18. Multivariate Analysis of Variance (35 and 30 Patients)

Multivariate analysis is a method that, simultaneously, assesses more than a single outcome variable. It is different from repeated measures analysis of variance and mixed models, that assess both the difference between the outcomes and the overall effects of the predictors on the outcomes. Multivariate analysis, simultaneously, assesses the separate effects of the predictors on one outcome adjusted for the other. E.g., it can answer clinically important questions like: does drug-compliance not only predict drug efficacy, but also, independently of the first effect, predict quality of life. Path statistics can be used as an alternative approach to multivariate analysis of variance (MANOVA) (Chap. 17). However, MANOVA is the real thing, because it produces an overall level of significance of a predictive model with multiple outcome and predictor variables.

Does the inclusion of additional outcome variables enable to make better use of predicting variables.

The effects of non compliance and counseling on treatment efficacy of a new laxative were assessed in the Chap. 16. For multivariate analysis quality of life scores were added as additional outcome variable. The first 10 patients of the data file also used in Chap. 17 is given underneath.

The entire data file is entitled “chapter17multivariatewithpath”, and is in extras.springer.com. Start by opening the data file in SPSS. The module General Linear Model consists of four statistical models:

We will use here the statistical model Multivariate.

We will first assess whether counseling frequency is a significant predictor of (1) both frequency improvement of stools and (2) improved quality of life.

The above table shows that MANOVA can be considered as another regression model with intercepts and regression coefficients. Just like analysis of variance (ANOVA) it is based on normal distributions and homogeneity of the variables. SPSS has checked the assumptions, and the results as given indicate that the model is adequate for the data. Generally, Pillai’s method gives the best robustness and Roy’s the best p-values. We can conclude that counseling is a strong predictor of both improvement of stools and improved quality of life. In order to find out which of the two outcomes is most important, two ANOVAs with each of the outcomes separately must be performed.

The above tables show that also in the ANOVAs counseling frequency is a strong predictor of not only improvement of frequency of stools but also of improved quality of life (improv freq stool = improvement of frequency of stools, improve qol = improved quality of life scores)

In order to find out whether the compliance with drug treatment is a contributory predicting factor, MANOVA with two predictors and two outcomes is performed. Instead of “counseling” both “counseling” and “compliance” are transfered to Fixed factors. The underneath table shows the results.

After including the second predictor variable the MANOVA is not significant anymore. Probably, the second predictor is a confounder of the first one. The analysis of this model stops here.

As a second example we use the data from Field (Discovering SPSS, Sage London, 2005, p 571) assessing the effect of three treatment modalities on compulsive behavior disorder estimated by two scores, a thought-score and an action-score (Var = variable).

The entire data file is in extras.springer.com, and is entitled “chapter18multivariateanova”. Start by opening the data file. The module General Linear Model consists of four statistical models:

We will use here again the statistical model Multivariate.

The Pillai test shows that the predictor (treatment modality) has a significant effect on both thoughts and actions at p = 0,049. Roy’s test being less robust gives an even better p-value of 0,020.

We will use again ANOVAs to find out which of the two outcomes is more important.

Do the same for variable “thought”.

The above two tables show that in the ANOVAs nor thoughts nor actions are significant outcomes of treatment modality anymore at p < 0,05. This would mean that the treatment modality is a rather weak predictor of either of the outcomes, and that it is not able to significantly predict a single outcome, but that it significantly predicts two outcomes pointing into a similar direction.

What advantages does MANOVA offer compared to multiple ANOVAs.

Multivariate analysis should not be used for explorative purposes and data dredging, but should be based on sound clinical arguments.

A problem with multivariate analysis with binary outcome variables is that after iteration the data often do not converse. Instead multivariate probit analysis available in STATA statistical software can be performed (see Chap. 25 in. Statistics Applied to clinical studies 5th edition, Springer Heidelberg Germany, 2012, from the same authors)

Multivariate analysis, simultaneously, assesses the separate effects of the predictors on one outcome variable adjusted for another outcome variable. For example, it can answer clinically important questions like: does drug-compliance not only predict drug efficacy, but also, independently of the first effect, predict quality of life. Path statistics can be used as an alternative approach to multivariate analysis of variance (MANOVA) (Chap. 17). However, MANOVA is the real thing, because it produces an overall level of significance of a predictive model with multiple outcome and predictor variables. Post hoc ANOVAS are required to find out which of the outcomes is more important.

More background, theoretical, and mathematical information of multivariate analysis with path statistics is given in Statistics applied to clinical trials 5th edition, Chap. 25, Springer Heidelberg Germany, 2012, from the same authors.