An Exploratory Analysis of Essential Tremor and Associated Phenotypes

Mendelian Randomization (MR)

The goal of this experiment was to measure the strength and direction of a causative correlation between ET and several other traits presumed to be related. To do this, full summary statistics were collected from the largest and most current publicly available GWASes for ET and other traits, as outlined in Table 1. Using cleaned summary statistics, significant SNPs (p-value < 5 × 10^–8) for each phenotype were selected as candidate instrumental variables (IVs). SNPs were harmonized using TwoSampleMR [35, 36]. Multiallelic SNPs and palindromic SNPs with intermediate allele frequencies (~0.5) were deemed ambiguous and discarded. Steiger filtering was then carried out to remove IVs explaining a greater variance in the outcome than the exposure, as they likely effect the outcome directly (through horizontal pleiotropy) [35]. MR results were calculated using the Egger Regression [39], Inverse Variance Weighted (IVW) [40], Weighted Median (WM) [41], and Simple and Weighted modes [42]. F-statistics were calculated both per-SNP and globally for each analysis [43]. The Egger regression is a method meant to be sensitive to pleiotropy, with its y-intercept serving as an estimate for how associated the two traits are [40]. Then the global F-statistic was calculated as described elsewhere [43].

Subsequently, a Leave-One-Out (LOO) plot was made, where the IVW score was recalculated with each IV iteratively left out, to ensure that no IV was significantly skewing the results, as this suggests confounding [36]. The Pleiotropy RESidual Sum Outlier (PRESSO) method was also used to detect outliers in the regression, based on the r² values and data simulations [44]. Linear regression plots were made for each analysis, as well as forest plots. Each analysis was conducted bidirectionally. Bonferroni correction was applied to the 26 analyses (13 traits × 2 directions), giving a minimum p-value significance threshold of 0.0019 [45].

PolarMorphism and Enrichr Gene Ontologies

Summary statistics from each trait (Table 1) were harmonized with ET on a pairwise basis. This was done using the PolarMorphism R package’s AlleleFlip function [46]. Polar coordinates for the trait-ET pairs were then calculated using the ConvertToPolar function from PolarMorphism [46]. SNPs that had a strong magnitude of effect (r > 4), intermediate angles, and a strong adjusted p-value for the angles (θ q-value < 0.05) were extracted as pleiotropic. The shared pleiotropic SNPs were retained if they resided in genes as determined by the NIH SNP database (dbSNP) API [37]. The Enrichr gene ontology dataset “GO Biological Processes 2025” was then used to find molecular pathways in which shared ET-trait genes are implicated [47, 48, 49].

Genomic Structural Equation Modelling

Using the same GWAS studies as for the MR experiment (Table 1), genomic structural equation modeling was carried out to characterize the pleiotropic relationships between traits. Summary statistics were reformatted and a covariance matrix was created using linkage disequilibrium score regression (LDSC) [50]. As all summary statistics were processed using effective sample sizes, sample prevalences were set to 0.5 for all binary traits (and NA for continuous traits), as is suggested by the GenomicSEM guidelines [38]. Population prevalences were manually inputted for Bipolar disorder (0.028) [51], Essential Hypertension (0.26) [52], ET (0.0032) [1], Hearing loss (0.20) [53], Insomnia (0.06) [54], Major Depressive Disorder (MDD) (0.083) [55], and Parkinson’s disease (0.00572) [56]. The 1000 Genomes LD score reference for European populations was used for the construction of the matrix [57]. An exploratory factor analysis was then run using the ‘stats’ R package and used to guide the partition of traits into various latent variables for the construction of a structural equation model [58]. Additionally, the Enrichr “GWAS Catalog 2023” dataset was used to identify phenotypes containing many overlapping genetic signals, to inform genetic sharedness for latent variable selection [48]. A handful of models were tested with different numbers of latent variables and different subsets of traits. The model with the highest Comparative Fit Index (CFI) [59] and lowest Standardized Root Mean Squared Residual (SRMR) [60] was chosen.

Mendelian Randomization

The overall objective of the mendelian randomization experiment was to infer directional association between ET and other traits, using SNP-derived instrument variables from the GWAS of each trait. No exposure trait was able to confer significant risk for ET across analytical methods. Similarly, ET as an exposure did not have significant associations with any outcome traits across analytical methods. Thus, the null hypothesis cannot be rejected for any of the trait-ET pairs in any direction (threshold p-value of 0.0019 after Bonferroni correction). These results are summarized in Figure 1, which presents a comprehensive forest plot of bidirectional MR results across all traits, and in Table 2, which lists the number of IVs retained per analysis and notes whether any MR analytical method detected any nominally significant effect.

Figure 1

While no causal or directional relationships were supported by the MR results, several analyses revealed notable features related to horizontal pleiotropy. In particular, the analysis of ET and Parkinson’s disease demonstrated a striking Egger intercept in one direction, consistent with a high degree of pleiotropy between these traits. Similarly, several analyses, such as those involving low-density-lipoprotein (LDL) levels, MDD, and alcohol intake, showed large shifts in MR effect estimates after outlier removal or Steiger filtering, further suggesting that shared genetic architecture may confound causal inference in these cases.

Detailed forest plots and sensitivity diagnostics for each trait pair, including Egger intercepts and LOO results, are presented in Supplemental Figures S1–S12 (sensitivity analyses) and Supplemental Figures S13–S23 (forest plots).

