A simple pooling method for variable selection in multiply imputed datasets outperformed complex methods

For the development of prognostic models, after multiple imputation, variable selection is advised to be applied from the pooled model. The aim of this study is to evaluate by using a simulation study and practical data example the performance of four different pooling methods for variable selection in multiple imputed datasets. These methods are the D1, D2, D3 and recently extended Median-P-Rule (MPR) for categorical, dichotomous, and continuous variables in logistic regression models.

Four datasets (n = 200 and n = 500), with 9 variables and correlations of respectively 0.2 and 0.6 between these variables, were simulated. These datasets included 2 categorical and 2 continuous variables with 20% missing at random data. Multiple Imputation (m = 5) was applied, and the four methods were compared with selection from the full model (without missing data). The same analyzes were repeated in five multiply imputed real-world datasets (NHANES) (m = 5, p = 0.05, N = 250/300/400/500/1000).

In the simulated datasets, the differences between the pooling methods were most evident in the smaller datasets. The MPR performed equal to all other pooling methods for the selection frequency, as well as for the P-values of the continuous and dichotomous variables, however the MPR performed consistently better for pooling and selecting categorical variables in multiply imputed datasets and also regarding the stability of the selected prognostic models. Analyzes in the NHANES-dataset showed that all methods mostly selected the same models. Compared to each other however, the D2-method seemed to be the least sensitive and the MPR the most sensitive, most simple, and easy method to apply.

Considering that MPR is the most simple and easy pooling method to use for epidemiologists and applied researchers, we carefully recommend using the MPR-method to pool categorical variables with more than two levels after Multiple Imputation in combination with Backward Selection-procedures (BWS). Because MPR never performed worse than the other methods in continuous and dichotomous variables we also advice to use MPR in these types of variables.