Introduction and Background

DNA methylation (DNAm) is one of the most studied epigenetic marks known to play a key role in human health and development [1]. DNAm marks are chemical modifications of DNA which occur predominantly as 5-methylcytosine (5mC) at CpG dinucleotides in mammals. DNAm profiles are relatively stable and inherited during cellular division, but they are susceptible to environmental exposures such as smoking and diet [2]. Once established, DNAm alterations can persist even in the absence of the factors that induced them. Therefore, DNAm has unique properties to serve as a biomarker of past and concurrent environmental exposures [3]. In addition, DNAm patterns have been shown to predict disease status and to be considered mediators of the effect of environmental factors on human diseases [4].

A common technology to profile DNAm uses microarrays to measure DNAm levels at approximately half to one million CpG sites for each DNA sample. These technologies for high-throughput DNAm measurements are highly reliable with a good trade-off between cost and coverage compared to other epigenetic marks [5]. These platforms have been widely used in epigenome studies in which DNAm levels are analyzed to uncover biological mechanisms that underlie prior environmental factors and subsequent health outcomes. However, most studies analyzing DNAm levels at individual CpG sites or regions of the epigenome have been focused on detecting differentially methylated levels, i.e., sites or regions different in their mean DNAm levels among exposure groups or concentrations. Only a few studies evaluated the variance in DNAm in relation to extrinsic environmental stimuli and health outcomes. Figure 1 illustrates three simulated scenarios of methylation levels at a given CpG site: (1a) difference in methylation mean, (2b) difference in methylation variance, and (3c) difference in both methylation mean and variance.

Fig. 1
figure 1

Violin plots illustrating simulated examples of a difference in methylation mean, b difference in methylation variance, and c difference in both methylation mean and variance

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Recent findings from cancer epigenomic studies highlight the importance of identifying differentially variable CpG sites as biologically relevant features for understanding and predicting phenotypes of interest [6,7,8,9]. Importantly, increased DNAm variability in tumors has been suggested to be linked to the environmental adaptive capacity of cancer cells and can predict neoplastic transformation of epithelial cells [7, 10]. The idea is linked to stochastic variation which suggests that certain genetic variants, which do not change the mean phenotype, could alter the variability of the phenotype through epigenetic mechanisms [6]. In fact, epigenetically hypervariable regions throughout the genome can distinguish different tissue types including normal versus cancer; thus, epigenetic variability could be driving both cellular differentiation and Darwinian selection at the tissue which could potentially underlie cancer and other diseases [8]. This leads to the proposition that exposure to environmental risk factors may be driving this epigenetic variation of key genes contributing to disease phenotypes [11, 12].

While analytical methods used to detect differences in mean methylation levels across individual CpG sites and genomic regions are well-established in the literature [13, 14], a small number of approaches have been developed to identify differentially variable methylation. Statistical analysis methods based on differential variability have been shown to improve the detection of risk biomarkers in the context of cancer genomic and epigenomic studies [7, 12]. The majority of studies examining DNAm variability have been centered in cancer outcomes [6,7,8,9,10]. More recently, some studies have evaluated interpersonal DNAm variability in other outcomes, including body mass index [11], age [15], type 1 diabetes [16], depression in monozygotic twins [17], Alzheimer’s disease [18], and inflammatory bowel disease [19].

Yet, the analysis of differentially variable DNAm sites has not yet gained widespread adoption in environmental studies. To date, variability in DNAm has only been analyzed in the context of tobacco smoking [20], where differential variability between never-smokers and current smokers was compared revealing 14 differentially variable CpG sites associated with smoking exposure, with a 50% (7/14) overlap found between differentially methylated and differentially variable sites; arsenic [21], where 23 differentially variable sites associated with high arsenic exposure through drinking water were identified in leukocytes (PBMCs) and buccal cells; trichloroethylene [22], where blood DNA methylation was compared among high and low trichloroethylene (TCE) exposed workers and a control group, the high and low exposed groups were found to be significantly different in terms of the global DNA methylation variance, with 288 differentially variable sites identified across the three comparison groups after filtering out sites matched with population-specific SNPs; and lead exposure [23], where increased variability in DNA methylation at 16 CpG sites were shown to be significantly associated with neonatal lead exposure in dried bloodspot samples collected from a cohort of children.

