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GWAS of Longitudinal Trajectories at Biobank Scale

Posted on (Update: )
Tags: GWAS, Longitudinal, Biobank

This post is for Ko, S., German, C. A., Jensen, A., Shen, J., Wang, A., Mehrotra, D. V., Sun, Y. V., Sinsheimer, J. S., Zhou, H., & Zhou, J. J. (2022). GWAS of longitudinal trajectories at biobank scale. The American Journal of Human Genetics, 109(3), 433–445.

Recent research reveals that not only the mean level of biomarker trajectories but also their fluctuations, or within-subject (WS) variability, are risk factors for many diseases.

It is crucial to identify the genetic factors that shift the mean or alter the WS variability of a biomarker trajectory.

Currently, no efficient tools for GWAS of biomarker trajectories at the biobank scale, even for just mean effects.

The paper proposes TrajGWAS, a linear mixed effect model-based method for testing genetic effects that shift the mean or alter the WS variability of a biomarker trajectory.

Assume there are $m$ independent individuals, individual $i$ has $n_i$ longitudinal measurements of a biomarker, and $n = \sum_{i=1}^m n_i$ is the total number of observations.

Consider an LMM for modeling different sources of variation in a biomarker in the longitudinal setting,

\[y_{ij} = \bfx_{ij}^T\bfbeta + g_i\beta_g + z_{ij}^T\gamma_i + \varepsilon_{ij}\]


  • $y_{ij}$: individual $i$’s measurement at occasion $j\in \{1,\ldots, n_i\}$
  • $\bfx_{ij}$: $p\times 1$ vector of regressors with corresponding regression coefficients $\bfbeta$
  • $g_i$: genotype dosage of individual $i$ with corresponding genetic mean effect $\beta_g$
  • the WS variability is captured by the random terms $\varepsilon_{ij}$ with mean zero and inhomogeneous variance $\sigma^2_{\varepsilon_{ij}} = \exp(w_{ij}^T\tau + g_i\tau_g +\omega_i)$

Given a longitudinal biomarker of interest, the primary goal is to test

  1. the mean effect of genotype, $H_0:\beta_g = 0$, i.e., whether a genotype shifts the mean of the biomarker trajectory
  2. the WS variance effect of genotype, $H_0:\tau_g = 0$, i.e., whether a genotype changes the WS variation of the biomarker trajectory around its mean
  3. the joint effect, $H_0: \beta_g = \tau_g = 0$, i.e., whether a genotype affects either the mean, or the WS variation, or both.

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