Post-prediction inference

Many modern problems in medicine and public health leverage machine learning methods to predict outcomes based on observable covariates [1, 2, 3, 4]. In an increasingly wide array of settings, these predicted outcomes are used in subsequent statistical analysis, often without accounting for the distinction between observed and predicted outcomes [1, 5, 6, 7, 8, 9]. We call inference with predicted outcomes post-prediction inference. In this paper, we develop methods for correcting statistical inference using outcomes predicted with an arbitrary machine learning method. Rather than trying to derive the correction from the first principles for each machine learning tool, we make the observation that there is typically a low-dimensional and easily modeled representation of the relationship between the observed and predicted outcomes. We build an approach for the post-prediction inference that naturally fits into the standard machine learning framework where the data is divided into training, testing, and validation sets. We train the prediction model in the training set, estimate the relationship between the observed and predicted outcomes on the testing set, and use that model of the relationship to correct inference on the validation set and subsequent statistical models. We show our postpi approach can correct bias and improve variance estimation (and thus subsequent statistical inference) with predicted outcome data. To show the broad range of applicability of our approach, we show postpi can improve inference in two totally distinct fields: modeling predicted phenotypes in re-purposed gene expression data [10] and modeling predicted causes of death in verbal autopsy data [11]. We have made our method available through an open-source R package: [https://github.com/leekgroup/postpi]