Robust model-based estimation for binary outcomes in genomics studies

In quantitative genetics, statistical modeling techniques are used to facilitate advances in the understanding of which genes underlie agronomically important traits and have enabled the use of genome-wide markers to accelerate genetic gain. The logistic regression model is a statistically optimal approach for quantitative genetics analysis of binary traits. To encourage more widespread use of the logistic model in such analyses, efforts need to be made to address separation, which occurs whenever a specific combination of predictors can perfectly predict the value of a binary trait. Data separation is especially prevalent in applications where the number of predictors is near the sample size. In this study we motivate a logistic model that is robust to separation, and we develop a novel prediction procedure for this robust model that is appropriate when separation exists. We show that this robust model offers superior inferences and comparable predictions to existing approaches while remaining true to the logistic model. This is an improvement to previously existing approaches which treats separation as a modeling shortcoming and not an antagonistic data configuration. Previous approaches, therefore, change the modeling paradigm to consider separation that, before our robust model exists, is problematic to logistic models. Our comparisons are conducted on several didactic examples and a genomics study on the kernel color in maize. The ensuing analyses reaffirm the billed superior inferences and comparable predictive performance of our robust model. Therefore, our approach provides scientists with an appropriate statistical modeling framework for analyses involving agronomically important binary traits.