Strategies for improving statistical power

We propose several strategies to further improve statistical power of longitudinal trait analysis, summarized as follows:

Strategies	Longitudinal mean	WS variability	Longitudinal trand
Rank-based inverse normal transformation	No impact	More powerful	No impact
Change correlation structure	Sometimes more powerful	Not evaluate	Not evaluate
Polygenic score (PGS) adjustment	More powerful	No impact	No impact

Rank-based inverse normal transformation

Model residuals from fitted null model can be highly unbalanced, especially when testing within-subject (WS) variability. In this context, we find that using a rank-based inverse normal transformation (INT) for model residuals can greatly improve empirical power. We propose SPA_GRM(INT) in which inverse normal transformed model residuals are taken as input, and SPA_GRM(CCT) in which p values from SPA_GRM and SPA_GRM(INT) are combined via Cauchy combination test (CCT).

Prepare model residuals for SPA_GRM(INT)

library(RNOmni)
ResidMatFile = system.file("extdata", "ResidMat.txt", package = "GRAB")
ResidMat = data.table::fread(ResidMatFile)
summary(ResidMat$Resid)
#     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
# -2.36875 -0.48665 -0.01213  0.00000  0.47614  2.57954

ResidMat$Resid = RankNorm(ResidMat$Resid)
data.table::fwrite(ResidMat, file = ResidMatFile, row.names = FALSE, col.names = TRUE) # Then we can pass this file as the input of SPAGRM
summary(ResidMat$Resid)
#    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
# -3.2273 -0.6735  0.0000  0.0000  0.6735  3.2273 

Change correlation structure

Repeated measurements within each subject can be correlated. Linear mixed effect models consider the correlation via the random effect (and random slope), while generalized estimation equations require pre-defined working correlation metrics (e.g, exchangeable and autoregressive working correlation structures). We find that these two methods are rubost against correlation structure missicification (i.e., well controlled type I error rates), while empirical power varies depending on the data generating mechanism. Since no methods are omnibus, indicating that different longitudinal traits could correspond to different architectures. We propose SPA_GRM(CCT) that combines p values from SPA_GRM using various working correlation structures. For preparing model residuals of GEE model with various correlation structures, user can refer to Generalized estimation equations. To combine p values via CCT, user can refer to ACAT.

Polygenic score (PGS) adjustment

Recent reports have shown that adjusting for PGSs can account for polygenic effects and increase statistical power. Similarly, SPA_GRM can further gain statistical power through incorporating polygenic scores (PGSs) as covariates with fixed effects. We employ this idea to implement a two-stage strategy, SPAGRM-PGS:

• In stage 1, we conduct the first round of GWAS via SPAGRM and then calculate the Leave One Chromosome Out (LOCO)-PGS based on the summary statistics.
• In stage 2, the LOCO-PGS is included as an additional covariate for a second round of GWAS via SPAGRM.

This is a general strategy, and currently, we do not possess a function that can directly execute this functionality. In SPA_GRM reproducibility, we displayed how to construct LOCO-PGSs via the clumping and thresholding (C+T) method based on summary statistics of SPA_GRM. We plan to add a function to approximate marginal genetic effects to facilitate PGS construction.