. The proposed methodology is illustrated on two real-world examples from HIV-AIDS studies and a simulation study under a variety of scenarios.

A skew factor analysis model based on the normal mean-variance mixture of Birnbaum-Saunders distribution.

This paper presents a robust extension of factor analysis model by assuming the multivariate normal mean-variance mixture of Birnbaum-Saunders distribution for the unobservable factors and errors. A computationally analytical EM-based algorithm is developed to find maximum likelihood estimates of the parameters. The asymptotic standard errors of parameter estimates are derived under an information-based paradigm. Numerical merits of the proposed methodology are illustrated using both simulated and real datasets.

Extending multivariate- t linear mixed models for multiple longitudinal data with censored responses and heavy tails.

The analysis of complex longitudinal data is challenging due to several inherent features: (i) more than one series of responses are repeatedly collected on each subject at irregularly occasions over a period of time; (ii) censorship due to limits of quantification of responses arises left- and/or right- censoring effects; (iii) outliers or heavy-tailed noises are possibly embodied within multiple response variables. This article formulates the multivariate- t linear mixed model with censored responses (MtLMMC), which allows the analysts to model such data in the presence of the above described features simultaneously. An efficient expectation conditional maximization either (ECME) algorithm is developed to carry out maximum likelihood estimation of model parameters. The implementation of the E-step relies on the mean and covariance matrix of truncated multivariate- t distributions. To enhance the computational efficiency, two auxiliary permutation matrices are incorporated into the procedure to determine the observed and censored parts of each subject. The proposed methodology is demonstrated via a simulation study and a real application on HIV/AIDS data.

Shortest service location model for planning waste pickup locations.

A municipal solid waste (MSW) and recycled material curbside pickup bus system was recently initiated in a Taiwan city to improve collection service. For such an MSW pickup system, selecting appropriate collection stops critically affects hauling costs and service efficiency. Conventionally, MSW collection points are heuristically and manually chosen, resulting in a hauling system that is not as effective as intended in terms of location suitability and the number of collection points. The Shortest Service Location (SSL) model, which minimizes the sum of service distances, was therefore proposed in this study. The SSL model was compared with two other models for a local MSW pickup system problem. Using georeferenced graphs generated by a geographical information system (GIS) and related programs, the performance of the three models was compared according to walking distance to a service stop, the coverage of a service stop, and the number of service stops. The results show that the SSL solution can shorten walking distances by approximately 10% and reduce the overlap of service areas covered.

Estimation and prediction in linear mixed models with skew-normal random effects for longitudinal data.

This paper extends the classical linear mixed model by considering a multivariate skew-normal assumption for the distribution of random effects. We present an efficient hybrid ECME-NR algorithm for the computation of maximum-likelihood estimates of parameters. A score test statistic for testing the existence of skewness preference among random effects is developed. The technique for the prediction of future responses under this model is also investigated. The methodology is illustrated through an application to Framingham cholesterol data and a simulation study.

Nasopharyngeal carcinoma during pregnancy.

OBJECTIVE: Nasopharyngeal carcinoma, particularly during pregnancy, rarely comes to medical attention before it spreads to the regional lymph nodes. CASE REPORT: We report a 26-year-old Taiwanese woman who suffered from persistent headache and purulent nasal discharge during mid-pregnancy. Magnetic resonance imaging examination showed a large soft tissue mass measuring 3 x 2 x 2 cm in the left nasopharynx at 31 weeks of gestation. Punch biopsy of the tumor was done, and the histopathologic report revealed poorly differentiated, non-keratinizing type of squamous cell carcinoma (T4N2M0). A female infant weighing 1,790 g was delivered by cesarean section at 33 weeks of gestation with Apgar scores of 5 and 8 at 1 and 5 minutes, respectively. The patient received chemotherapy and radiation therapy after delivery. She was disease-free for 3 years. Subsequently, the patient delivered a second healthy infant weighing 3,084 g in a consecutive pregnancy, with a 3-year birth interval. Her first and second child showed normal psychomotor development at 3 years and 6 months of age, respectively. CONCLUSION: The possibility of rare nasopharyngeal carcinoma should be considered in any pregnant woman with presenting symptoms of persistent headache and abnormal nasal discharge, and a detailed thorough investigation is indicated. Successful pregnancy outcome can be achieved after tailored use of a combination of chemotherapy and radiotherapy.

A robust approach to t linear mixed models applied to multiple sclerosis data.

We discuss a robust extension of linear mixed models based on the multivariate t distribution. Since longitudinal data are successively collected over time and typically tend to be auto-correlated, we employ a parsimonious first-order autoregressive dependence structure for the within-subject errors. A score test statistic for testing the existence of autocorrelation among the within-subject errors is derived. Moreover, we develop an explicit scoring procedure for the maximum likelihood estimation with standard errors as a by-product. The technique for predicting future responses of a subject given past measurements is also investigated. Results are illustrated with real data from a multiple sclerosis clinical trial.