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Abstract:
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An important phenomenon in high dimensional biological data is the presence of latent covariates that can have a significant impact on the measured response. When these factors are also correlated with the covariate(s) of interest (i.e. disease status), ignoring them can lead to increased type I error and spurious false discovery rate estimates. We show that depending on the strength of this correlation and the informativeness of the observed data for the latent factors, previously proposed estimators for the effect of the covariate of interest that attempt to account for unobserved covariates are asymptotically biased, which corroborates previous practitioners' observations that these estimators tend to produce inflated test statistics. We then provide an estimator that corrects the bias and prove it has the same asymptotic distribution as the ordinary least squares estimator when every covariate is observed. Lastly, we use previously published lung DNA methylation data to show our method can more accurately estimate the direct effect of asthma on methylation than previously published methods, which underestimate the correlation between asthma and latent cell type heterogeneity.
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