L'analyse en composantes principales comme outil biostatistique : une routine pour étudier une structure de biomarqueurs

En statistiques, l'analyse en composantes principales (ACP) est une technique couramment utilisée afin de détecter la présence de processus gérant une base de données, c'est-à-dire des principaux axes de variation des données. Toutefois, on se contente trop souvent d'exécuter l'algorithme et d'interpréter directement les résultats sans analyses postérieures concernant la stabilité ou la généralisation des résultats. Pourtant, comme toute mesure statistique prélevée sur un échantillon, l'ACP peut présenter des résultats spécifiques à l'échantillon et difficilement rendre compte de la population étudiée. Il est donc important de développer des analyses complémentaires nous permettant d'évaluer la stabilité des résultats de l'ACP et de déterminer si, oui ou non, les résultats tirés de l'échantillon sont dignes de confiance. On construira et mettra cette nouvelle routine à l'épreuve en étudiant deux sujets distincts tant par leur nature que par leur complexité. On étudie en un premier temps le syndrome métabolique, syndrome considéré comme un facteur important dans le développement du diabète et des maladies cardiovasculaires. Ensuite, on étudie un phénomène beaucoup plus complexe et surtout moins bien défini que le syndrome métabolique, le processus physiologique du vieillissement

Quaternions et rotations

Les quaternions sont un outil fort utile pour représenter les rotations dans l'espace. On expliquera donc pourquoi et comment ils sont passés maîtres des mouvements de l'espace allant même surpasser leurs prédécesseurs. Toutefois, on traitera a priori de la construction des quaternions pour en déduire les différentes propriétés analytiques et algébriques de ceux-ci ainsi que leurs différentes représentations

Validating metabolic syndrome through principal component analysis in a medically diverse, realistic cohort

Abstract: Background: The concept of metabolic syndrome has been subject to etiological and clinical controversies in recent years. Associations among the five risk factors (obesity, high blood pressure, high blood sugar, high triglyceride levels and low HDL cholesterol) may help establish the validity of the concept and its application, but most such studies have been conducted on targeted cohorts not representative of an actual population. Methods: We used principal component analysis (PCA) to analyze the structure of the physiological components of metabolic syndrome in 7213 patients contained in an administrative database for the CHUS hospital in Sherbrooke, Quebec, a realistic cohort with diverse medical histories. We validated the results by repeating the analysis on stratified and random subgroups of patients, and on different combinations of risk factors. The first axis of the PCA was used to predict coronary heart disease (CHD) and diabetes. Results: The two first axes explained 53% of the variance. The first axis (33%) was associated in the expected direction with all five predictor variables, consistent with its interpretation as metabolic syndrome. All validation analyses strongly confirmed this interpretation. The scores from the first axis were more predictive of subsequent CHD and diabetes than the formal definition of metabolic syndrome. Conclusions: These results suggest that the concept of metabolic syndrome accurately captures an existing underlying physiological process. A continuous indicator could be constructed to identify more accurately metabolic syndrome thus improving risk assessment for CHD and diabetes mellitus. Metabolic syndrome can be measured well even without all five predictors, though measurement is improved by PCA relative to dichotomized definitions. However, discrepancies with other studies suggest that our results may not be generalizable, perhaps because our cohort tends to be sicker

Detection of a novel, integrative aging process suggests complex physiological integration

Abstract: Many studies of aging examine biomarkers one at a time, but complex systems theory and network theory suggest that interpretations of individual markers may be context-dependent. Here, we attempted to detect underlying processes governing the levels ofmany biomarkers simultaneously by applying principal components analysis to 43 common clinical biomarkers measured longitudinally in 3694 humans from three longitudinal cohort studies on two continents (Women’s Health and Aging I & II, InCHIANTI, and the Baltimore Longitudinal Study on Aging). The first axis was associated with anemia, inflammation, and low levels of calcium and albumin. The axis structure was precisely reproduced in all three populations and in all demographic sub-populations (by sex, race, etc.); we call the process represented by the axis “integrated albunemia.” Integrated albunemia increases and accelerates with age in all populations, and predicts mortality and frailty – but not chronic disease – even after controlling for age. This suggests a role in the aging process, though causality is not yet clear. Integrated albunemia behaves more stably across populations than its component biomarkers, and thus appears to represent a higher-order physiological process emerging from the structure of underlying regulatory networks. If this is correct, detection of this process has substantial implications for physiological organizationmore generally

L'analyse en composantes principales comme outil biostatistique : une routine pour étudier une structure de biomarqueurs

