Methods for handling missing variables in risk prediction models

Abstract

Prediction models should be externally validated before being used in clinical practice. Many published prediction models have never been validated. Uncollected predictor variables in otherwise suitable validation cohorts are the main factor precluding external validation. We used individual patient data from 9 different cohort studies conducted in the United States, Europe, and Latin America that included 7,892 patients with chronic obstructive pulmonary disease who enrolled between 1981 and 2006. Data on 3-year mortality and the predictors of age, dyspnea, and airflow obstruction were available. We simulated missing data by omitting the predictor dyspnea cohort-wide, and we present 6 methods for handling the missing variable. We assessed model performance with regard to discriminative ability and calibration and by using 2 vignette scenarios. We showed that the use of any imputation method outperforms the omission of the cohort from the validation, which is a commonly used approach. Compared with using the full data set without the missing variable (benchmark), multiple imputation with fixed or random intercepts for cohorts was the best approach to impute the systematically missing predictor. Findings of this study may facilitate the use of cohort studies that do not include all predictors and pave the way for more widespread external validation of prediction models even if 1 or more predictors of the model are systematically missing.