The technological progress of data management systems has provided clinical researchers with a sophisticated statistical framework within which to examine the multifaceted and complex relationships inherent in many clinical phenomena. Multivariate analysis refers to a set of statistical procedures that are distinguished by the ability to examine several response variables within a single study and to account for their potential interrelationships in the analysis of the data. These tests are distinguished from univariate analysis procedures, such as the t-test and analysis of variance, in that univariate methods accommodate only one dependent variable.
Given the types of questions being asked today and the types of data being used to examine clinical procedures, multivariate statistics have become quite important for those who do research and those who read research reports. The purpose of this chapter is to introduce the basic concepts behind several of the most commonly used multivariate methods: partial correlation, multiple regression, logistic regression, discriminant analysis, factor analysis, multivariate analysis of variance and survival analysis.
The application of multivariate procedures necessitates the use of a computer, and may require the assistance of a statistician for more advanced operations. In a short introduction such as this, it is not possible to cover the full scope of these procedures. Therefore, this discussion focuses on a conceptual understanding of multivariate tests and interpretation of the output a computer analysis will generate.
The product-moment correlation coefficient, r, offers the researcher a simple and easily understood measure of the association between two variables, X and Y. The interpretation of r is limited, however, because it cannot account for the possible influence of other variables on that relationship. For instance, in a study of the relationship between age and length of hospital stay, we might find a correlation of .70, suggesting that older patients tend to have longer hospital stays (as shown by the shaded overlapped portion in Figure 29.1A). If, however, older patients also tend to have greater functional limitations, then the observed relationship between hospital stay and age may actually be the result of their mutual relationship with function; that is, the hospital stay may actually be explained by the patient's functional status. We can resolve this dilemma by looking at the relationship between hospital stay and age with the effect of functional status controlled, using a procedure called partial correlation.
Representation of partial correlation between hospital stay (Y) and age (X), with the effect of function (Z) removed. In (A), (B) and (C), the simple correlations between each pair of variables are illustrated. In (D) the shaded area represents those parts of hospital stay and age that are explained by function. The black area shows the common variance in hospital stay and age that is not related to function, ...