A benchmark for evaluation of algorithms for identification of cellular correlates of clinical outcomes.

The Flow Cytometry: Critical Assessment of Population Identification Methods (FlowCAP) challenges were established to compare the performance of computational methods for identifying cell populations in multidimensional flow cytometry data. Here we report the results of FlowCAP-IV where algorithms from seven different research groups predicted the time to progression to AIDS among a cohort of 384 HIV+ subjects, using antigen-stimulated peripheral blood mononuclear cell (PBMC) samples analyzed with a 14-color staining panel. Two approaches (FlowReMi.1 and flowDensity-flowType-RchyOptimyx) provided statistically significant predictive value in the blinded test set. Manual validation of submitted results indicated that unbiased analysis of single cell phenotypes could reveal unexpected cell types that correlated with outcomes of interest in high dimensional flow cytometry datasets.

Testing for group structure in high-dimensional data.

With the use of finite mixture models for the clustering of a data set, the crucial question of how many clusters there are in the data can be addressed by testing for the smallest number of components in the mixture model compatible with the data. We investigate the performance of a resampling approach to this latter problem in the context of high-dimensional data, where the number of variables p is extremely large relative to the number of observations n. In order to be able to fit normal mixture models to such data, some form of dimension reduction has to be performed. This raises the question of whether a practically significant bias results if the bootstrapping is undertaken solely on the basis of the reduced dimensional form of the data, rather than using the full data from which to draw the bootstrap sample replications.

A mixture model with random-effects components for clustering correlated gene-expression profiles.

MOTIVATION: The clustering of gene profiles across some experimental conditions of interest contributes significantly to the elucidation of unknown gene function, the validation of gene discoveries and the interpretation of biological processes. However, this clustering problem is not straightforward as the profiles of the genes are not all independently distributed and the expression levels may have been obtained from an experimental design involving replicated arrays. Ignoring the dependence between the gene profiles and the structure of the replicated data can result in important sources of variability in the experiments being overlooked in the analysis, with the consequent possibility of misleading inferences being made. We propose a random-effects model that provides a unified approach to the clustering of genes with correlated expression levels measured in a wide variety of experimental situations. Our model is an extension of the normal mixture model to account for the correlations between the gene profiles and to enable covariate information to be incorporated into the clustering process. Hence the model is applicable to longitudinal studies with or without replication, for example, time-course experiments by using time as a covariate, and to cross-sectional experiments by using categorical covariates to represent the different experimental classes. RESULTS: We show that our random-effects model can be fitted by maximum likelihood via the EM algorithm for which the E(expectation)and M(maximization) steps can be implemented in closed form. Hence our model can be fitted deterministically without the need for time-consuming Monte Carlo approximations. The effectiveness of our model-based procedure for the clustering of correlated gene profiles is demonstrated on three real datasets, representing typical microarray experimental designs, covering time-course, repeated-measurement and cross-sectional data. In these examples, relevant clusters of the genes are obtained, which are supported by existing gene-function annotation. A synthetic dataset is considered too. AVAILABILITY: A Fortran program blue called EMMIX-WIRE (EM-based MIXture analysis WIth Random Effects) is available on request from the corresponding author.

Clustering.

Clustering techniques are used to arrange genes in some natural way, that is, to organize genes into groups or clusters with similar behavior across relevant tissue samples (or cell lines). These techniques can also be applied to tissues rather than genes. Methods such as hierarchical agglomerative clustering, k-means clustering, the self-organizing map, and model-based methods have been used. Here we focus on mixtures of normals to provide a model-based clustering of tissue samples (gene signatures) and of gene profiles, including time-course gene expression data.

An analysis of valve re-replacement after aortic valve replacement with biologic devices.

Biologic valve re-replacement was examined in a series of 1343 patients who underwent aortic valve replacement at The Prince Charles Hospital, Brisbane, with a cryopreserved or 4 degrees C stored allograft valve or a xenograft valve. A parametric model approach was used to simultaneously model the competing risks of death without re-replacement and re-replacement before death. One hundred eleven patients underwent a first re-replacement for a variety of reasons (69 patients with xenograft valves, 28 patients with 4 degrees C stored allograft valves, and 14 patients with cryopreserved allograft valves). By multivariable analysis younger age at operation was associated with xenograft, 4 degrees C stored allograft, and cryopreserved allograft valve re-replacement. However, this effect was examined in the context of longer survival of younger patients, which increases their exposure to the risk of re-replacement as compared with that in older patients whose decreased survival reduced their probability of requiring valve re-replacement. In patients older than 60 years at the time of aortic valve replacement, the probability of re-replacement (for any reason) before death was similar for xenografts and cryopreserved allograft valves but higher for 4 degrees C stored valves. However, in patients younger than 60 years, the probability of re-replacement at any time during the remainder of the life of the patient was lower with the cryopreserved allograft valve compared with the xenograft valve and 4 degrees C stored allografts.

