High-dimensional, outcome-dependent missing data problems: models for the human KIR loci

Abstract

Missing data problems are common in biological, high-dimensional data, where data can be completely missing or ambiguous, i.e. partially missing. Algorithms have been developed to reconstruct the missing values by means of imputation or expectation-maximization (EM-)algorithms. For missing data problems, it has been suggested that the regression model of interest, i.e. the substantive model, should be incorporated into the imputation procedure to reduce bias of the regression coefficients and increase model efficiency.

We here consider a challenging missing data problem, where diplotypes of the KIR loci are to be reconstructed. These loci are difficult to genotype, resulting in ambiguous genotype calls; in addition they contain copy-number-variation. We extend a previously proposed EM-algorithm by incorporating a potentially high-dimensional regression model to model the outcome. Three strategies are evaluated: 1) only use allelic predictors, 2) use the same allelic predictors and forward-backward selection on haplotype predictors 3) use penalized regression on a saturated model with an elastic-net penalty.

In a simulation study, we compared these strategies with a baseline EM-algorithm without an outcome model with respect to haplotype reconstruction precision and regression coefficient estimation for these haplotypes. For extreme choices of effect sizes, ambiguity levels and correlation structure, the outcome-based EM-algorithms outperformed the no-outcome EM-algorithm. However, in all other cases the no-outcome EM-algorithm performed either superior or comparable to the three strategies, suggesting the outcome model can have a harmful effect. In a data analysis concerning death after allogeneic hematopoietic stem cell transplantation as a function of donor KIR genes, EM-algorithms with and without outcome showed very similar results. In conclusion, outcome based missing data models in the high-dimensional setting have to be used with care and are likely to lead to biased results.