Advanced Statistics: Linear Regression, Part II: Multiple Linear Regression

Abstract

The applications of simple linear regression in medical research are limited, because in most situations, there are multiple relevant predictor variables. Univariate statistical techniques such as simple linear regression use a single predictor variable, and they often may be mathematically correct but clinically misleading. Multiple linear regression is a mathematical technique used to model the relationship between multiple independent predictor variables and a single dependent outcome variable. It is used in medical research to model observational data, as well as in diagnostic and therapeutic studies in which the outcome is dependent on more than one factor. Although the technique generally is limited to data that can be expressed with a linear function, it benefits from a well-developed mathematical framework that yields unique solutions and exact confidence intervals for regression coefficients. Build-ing on Part I of this series, this article acquaints the reader with some of the important concepts in multiple regression analysis. These include multicollinearity, interaction effects, and an expansion of the discussion of inference testing, leverage, and variable transformations to multivariate models. Examples from the first article in this series are expanded on using a primarily graphic, rather than mathematical, approach. The importance of the relationships among the predictor variables and the dependence of the multivariate model coefficients on the choice of these variables are stressed. Finally, concepts in regression model building are discussed.

Escore de risco Dante Pazzanese para síndrome coronariana aguda sem supradesnivelamento do segmento ST

“…At a first moment, ST-segment depression was not observed to be a prognostic variable at 5% significance level. That allowed the assessment of the possibility of multicollinearity 22,23 between cTnI and ST-segment depression, through a separate analysis of two independent models -those variables were not included in one of them. ST-segment depression emerges as an independent variable when cTnI is not included in the model.…”

Changes in lifestyle and total homocysteine in relation to MTHFR(C677T) genotype: the Inter99 study

“…All P-values reported are two-tailed and statistical significance was defined as Po0.05. Potential influence-rich observations were identified by statistical plots of influential statistics (leverage, Cook's D) (Cook, 1979;Marill, 2004). The regression analyses were repeated excluding these observations to confirm the findings.…”

Comparação entre troponina I cardíaca e CK-MB massa em síndrome coronariana aguda sem supra de ST

“…CK-MB mass emerges as an independent prognostic variable for the event of death or infarction (reinfarction) within 30 days. The non-continuance of CK-MB mass as a prognostic variable, when cTnI is also included in the analysis, can be explained by the problem of collinearity 23,24 between these two biomarkers. This should reflect the greater specificity that is inherent in cardiac troponins, in the detection of myocardial injury that adversely implies adverse outcomes 25 .…”