Fig 1.
Performance of different multivariate statistics.
Example plots show empirical type I error and power of the MANOVA test using four common multivariate test statistics. Type I error rate is shown for the simulation scenario with no treatment effects, equal variance in all groups and data drawn from a multivariate normal distribution. An example of power analysis is shown for a simulation with large treatment effects (Cohen’s d equal to 0.8), equal variance in all groups and data sampled from a multivariate normal distribution. Hotelling: Lawley-Hotelling trace; Pillai: Pillai’s trace; Roy: Roy’s largest characteristic root; Wilks: Wilks’ lambda.
Fig 2.
Type I error rate of univariate and multivariate techniques under different simulation conditions.
The title of each plot reports the multivariate distribution from which the data were sampled as well as the variance ratio between the simulated control and treatment groups. ANOVA: Analysis of variance; MANOVA: Multivariate analysis of variance; Mixed: Linear mixed effects model; MV: Multivariate; PCA: Principal component analysis.
Fig 3.
Empirical power of univariate and multivariate techniques in case of large treatment effects (Cohen’s d equal to 0.8).
The multivariate distribution from which the data were drawn as well as the variance ratio between simulated control and treatment groups are summarized in the title of each respective plot. ANOVA: Analysis of variance; MANOVA: Multivariate analysis of variance; Mixed: Linear mixed effects model; MV: Multivariate; PCA: Principal component analysis.
Fig 4.
Empirical power of univariate and multivariate techniques in case of moderate treatment effects (Cohen’s d equal to 0.5).
The multivariate distribution from which the data were drawn as well as the variance ratio between simulated control and treatment groups are summarized in the title of each respective plot. ANOVA: Analysis of variance; MANOVA: Multivariate analysis of variance; Mixed: Linear mixed effects model; MV: Multivariate; PCA: Principal component analysis.
Fig 5.
Empirical power of univariate and multivariate techniques in case of small treatment effects (Cohen’s d equal to 0.2).
The multivariate distribution from which the data were drawn as well as the variance ratio between simulated control and treatment groups are summarized in the title of each respective plot. ANOVA: Analysis of variance; MANOVA: Multivariate analysis of variance; Mixed: Linear mixed effects model; MV: Multivariate; PCA: Principal component analysis.
Fig 6.
Comparison of ordination techniques for pattern analysis in the case when no treatment effects were simulated.
Plots show results for one out of 1000 simulations with 5 measurements per group drawn from a multivariate normal distribution with equal variance between control and treatment groups. The ordination technique was considered to falsely capture a treatment effect pattern in the data in case of non-overlapping 95% confidence ellipse of the control group with the confidence ellipses for the treatment groups (dose1 to dose3). LDA: Linear discriminant analysis; PCA: Principal component analysis; PLS-DA: Partial least squares discriminant analysis; RDA; Redundancy analysis.
Fig 7.
Partial least squares discriminant analysis (PLS-DA) to identify treatment effect patterns.
We simulated a data set with 5 measurements per group and huge treatment effects for 9 randomly selected endpoints out of the 18 variables in the data set. The control group was separated from the treatment groups along the first multivariate dimension in the PLS-DA analysis We calculated the correlation of the original variables with this dimension to identify which original endpoints explained the multivariate pattern. Correlations with an absolute value below 0.5 were set to 0 in order to filter out unimportant variables. All 9 variables with simulated treatment effects were significantly correlated with the first multivariate axis. Two additional variables without simulated treatment effects (lesion volume at day 14 and T2 lesion at day 14) were also significantly correlated with the first multivariate axis.
Table 1.
Post-hoc analysis following linear mixed effects models for variables with repeated measures.