Robust Score Tests With Missing Data in Genomics Studies

Abstract

Analysis of genomic data is often complicated by the presence of missing values, which may arise due to cost or other reasons. The prevailing approach of single imputation is generally invalid if the imputation model is misspecified. In this paper, we propose a robust score statistic based on imputed data for testing the association between a phenotype and a genomic variable with (partially) missing values. We fit a semiparametric regression model for the genomic variable against an arbitrary function of the linear predictor in the phenotype model and impute each missing value by its estimated posterior expectation. We show that the score statistic with such imputed values is asymptotically unbiased under general missing-data mechanisms, even when the imputation model is misspecified. We develop a spline-based method to estimate the semiparametric imputation model and derive the asymptotic distribution of the corresponding score statistic with a consistent variance estimator using sieve approximation theory and empirical process theory. The proposed test is computationally feasible regardless of the number of independent variables in the imputation model. We demonstrate the advantages of the proposed method over existing methods through extensive simulation studies and provide an application to a major cancer genomics study.

Keywords: Association tests; Imputation; Integrative analysis; Multiple genomics platforms; Semiparametric models; Sieve estimation.

Figure 1.

Rejection Probabilities for the Continuous Phenotype Under the Null and Alternative Hypotheses for Mechanisms 1 and 2.

Figure 2.

Quantile-Quantile Plots for the RNA-Seq Analysis of the TCGA Ovarian Cancer Data. The left plot shows the results for the original data, and the right plot shows the results with the missing proportion increcased to 60%. The p-values are truncated at 10⁻¹⁰.