Modelling High-Dimensional Data by Mixtures of Factor Analyzers

We focus on mixtures of factor analyzers from the perspective of a method for model-based density estimation from high-dimensional data, and hence for the clustering of such data. This approach enables a normal mixture model to be fitted to a sample of n data points of dimension p, where p is large relative to n. The number of free parameters is controlled through the dimension of the latent factor space. By working in this reduced space, it allows a model for each component-covariance matrix with complexity lying between that of the isotropic and full covariance structure models. We shall illustrate the use of mixtures of factor analyzers in a practical example that considers the clustering of cell lines on the basis of gene expressions from microarray experiments. (C) 2002 Elsevier Science B.V. All rights reserved

Lipid-Related Markers and Cardiovascular Disease Prediction

Cardiolog

Statistical methods for the time-to-event analysis of individual participant data from multiple epidemiological studies

Background Meta-analysis of individual participant time-to-event data from multiple prospective epidemiological studies enables detailed investigation of exposure-risk relationships, but involves a number of analytical challenges. Methods This article describes statistical approaches adopted in the Emerging Risk Factors Collaboration, in which primary data from more than 1 million participants in more than 100 prospective studies have been collated to enable detailed analyses of various risk markers in relation to incident cardiovascular disease outcomes. Results Analyses have been principally based on Cox proportional hazards regression models stratified by sex, undertaken in each study separately. Estimates of exposure-risk relationships, initially unadjusted and then adjusted for several confounders, have been combined over studies using meta-analysis. Methods for assessing the shape of exposure-risk associations and the proportional hazards assumption have been developed. Estimates of interactions have also been combined using meta-analysis, keeping separate within-and between-study information. Regression dilution bias caused by measurement error and within-person variation in exposures and confounders has been addressed through the analysis of repeat measurements to estimate corrected regression coefficients. These methods are exemplified by analysis of plasma fibrinogen and risk of coronary heart disease, and Stata code is made available. Conclusion Increasing numbers of meta-analyses of individual participant data from observational data are being conducted to enhance the statistical power and detail of epidemiological studies. The statistical methods developed here can be used to address the needs of such analyses. © The Author 2010; all rights reserved

Adult height and the risk of cause-specific death and vascular morbidity in 1 million people: individual participant meta-analysis

Cardiolog

Lipoprotein(a) concentration and the risk of coronary heart disease, stroke, and nonvascular mortality

Context Circulating concentration of lipoprotein(a) (Lp[a]), a large glycoprotein attached to a low-density lipoprotein–like particle, may be associated with risk of coronary heart disease (CHD) and stroke. Objective To assess the relationship of Lp(a) concentration with risk of major vascular and nonvascular outcomes. Study Selection Long-term prospective studies that recorded Lp(a) concentration and subsequent major vascular morbidity and/or cause-specific mortality published between January 1970 and March 2009 were identified through electronic searches of MEDLINE and other databases, manual searches of reference lists, and discussion with collaborators. Data Extraction Individual records were provided for each of 126 634 participants in 36 prospective studies. During 1.3 million person-years of follow-up, 22 076 firstever fatal or nonfatal vascular disease outcomes or nonvascular deaths were recorded, including 9336 CHD outcomes, 1903 ischemic strokes, 338 hemorrhagic strokes, 751 unclassified strokes, 1091 other vascular deaths, 8114 nonvascular deaths, and 242 deaths of unknown cause. Within-study regression analyses were adjusted for within-person variation and combined using meta-analysis. Analyses excluded participants with known preexisting CHD or stroke at baseline. Data Synthesis Lipoprotein(a) concentration was weakly correlated with several conventional vascular risk factors and it was highly consistent within individuals over several years. Associations of Lp(a) with CHD risk were broadly continuous in shape. In the 24 cohort studies, the rates of CHD in the top and bottom thirds of baseline Lp(a) distributions, respectively, were 5.6 (95% confidence interval [CI], 5.4-5.9) per 1000 personyears and 4.4 (95% CI, 4.2-4.6) per 1000 person-years. The risk ratio for CHD, adjusted for age and sex only, was 1.16 (95% CI, 1.11-1.22) per 3.5-fold higher usual Lp(a) concentration (ie, per 1 SD), and it was 1.13 (95% CI, 1.09-1.18) following further adjustment for lipids and other conventional risk factors. The corresponding adjusted risk ratios were 1.10 (95% CI, 1.02-1.18) for ischemic stroke, 1.01 (95% CI, 0.98-1.05) for the aggregate of nonvascular mortality, 1.00 (95% CI, 0.97-1.04) for cancer deaths, and 1.00 (95% CI, 0.95-1.06) for nonvascular deaths other than cancer. Conclusion Under a wide range of circumstances, there are continuous, independent, and modest associations of Lp(a) concentration with risk of CHD and stroke that appear exclusive to vascular outcomes. ©2009 American Medical Association. All rights reserved