En statistiques, l'analyse en composantes principales (ACP) est une technique couramment utilisée afin de détecter la présence de processus gérant une base de données, c'est-à-dire des principaux axes de variation des données. Toutefois, on se contente trop souvent d'exécuter l'algorithme et d'interpréter directement les résultats sans analyses postérieures concernant la stabilité ou la généralisation des résultats. Pourtant, comme toute mesure statistique prélevée sur un échantillon, l'ACP peut présenter des résultats spécifiques à l'échantillon et difficilement rendre compte de la population étudiée. Il est donc important de développer des analyses complémentaires nous permettant d'évaluer la stabilité des résultats de l'ACP et de déterminer si, oui ou non, les résultats tirés de l'échantillon sont dignes de confiance. On construira et mettra cette nouvelle routine à l'épreuve en étudiant deux sujets distincts tant par leur nature que par leur complexité. On étudie en un premier temps le syndrome métabolique, syndrome considéré comme un facteur important dans le développement du diabète et des maladies cardiovasculaires. Ensuite, on étudie un phénomène beaucoup plus complexe et surtout moins bien défini que le syndrome métabolique, le processus physiologique du vieillissement

Quaternions et rotations

Les quaternions sont un outil fort utile pour représenter les rotations dans l'espace. On expliquera donc pourquoi et comment ils sont passés maîtres des mouvements de l'espace allant même surpasser leurs prédécesseurs. Toutefois, on traitera a priori de la construction des quaternions pour en déduire les différentes propriétés analytiques et algébriques de ceux-ci ainsi que leurs différentes représentations

Detection of a novel, integrative aging process suggests complex physiological integration.

Many studies of aging examine biomarkers one at a time, but complex systems theory and network theory suggest that interpretations of individual markers may be context-dependent. Here, we attempted to detect underlying processes governing the levels of many biomarkers simultaneously by applying principal components analysis to 43 common clinical biomarkers measured longitudinally in 3694 humans from three longitudinal cohort studies on two continents (Women's Health and Aging I & II, InCHIANTI, and the Baltimore Longitudinal Study on Aging). The first axis was associated with anemia, inflammation, and low levels of calcium and albumin. The axis structure was precisely reproduced in all three populations and in all demographic sub-populations (by sex, race, etc.); we call the process represented by the axis "integrated albunemia." Integrated albunemia increases and accelerates with age in all populations, and predicts mortality and frailty--but not chronic disease--even after controlling for age. This suggests a role in the aging process, though causality is not yet clear. Integrated albunemia behaves more stably across populations than its component biomarkers, and thus appears to represent a higher-order physiological process emerging from the structure of underlying regulatory networks. If this is correct, detection of this process has substantial implications for physiological organization more generally

Treatise on the Conflict of Laws

<p>Loading importance is calculated as the loading divided by the sum of the absolute values of all loadings. These values are ordered from high (red, on bottom) to low (magenta, on top) for the first 20 loadings; remaining loadings are grouped together as “Other” in white. Accordingly, neutrophils have the strongest loading, then AST, then lymphocytes, etc. The order and colors are derived from the full analysis combining the three data sets (left column, top-left panel “All”) and applied to all other columns in the figure. Stability of loadings is indicated by conservation of loading heights across bars. For each panel, the loadings for the full data set are at left. Numbers indicate subset sample sizes. For all panels except BLSA, the 43-variable set is used; for BLSA there was insufficient sample size to perform PCA on subsets with 43 variables, so the 34-variable analysis is presented.</p

Biomarker loading order and stability for PCA1 across datasets and subsets.

<p>Loading importance is calculated as the loading divided by the sum of the absolute values of all loadings. These values are ordered from high (red, on bottom) to low (magenta, on top) for the first 20 loadings; remaining loadings are grouped together as “Other” in white. Accordingly, hemoglobin has the strongest loading, then hematocrit, then albumin, etc. The order and colors are derived from the full analysis combining the first visits of individuals in all three datasets (top-left panel, left column, “All”) and applied to all other columns in the figure. Stability of loadings is indicated by conservation of loading heights across bars. (For an example of unstable loadings, see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0116489#pone.0116489.g005" target="_blank">Fig. 5</a>.) For each panel, the loadings for the full dataset are at left. Numbers indicate subset sample sizes. For all panels except BLSA, the 43-variable set is used; for BLSA there was insufficient sample size to perform PCA on subsets with 43 variables, so the 34-variable analysis is presented.</p

Biomarker loading order and stability for PCA25 (the 25^th axis, chosen randomly as an example of an unstable axis) across data sets and subsets.

<p>Loading importance is calculated as the loading divided by the sum of the absolute values of all loadings. These values are ordered from high (red, on bottom) to low (magenta, on top) for the first 20 loadings; remaining loadings are grouped together as “Other” in white. Accordingly, magnesium has the strongest loading, then glucose, then eosinophils, etc. The order and colors are derived from the full analysis combining the three data sets (left column, top-left panel “All”) and applied to all other columns in the figure. Stability of loadings is indicated by conservation of loading heights across bars. For each panel, the loadings for the full data set are at left. Numbers indicate subset sample sizes. For all panels except BLSA, the 43-variable set is used; for BLSA there was insufficient sample size to perform PCA on subsets with 43 variables, so the 34-variable analysis is presented.</p