Our goal in this paper is to shed light on the current state of statistical methods developed for differential variability analysis focusing on DNAm data, with the aim of providing a convenient and concise reference to expand their statistical analysis toolkit.

Methods for Differential Variability Analysis

In this section, we describe the most widely used statistical approaches for analyzing differential variability of DNAm levels: F-test, Bartlett’s test, Brown-Forsythe, and DiffVar. Next, we describe more recent methods which jointly test differences in mean and variance: penalized Exponential Tilt Model (pETM), and Joint Location and Scale score test (JLSsc). The reader is referred to Table 1 for a concise summary.

Table 1 Summary table of methods for assessing differential variability
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The classical F-test approach is used to test for equality of variances between two groups (e.g., cases and controls) using the F-statistic based on the ratio of variances from each group [7, 25]. This method is sensitive to outliers and departure from normality assumptions on DNAm levels, and covariate adjustment is not straightforward. One way to mitigate sensitivity to outliers is to perform a pre-processing step whereby outliers are removed from the original data set before performing the F-test. Other approaches include using variations of the F-statistic based on median absolute deviations instead of standard deviation for more robust statistical inference [25].

The Bartlett’s test extends the F-test for equality of variances across multiple groups against the alternative hypothesis that variances are unequal for at least two groups [35]. This method inherits the same shortcomings as the F-test in terms of sensitivity to outliers and departure from normality assumptions; and it does not support covariate adjustment.

The Epigenetic Variable Outliers for Risk Prediction Analysis (EVORA) is a popular algorithm using Bartlett’s test as a feature selection step to identify significant CpGs. EVORA assigns each sample a scale independent score determining if it is an outlier with respect to each CpG. Then, a risk score for each sample is calculated based on the proportion of risk CpGs with that particular sample as an outlier [10]. An important EVORA assumption is that sensitivity to outliers in the Bartlett’s test is considered a feature rather than a limitation. The authors argue that variability due to outliers is of biological importance, particularly in the context of pre-cancerous lesions. More recently, a regularized version called iEVORA was developed whereby the initial set of CpG identified via Bartlett’s test are re-ranked according to a specified test statistic based on differences in average methylation [26]. This approach assigns higher importance to more differentially variable CpGs which exhibit significant differences in mean methylation.

The Brown-Forsythe is a Levene’s test variation. Levene’s test is a Bartlett’s test alternative which also tests for equality of variances across multiple groups; however, it has the advantage of being more robust to departures from normality assumptions [36]. Therefore, Levene’s test is preferred when the investigator has strong evidence that the DNAm data are generated from a non-normal distribution. The Brown-Forsythe test uses either the DNAm median or the trimmed median in addition to the mean to calculate the test statistic, as opposed to the original Levene’s test which uses only the mean [37]. The Brown-Forsythe test was shown to perform favorably against competing tests in multiple simulation scenarios using real DNA methylation array data, and it is robust to deviations from normality assumptions [38]. However, this test does not support direct covariate adjustment.

The DiffVar method tests for equality of variances across multiple groups using a method inspired by Levene’s test statistic. Specifically, DiffVar calculates absolute (or squared) deviations from the DNAm mean in each group. The rationale is that more variable groups will have larger deviations on average, while more consistent groups will have smaller deviations; and testing for equality between the average deviations across groups is equivalent to testing for equality between the variability across the same groups. DiffVar also uses moderated t-statistics instead of ordinary t-statistics to perform multiple comparisons across the large number of CpGs in order to mitigate the issue of false positives [39]. Additionally, the use of linear models within DiffVar allows for the inclusion of adjustment covariates.

