Estimating prediction error for complex samples
This addresses the need for accurate error estimation in prediction models using complex sampling designs, which is incremental as it builds on existing methods.
The paper tackles the problem of estimating prediction error for models trained on non-representative samples by extending Efron's estimator to incorporate Horvitz-Thompson sampling weights, showing consistency for true generalization error and applying it to simulations and NHANES data.
With a growing interest in using non-representative samples to train prediction models for numerous outcomes it is necessary to account for the sampling design that gives rise to the data in order to assess the generalized predictive utility of a proposed prediction rule. After learning a prediction rule based on a non-uniform sample, it is of interest to estimate the rule's error rate when applied to unobserved members of the population. Efron (1986) proposed a general class of covariance penalty inflated prediction error estimators that assume the available training data are representative of the target population for which the prediction rule is to be applied. We extend Efron's estimator to the complex sample context by incorporating Horvitz-Thompson sampling weights and show that it is consistent for the true generalization error rate when applied to the underlying superpopulation. The resulting Horvitz-Thompson-Efron (HTE) estimator is equivalent to dAIC, a recent extension of AIC to survey sampling data, but is more widely applicable. The proposed methodology is assessed with simulations and is applied to models predicting renal function obtained from the large-scale NHANES survey.