On the potential of models for location and scale for genome-wide DNA methylation data

With the help of epigenome-wide association studies (EWAS), increasing knowledge on the role of epigenetic mechanisms such as DNA methylation in disease processes is obtained. In addition, EWAS aid the understanding of behavioral and environmental effects on DNA methylation. In terms of statistical analysis, specific challenges arise from the characteristics of methylation data. First, methylation β-values represent proportions with skewed and heteroscedastic distributions. Thus, traditional modeling strategies assuming a normally distributed response might not be appropriate. Second, recent evidence suggests that not only mean differences but also variability in site-specific DNA methylation associates with diseases, including cancer. The purpose of this study was to compare different modeling strategies for methylation data in terms of model performance and performance of downstream hypothesis tests. Specifically, we used the generalized additive models for location, scale and shape (GAMLSS) framework to compare beta regression with Gaussian regression on raw, binary logit and arcsine square root transformed methylation data, with and without modeling a covariate effect on the scale parameter.

Using simulated and real data from a large population-based study and an independent sample of cancer patients and healthy controls, we show that beta regression does not outperform competing strategies in terms of model performance. In addition, Gaussian models for location and scale showed an improved performance as compared to models for location only. The best performance was observed for the Gaussian model on binary logit transformed β-values, referred to as M-values. Our results further suggest that models for location and scale are specifically sensitive towards violations of the distribution assumption and towards outliers in the methylation data. Therefore, a resampling procedure is proposed as a mode of inference and shown to diminish type I error rate in practically relevant settings. We apply the proposed method in an EWAS of BMI and age and reveal strong associations of age with methylation variability that are validated in an independent sample.

Models for location and scale are promising tools for EWAS that may help to understand the influence of environmental factors and disease-related phenotypes on methylation variability and its role during disease development.