The penalized Exponential Tilt Model (pETM) is part of a more recent approach to differential methylation analysis where both the average and variance of the DNAm levels are jointly modeled within one statistical framework. In particular, the penalized exponential tilt model uses network-based regularization which takes into account the correlation among CpG sites within a genomic region to identify differences in both methylation mean and variance between two groups [32]. The approach detects either differences in mean, differences in variance, or differences in both means and variance. Covariate adjustment is possible with this method, and the user can even specify grouping parameters to control the correlation between CpG sites within a genetic region.

The JLSsc test is a novel approach to combine location and scale tests; in other words, it uses the results from running a differential analysis based on mean value (location test) and one based on variability (scale test) and then combines them in a way that accounts for correlations between the results of the two tests [34]. The combination is performed via the residuals from fitting linear regression models, which allows for the inclusion of adjustment covariates and supports continuous or categorical exposures. Another advantage of the JLSsc test is that it allows the user to specify their choice of methods for conducting the difference in mean and variance tests.

Conclusion

The identification of differentially methylated CpG sites and regions associated with environmental factors and health outcomes has been the core of epigenetic analyses in population studies. However, it is also important to examine the effects of environmental exposures on inter-individual epigenetic variability, as these changes may provide mechanistic insight into adaptive responses of the epigenome to environmental stimuli. Statistically, differences in mean in the absence of a difference in variance means that the distribution is simply shifted in a certain direction, while a difference in variance implies a stretching or change in the shape of the distribution. Thus, novel, adaptable, and robust statistical tools—able to capture differences in DNAm variability—are necessary to adequately infer conclusions and extract biologically sound insight from DNAm information.

In this manuscript, we reviewed six methods (F-test, Bartlett’s test, Browne-Forsythe’s test, DiffVar, pETM, and JLSsc test) which have been used in the context of genomic and epigenomic studies to identify inter-individual biomarker variability. In general, these approaches are easy to implement in R, and most of them, with the exception of pETM, assume normality of the biomarkers, implying the use of M-values. Importantly, the majority of these methods lack key features such as covariate adjustments and support for identifying contrasts with continuous exposures. Covariate adjustments are vital to accommodate variables like age, sex, race, ethnicity, and cell type proportions that are known to contribute to inter-individual epigenetic variability. Similarly, continuous exposure measures are quite common in epidemiological studies. Some studies have overcome those issues using residuals of linear regressions after correcting for cell type proportions and categorizing exposures [34, 39]. However, this 2-step approach is more prone to bias and variability than a direct approach, especially when the covariates being adjusted are confounder of the exposure-outcome relationship or if they are not linearly associated with the outcome [40]. Novel methods should aim to overcome these limitations.

Another major challenge in variability analysis is statistical power. Indeed, in order to accurately capture differences in variability, the sample size of the study needs to be larger than that required for analyzing differences in mean methylation levels. This is further exacerbated by the presence of technical artefacts introduced during sample collection, sample handling, and measurement procedures, thus making it harder to disentangle biological and technical variability [41]. Robust methods to account for batch effects such as ComBat are particularly useful to help reduce technical variability [42]; however, one must be careful to check for presence of batch effects before applying such methods to avoid over-correction which could inadvertently impact biological variability.

In the context of DNAm variability, some studies have shown that an association between mean DNA methylation levels and variance could potentially introduce unwarranted confounding bias in the analysis of differential variability [43, 44]. One possible solution to mitigate this issue is to rely on methods, such as pETM and JLSc, which jointly model the mean and the variance; another solution involves the introduction of an additional measure which corrects for the dependency of the variability on the mean methylation levels [44].

With this paper, we aim to bring more attention to analysis on differential variability, especially in the context of environmental exposures. We designed this work to be a concise and handy reference for investigators wishing to uncover differential variability patterns in their DNAm studies, while highlighting state-of-the-art methods along with the current challenges facing variability analysis studies.