A Statistical Framework to Identify Deviation from Time Linearity in Epigenetic Aging

In multiple studies DNA methylation has proven to be an accurate biomarker of age. To develop these biomarkers, the methylation of multiple CpG sites is typically linearly combined to predict chronological age. By contrast, in this study we apply the Universal PaceMaker (UPM) model to investigate changes in DNA methylation during aging. The UPM was initially developed to study rate acceleration/deceleration in sequence evolution. Rather than identifying which linear combinations of sites predicts age, the UPM models the rates of change of multiple CpG sites, as well as their starting methylation levels, and estimates the age of each individual to optimize the model fit. We refer to the estimated age as the “epigenetic age”, which is in contrast to the known chronological age of each individual. We construct a statistical framework and devise an algorithm to determine whether a genomic pacemaker is in effect (i.e rates of change vary with age). The decision is made by comparing two competing likelihood based models, the molecular clock (MC) and UPM. For the molecular clock model, we use the known chronological age of each individual and fit the methylation rates at multiple sites, and express the problem as a linear least squares and solve it in polynomial time. For the UPM case, the search space is larger as we are fitting both the epigenetic age of each individual as well as the rates for each site, yet we succeed to reduce the problem to the space of individuals and polynomial in the more significant space—the methylated sites. We first tested our algorithm on simulated data to elucidate the factors affecting the identification of the pacemaker model. We find that, provided with enough data, our algorithm is capable of identifying a pacemaker even when a weak signal is present in the data. Based on these results, we applied our method to DNA methylation data from human blood from individuals of various ages. Although the improvement in variance across sites between the UPM and MC was small, the results suggest that the existence of a pacemaker is highly significant. The PaceMaker results also suggest a decay in the rate of change in DNA methylation with age.Author Summary: DNA methylation is an important component of the epigenetic code that defines and maintains the state of cells. Recently, it has been found that certain sites in the genome undergo methylation changes at different rates during aging. The seminal work of Steve Horvath found that the methylation of a couple hundred CpG sites could be linearly combined to accurately predict the age of an individual in a number of tissues. Such a pattern resembles the Molecular Clock (MC) concept prevailing in molecular evolution, which suggests that there are sites in the genome that change linearly with age. In this work, we adapt the Universal PaceMaker (UPM) model to the setting of DNA methylation changes during aging. UPM relaxes the rate constancy of MC and was found to provide a better statistical explanation for genome evolution across the entire tree of life. This adaptation requires the solution of a complex optimization problem. Nevertheless, in a series of observations we show that the problem can be solved efficiently under the MC model and slightly less efficiently under the UPM model. This allows us to solve problems of non-trivial size. We chose as a proof of concept to analyze DNA methylation data collected from the blood of humans of different ages. Our results show that, similarly to genome evolution, the UPM provided an improvement of about 2% in the fit to the data. The statistical significance of this improvement is very high. Although tested on a small data set, this improvement demonstrates that the UPM more accurately captures age related DNA methylation changes than the MC model.