Transcriptome-wide association study (TWAS) has become popular in integrating a reference eQTL dataset with an independent main GWAS dataset to identify (putatively) causal genes, shedding mechanistic insights to biological pathways from genetic variants to a GWAS trait mediated by gene expression. Statistically TWAS is a (two-sample) 2- stage least squares (2SLS) method in the framework of instrumental variables analysis for causal inference: in Stage 1 it uses the reference eQTL data to impute a gene's expression for the main GWAS data, then in Stage 2 it tests for association between the imputed gene expression and the GWAS trait; if an association is detected in Stage 2, a (putatively) causal relationship between the gene and the GWAS trait is claimed. If a non-linear model or a generalized linear model (GLM) is fitted in Stage 2 (e.g. for a binary GWAS trait), it is known that using only imputed gene expression, as in standard TWAS, in general does not lead to a consistent (i.e. asymptotically unbiased) estimate for the causal effect; accordingly, a variation of 2SLS, called two-stage residual inclusion (2SRI), has been proposed to yield better estimates (e.g. being consistent under suitable conditions). Our main goal is to investigate whether it is necessary or even better to apply 2SRI, instead of the standard 2SLS. In addition, due to the use of imputed gene expression (i.e. with measurement errors), it is known that in general some correction to the standard error estimate of the causal effect estimate has to be applied, while in the standard TWAS no correction is applied. Is this an issue? We also compare one-sample 2SLS with two-sample 2SLS (i.e. the standard TWAS). We used the ADNI data and simulated data mimicking the ADNI data to address the above questions. At the end, we conclude that, in practice with the large sample sizes and small effect sizes of genetic variants, the standard TWAS performs well and is recommended.
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