A new meta-ANOVA approach for synthesizing information under signal-heterogeneity setting with application to nuclear magnetic resonance spectroscopic data

A new synthesizing statistical methodology is proposed to resolve issues of signal-heterogeneity in data sets collected through high-resolution ¹H nuclear magnetic resonance (NMR) spectroscopy. This signal-heterogeneity is typically caused by subjective operations for processing spectral profiles and measuring peak areas, non-homogeneous biological phases of experimental subjects, and variations of systems in multi-center. All these causes are likely to simultaneously impact signals of metabolic changes and their precision in a nonlinear fashion. As a combined effect, signal-heterogeneity chiefly manifests through non-homomorphic patterns of standardized treatment mean deviations spanning all experiments, and makes most remedial statistical models with linearity structure invalid. By avoiding a huge and very complex model, we develop a simple meta-ANOVA approach to synthesize many one-way-layout ANOVA analyses from individual experiments. A scale-invariant F-ratio statistic is taken as the summarizing sufficient statistic of a non-centrality parameter that supposedly captures the information about metabolic change from each experiment. Then a joint-likelihood function of a common non-centrality is constructed as the basis for maximum likelihood estimation and Chi-square likelihood ratio testing for statistical inference. We apply the meta-ANOVA to detect metabolic changes of three metabolites identified through pattern recognition on NMR spectral profiles obtained from muscle and liver tissues. We also detect effect differences among different treatments via meta-ANOVA multiple comparison.