Aortic valve infection. Risk factors for death and recurrent endocarditis after aortic valve replacement.

Patients (n = 195) undergoing aortic valve replacement (n = 209) for native or prosthetic valve endocarditis were studied to determine risk factors for death and recurrent endocarditis and also to determine the valve type least likely to be associated with recurrent endocarditis. Ten-year survival was 60%, the highest risk of dying occurring within the first 3 postoperative months. Risk factors for death in this early phase included increased urea concentration, higher New York Heart Association functional class, prosthetic valve endocarditis, infection status (lower in patients with healed endocarditis), longer duration of cardiopulmonary bypass, and nonuse of an allograft valve. In the late phase (beyond 3 months), risk factors included age at operation and Staphylococcus aureus infection (only in New York Heart Association functional class V). Ten years after aortic valve replacement, 79% of valves were free of recurrent endocarditis. The highest risk of recurrence was in the first 4 months. Longer duration of cardiopulmonary bypass was a weak risk factor for recurrent endocarditis in the early phase, and in the late phase risk factors were S. aureus infection (only in New York Heart Association functional classes III, IV, and V) and the use of now discontinued biologic valves. Allograft aortic valve replacement was shown to be associated with a low and constant risk of recurrent endocarditis, whereas other valve types were associated with a high early risk. The allograft valve should be the preferred replacement device for aortic root infection.

An analysis of risk factors for death and mode-specific death after aortic valve replacement with allograft, xenograft, and mechanical valves.

From September 1967 to January 1990, a total of 2100 patients underwent 2366 aortic valve replacements with a variety of allograft, xenograft, and mechanical valves. Concomitant procedures were performed in 764 patients. Actuarial survival at 12 years was 59.6% (70% confidence limits 57.8% to 61.4%). Hazard function for death was highest immediately after operation, falling to merge with a slowly rising phase of risk at approximately 3 months. Actuarial freedom from sudden death at 12 years was 88.0% (70% confidence limits 86.7% to 89.3%). The shape of the hazard function for sudden death was similar to that for death. Actuarial freedom from death with cardiac failure at 12 years was 87.9% (70% confidence limits 86.5% to 89.2%). The shape of the hazard function for death with cardiac failure was also similar to that for death. Risk factor analysis revealed the important deleterious impact on long-term survival resulting from impaired left ventricular structure and function because of aortic valve disease. No current-era valve used in this study (allograft, xenograft, or mechanical) was a risk factor for death. Both aortic wall disease and endocarditis necessitating aortic valve replacement substantially decreased long-term patient survival. Aortic valve replacement is advisable much earlier in the natural history of aortic valve disease before secondary left ventricular damage occurs.

On the EM algorithm for overdispersed count data.

In this paper, we consider the use of the EM algorithm for the fitting of distributions by maximum likelihood to overdispersed count data. In the course of this, we also provide a review of various approaches that have been proposed for the analysis of such data. As the Poisson and binomial regression models, which are often adopted in the first instance for these analyses, are particular examples of a generalized linear model (GLM), the focus of the account is on the modifications and extensions to GLMs for the handling of overdispersed count data.

Cluster analysis and related techniques in medical research.

In this paper we review methods of cluster analysis in the context of classifying patients on the basis of clinical and/or laboratory type observations. Both hierarchical and non-hierarchical methods of clustering are considered, although the emphasis is on the latter type, with particular attention devoted to the mixture likelihood-based approach. For the purposes of dividing a given data set into g clusters, this approach fits a mixture model of g components, using the method of maximum likelihood. It thus provides a sound statistical basis for clustering. The important but difficult question of how many clusters are there in the data can be addressed within the framework of standard statistical theory, although theoretical and computational difficulties still remain. Two case studies, involving the cluster analysis of some haemophilia and diabetes data respectively, are reported to demonstrate the mixture likelihood-based approach to clustering.

Mixture modelling for cluster analysis.

Cluster analysis via a finite mixture model approach is considered. With this approach to clustering, the data can be partitioned into a specified number of clusters g by first fitting a mixture model with g components. An outright clustering of the data is then obtained by assigning an observation to the component to which it has the highest estimated posterior probability of belonging; that is, the ith cluster consists of those observations assigned to the ith component (i = 1,..., g). The focus is on the use of mixtures of normal components for the cluster analysis of data that can be regarded as being continuous. But attention is also given to the case of mixed data, where the observations consist of both continuous and discrete variables.