  This paper presents an alternative approach to p-values in regression
settings. This approach, whose origins can be traced to machine learning, is
based on the leave-one-out bootstrap for prediction error. In machine learning
this is called the out-of-bag (OOB) error. To obtain the OOB error for a model,
one draws a bootstrap sample and fits the model to the in-sample data. The
out-of-sample prediction error for the model is obtained by calculating the
prediction error for the model using the out-of-sample data. Repeating and
averaging yields the OOB error, which represents a robust cross-validated
estimate of the accuracy of the underlying model. By a simple modification to
the bootstrap data involving "noising up" a variable, the OOB method yields a
variable importance (VIMP) index, which directly measures how much a specific
variable contributes to the prediction precision of a model. VIMP provides a
scientifically interpretable measure of the effect size of a variable, we call
the "predictive effect size", that holds whether the researcher's model is
correct or not, unlike the p-value whose calculation is based on the assumed
correctness of the model. We also discuss a marginal VIMP index, also easily
calculated, which measures the marginal effect of a variable, or what we call
"the discovery effect". The OOB procedure can be applied to both parametric and
nonparametric regression models and requires only that the researcher can
repeatedly fit their model to bootstrap and modified bootstrap data. We
illustrate this approach on a survival data set involving patients with
systolic heart failure and to a simulated survival data set where the model is
incorrectly specified to illustrate its robustness to model misspecification.