Once again, no causal and directional associations could be made between ET and other traits via MR. However, interesting horizontal pleiotropy was noted in many analyses, which may partially be obscuring MR, which seeks to regress out genetic correlations.

PolarMorphism and Enrichr Gene Ontologies

The objective of this experiment was to identify SNPs having a high degree of effect shared between ET pairwise with the other tested traits. This was done using PolarMorphism [46], an R package that identifies pleiotropic SNPs, and Enrichr Gene ontologies [49], to map genes containing those SNPs to biomolecular pathways.

Among all trait pairs analyzed, the strongest result was found between ET and bipolar disorder, for which PolarMorphism identified 616 pleiotropic SNPs belonging to 86 unique genes. The top ten terms most significantly enriched across biological pathways described in the Enrichr “GO Biological Processes 2025” catalogue is shown in Supplemental Figure S24 for the ET-bipolar disorder pair. The most significantly enriched pathway shared between ET and bipolar disorder identified was the “Regulation of Potassium Ion Transport” term (p_adjusted = 0.0126), with an odds ratio (OR) of 28.5 and a gene overlap count of four.

Another significant enrichment was observed between ET and hearing loss, with 166 shared SNPs across 36 genes. One pathway, “Anterograde Dendritic Transport,” reached statistical significance (p_adjusted = 0.018), with an OR of 234.8. However, this enrichment was based on just two overlapping genes out of a total of seven in the pathway, raising concerns that the result may be driven by the small size of the gene set.

Between ET and LDL cholesterol, 413 pleiotropic SNPs belonged to 62 unique genes. Two pathways (“Positive Regulation of Transcription by RNA Polymerase II” and “Regulation of Vascular Associated Smooth Muscle Cell Apoptotic Process”) had adjusted p-values of 0.0217 and 0.0370, respectively. Both results were marginal and potentially misleading: the first term is very broad (983 genes), and the second was driven by only two overlapping genes.

All other trait pairs yielded no statistically significant enrichment results after correction for multiple testing. This meant no significant pathway enrichment for genes relevant to ET and cigarettes smoked per day (203 pleiotropic SNPs belonging to 56 genes), or coffee consumption (1,816 pleiotropic SNPs belonging to 158 genes), or insomnia (1,381 pleiotropic SNPs belonging to 88 genes), or cognition (3,055 pleiotropic SNPs belonging to 318 genes), or alcohol intake (500 pleiotropic SNPs belonging to 83 genes), or essential hypertension (237 pleiotropic SNPs belonging to 42 genes), or MDD (531 pleiotropic SNPs belonging to 112 genes), or vitamin D levels (68 pleiotropic SNPs belonging to 17 genes). There was also no significant association for ET and Parkinson’s disease, though notably only 3 pleiotropic SNPs were identified, mapping to just 2 genes. Although Mendelian randomization suggested shared architecture, the paucity of SNPs in this analysis precluded meaningful pathway interpretation.

Overall, while some results did have significant adjusted p-values, upon closer inspection none hold up to rigor, with the possible exception of “Regulation of Potassium Ion Transport” in the analysis between ET and bipolar disorder. This result, however, is also more dubious because bipolar disorder is far less associated with ET than other psychiatric phenotypes, like MDD.

Genomic SEM

The objective of this experiment was to model the pleiotropy between ET and other traits, by creating a structural equation model linking traits to ET through overarching latent variables. This was done using the GenomicSEM R package [38]. Partitioning of traits into latent variables was informed by exploratory factor analysis, the correlation matrix (shown in Supplemental Figure S35) and by Enrichr GWAS Catalog results. The final model is shown in Figure 2.

Figure 2

In the covariance matrix (Supplemental Figure S35), ET is seen to have little genetic correlation with other traits, except MDD (which has been previously reported in the GWAS used in our experiment) [6]. Other well-known associations are also noticed, like between bipolar disorder and MDD. From this covariance matrix, we observe that bipolar disorder, MDD, and insomnia have shared genetic architecture, therefore informing a candidate latent variable. Alcohol intake (drinks per week) and coffee consumption also share some correlation. Additionally, in examining the Enrichr results for GWAS associations from the gene lists compiled earlier between ET and drinks per week, and between ET and coffee consumption, it was seen both pointed to each other’s GWAS. Thus, we hypothesize that they will affect ET in a group, as a latent variable. A similar observation was made with LDL levels, smoking, and hypertension. Smoking and coffee consumption also have correlation, as seen in Supplemental Figure S35, and load onto the same latent variable. The final constructed structural equation model is shown below, in Figure 2.

Both performance metrics point to the model being significant, however the actual information given by the model is less informative. Looking at the model, we see that the amount of variance unexplained by loading onto any of the three factors for ET is 0.98, with a standard error of 0.09. Thus, most of the variance in ET cannot be explained by our analysis. Furthermore, across all factors, ET is the trait with the lowest loading, in fact being less than the amount of intercorrelation between traits. Thus, we cannot partition the pathophysiology of ET into phenotypically distinct genetic architectures. Furthermore, the high degree of uncertainty in the drinks per week trait both in the loading onto F2 and especially in the degree of variance unexplained by that loading are concerning. This is likely a result of the fact that it is the only trait loading uniquely onto F2, as both ET and coffee consumption load onto other factors as well.