Combining distance matrices on identical taxon sets for multi-gene analysis with singular value decomposition.

We present a simple and effective method for combining distance matrices from multiple genes on identical taxon sets to obtain a single representative distance matrix from which to derive a combined-gene phylogenetic tree. The method applies singular value decomposition (SVD) to extract the greatest common signal present in the distances obtained from each gene. The first right eigenvector of the SVD, which corresponds to a weighted average of the distance matrices of all genes, can thus be used to derive a representative tree from multiple genes. We apply our method to three well known data sets and estimate the uncertainty using bootstrap methods. Our results show that this method works well for these three data sets and that the uncertainty in these estimates is small. A simulation study is conducted to compare the performance of our method with several other distance based approaches (namely SDM, SDM* and ACS97), and we find the performances of all these approaches are comparable in the consensus setting. The computational complexity of our method is similar to that of SDM. Besides constructing a representative tree from multiple genes, we also demonstrate how the subsequent eigenvalues and eigenvectors may be used to identify if there are conflicting signals in the data and which genes might be influential or outliers for the estimated combined-gene tree.

Phylogenetic analysis based on spectral methods.

Whole-genome or multiple gene phylogenetic analysis is of interest since single gene analysis often results in poorly resolved trees. Here, the use of spectral techniques for analyzing multigene data sets is explored. The protein sequences are treated as categorical time series, and a measure of similarity between a pair of sequences, the spectral covariance, is based on the common periodicity between these two sequences. Unlike the other methods, the spectral covariance method focuses on the relationship between the sites of genetic sequences. By properly scaling the dissimilarity measures derived from different genes between a pair of species, we can use the mean of these scaled dissimilarity measures as a summary statistic to measure the taxonomic distances across multiple genes. The methods are applied to three different data sets, one noncontroversial and two with some dispute over the correct placement of the taxa in the tree. Trees are constructed using two distance-based methods, BIONJ and FITCH. A variation of block bootstrap sampling method is used for inference. The methods are able to recover all major clades in the corresponding reference trees with moderate to high bootstrap support. Through simulations, we show that the covariance-based methods effectively capture phylogenetic signal even when structural information is not fully retained. Comparisons of simulation results with the bootstrap permutation results indicate that the covariance-based methods are fairly robust under perturbations in sequence similarity but more sensitive to perturbations in structural similarity.

How should we grade frailty in nursing home patients?

OBJECTIVES: To compare 3 methods of describing the frailty of older adults in nursing homes. DESIGN: Secondary analysis of a prospective cohort study. SETTING: Canadian long-term care institutions. PARTICIPANTS: Institutionalized older adults in the second clinical examination cohort of the Canadian Study of Health and Aging (CSHA-2; n = 728). MEASURES: Frailty was measured using the Cardiovascular Health Survey definition (Frail-CHS); the CSHA- Clinical Frailty Scale (CSHA-CFS) and a frailty index (FI). RESULTS: The sample was very elderly (87.7 +/- 6.7 years), disabled (83%), and showed a high level of mobility impairment (83%). Each frailty measure correlated moderately well with each other (0.61-0.71) and with a disability measure (-0.45 to -0.53) but only weakly with age (0.13-0.19). By each measure, frailty was significantly associated (P < .01) with an increased risk of mortality, disability and cognitive decline. In a model that included both the frailty-CHS definition and the Frailty Index only the latter was associated with a higher risk of mortality (P < .01 for FI, P = .18 for Frail-CHS) and decline in the 3MS (P < .01 for FI, P = .20 for the Frail-CHS definition). Both measures were significantly associated with new onset disability (P < .01). Similar results were found when both the CSHA-CFS and Frailty Index were included in the models. Random combinations of 15 variables used to make up alternate 5-item Frail-CHS definitions showed that any stratification based on 5 variables allowed tertiles of risk to be discriminated. CONCLUSIONS: Frailty is a robust concept and however defined, elderly people who are frail have worse outcomes than those who are not frail. The 3 measures showed varying ability to express grades of frailty.