PubMed · 974536
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T D Swinscow. 1976-09-18. Statistics at square one: XVIII-Correlation.. https://doi.org/10.1136/bmj.2.6037.680
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MOTIVATION: Compositional data are frequently encountered in many disciplines, such as in next-generation sequencing experiments widely used in biomedical studies. Regression analysis with compositional data as either responses or predictors has been well studied. However, when both responses and predictors are compositional, the inventory of analysis tools is surprisingly limited, especially in the high-dimensional setting. Among the few existing methods, most of them rely on a log-ratio transformation to move compositional data from the simplex to real numbers. Yet, a serious weakness of these methods is their failure to handle the substantial fraction of zeroes observed in data collected from next-generation sequencing experiments. RESULTS: To investigate associations between two high-dimensional multi-omics compositions, we propose a composition-on-composition (COC) regression analysis method which does not require log-ratio transformations and hence can handle zeroes in the data. To account for high dimensionality, we estimate regression coefficients using a penalized estimation equation approach. Finally, inference procedures for COC regression are also proposed. Superior performance of COC is demonstrated through both comprehensive numerical simulations and case studies. AVAILABILITY AND IMPLEMENTATION: Source R codes to implement COC method is available at https://github.com/nrios4/COC.
The paper introduces all indices of multicollinearity diagnoses, the basic principle of principal component regression and determination of 'best' equation method. The paper uses an example to describe how to do principal component regression analysis with SPSS 10.0: including all calculating processes of the principal component regression and all operations of linear regression, factor analysis, descriptives, compute variable and bivariate correlations procedures in SPSS 10.0. The principal component regression analysis can be used to overcome disturbance of the multicollinearity. The simplified, speeded up and accurate statistical effect is reached through the principal component regression analysis with SPSS.
Bland-Altman analysis for comparison of two methods of clinical measurement is frequently used in scientific publications. This article is more appropriate than the conventional linear regression analysis. This paper gives an overview of the principles for the use of Bland-Altman analysis as well as the specific terminology attached to it. The Bland-Altman comparison analysis is mainly a tool for clinical interpretation. The bias and the agreement limits provide the variation of the values of the technique compared to the other. The difference between the two methods of measurement is plotted against the average obtained with each of the two techniques. Bland-Altman analysis can also be used to check the repeatability of a measurement technique within the same subject and to determine a repeatability coefficient. With an adaptation of the calculation of the agreement limits, the average of multiple measurements for each subject with two measurement techniques can be used for the Bland-Altman analysis.