A multiple-phenotype imputation method for genetic studies

Abstract

Genetic association studies have yielded a wealth of biological discoveries. However, these studies have mostly analyzed one trait and one SNP at a time, thus failing to capture the underlying complexity of the data sets. Joint genotype-phenotype analyses of complex, high-dimensional data sets represent an important way to move beyond simple genome-wide association studies (GWAS) with great potential. The move to high-dimensional phenotypes will raise many new statistical problems. Here we address the central issue of missing phenotypes in studies with any level of relatedness between samples. We propose a multiple-phenotype mixed model and use a computationally efficient variational Bayesian algorithm to fit the model. On a variety of simulated and real data sets from a range of organisms and trait types, we show that our method outperforms existing state-of-the-art methods from the statistics and machine learning literature and can boost signals of association.

Figure 1. Simulation results

Model 1 – scenario simulated using an empirical kinship matrix derived from the human NSPHS study. Model 2 – scenario simulated using 75 families of 4 sibs. Datasets were simulated at various levels of heritability (x-axis) for the traits. 300 individuals at 15 traits were simulated. 5% of phenotype values were set as missing before imputation. 7 different methods (legend) were applied to impute the missing values. The correlation of the imputed values with the true values is plotted on the y-axis for each method. The lines for TRCMA, MVN and SOFTIMPUTE lie almost exactly on top of each other.

Figure 2. Imputation performance in real datasets

There is one plot for each of the six real datasets. The vertical dotted black line shows the true level of missingness in the dataset. Extra missingness was added to each dataset , and the x-axis shows the amount of missing data in these reduced datasets. The y-axis shows imputation correlation between the imputed missing data and the held out data. The legend denotes the different methods that were applied to the datasets. Not all methods were run on all datasets. TRCMA and MPMM were only run on the human NSPHS and wheat datasets for computational reasons.

Figure 3. Missing phenotype imputation in 140 rat GWAS

The x-axis and y-axis show the −log10(p) for the GWAS on the un-imputed and imputed phenotypes respectively. Each point corresponds to a region in both scans. The dashed black lines denote a conservative threshold of −log10(p)>10 that was applied to highlight associated regions (large points). Points in grey have imputation r²<0.36. Associations with platelet phenotypes on chr 9 and T cell phenotypes on chr 10 are highlighted with red and blue points respectively.

Figure 4. Platelet phenotype associations

GWAS results for un-imputed (blue points) and imputed phenotypes (red points) for three platelet phenotypes (MPC, MPV, PDW) measured in rats, on rat chromosome 9 (50-80Mb). Genes are shown below the plots, with some (named) genes with relevant annotation to platelet function, adhesion and aggregation highlighted in a separate track. Histograms on the right show the distribution of observed (cyan) and imputed (purple) phenotypes, together with missingness and r² metrics.

Figure 5. T cell phenotype associations

GWAS results for un-imputed (blue points) and imputed phenotypes (red points) for three T cell phenotypes (CD25highCD4, Abs_CD25CD8, pctDP) measured in rats, on rat chromosome 10 (83-89Mb). Genes are shown below the plots, with some (named) genes with relevant annotation to T cell phenotypes highlighted in a separate track. Histograms on the right show the distribution of observed (cyan) and imputed (purple) phenotypes, together with missingness and r² metrics.