Statistical Modelling of Cardiovascular Data. An Introduction to Linear Mixed Models

Most of statistical approaches in cardiovascular research were based on variance analysis (ANOVA). However, most of the time, the assumption that data are independent is violated since several measures are performed on the same subject (repeated measures). In addition, the presence of intra- and inter-observers variability can potentially obscure significant differences. The linear mixed model (LMM) is an extended multivariate linear regression method of analysis that accounts for both fixed and random effects. LMM allows for addressing incomplete design cases. In this paper, LMM was applied to two sets of cardiovascular research data and compared to ANOVA. The first example is an analysis of heart rate in mice after atropine and propranolol injections. LMM shows an important mouse random effects that depends on pharmacological treatment and provides with accurate estimates for each significant experimental factors. When randomly suppressing observations from the data sets (20-30%) the time factor of Anova model becomes non significant while LMM still remains significant. The second example is the analysis of isolated coronary-perfused pressure of transgenic mice hearts. LMM evidenced a significant transgenic effect in both male and female animals, while, with ANOVA, the transgenic effects was limited to male mice only. In both cases, as compared to ANOVA, the LMM separately accounts for fixed and random effects, allowing thus for studying more adequately incomplete designs on repeated measures.