Variable selection with multiply-imputed datasets: choosing between stacked and grouped methods

Abstract

Penalized regression methods, such as lasso and elastic net, are used in many biomedical applications when simultaneous regression coefficient estimation and variable selection is desired. However, missing data complicates the implementation of these methods, particularly when missingness is handled using multiple imputation. Applying a variable selection algorithm on each imputed dataset will likely lead to different sets of selected predictors, making it difficult to ascertain a final active set without resorting to ad hoc combination rules.In this paper we consider a general class of penalized objective functions which, by construction, force selection of the same variables across multiplyimputed datasets. By pooling objective functions across imputations, optimization is then performed jointly over all imputed datasets rather than separately for each dataset. We consider two objective function formulations that exist in the literature, which we will refer to as "stacked" and "grouped" objective functions. Building on existing work, we (a) derive and implement efficient cyclic coordinate descent and majorization-minimization optimization algorithms for both continuous and binary outcome data, (b) incorporate adaptive shrinkage penalties, (c) compare these methods through simulation, and (d) develop an R package miselect for easy implementation. Simulations demonstrate that the "stacked" objective function approaches tend to be more computationally efficient and have better estimation and selection properties. We apply these methods to data from the University of Michigan ALS Patients Repository (UMAPR) which aims to identify the association between persistent organic pollutants and ALS risk.

Psychotic relapse in people with schizophrenia within 12 months of discharge from acute inpatient care: protocol for development and validation of a prediction model based on a retrospective cohort study in three psychiatric hospitals in Japan

“…We will assess this flexible model in our sensitivity analysis. To avoid overfitting, we will employ the elastic net for a penalized estimation of regression coefficients [28,29]. The elastic net allows both selection and penalization of main effects by introducing two tuning parameters.…”

Variable Selection for Multiply-imputed Data: A Bayesian Framework

“…Although various models were proposed to solve the inconsistency of variable selection in MI settings, it was the first time that MI-LASSO [17] introduced the Group-LASSO [24] penalty into this problem. Different from stacking methods [10,11,15] which"stacks" multiply-imputed data as a single dataset and applies weighted models to select important variables, MI-LASSO treats the same variable across all imputed sets as a group of variables, and adopts Group-LASSO to jointly include or exclude the group of variables together. To make it clear, the mathematical loss function for Group-LASSO is:…”

“…Therefore information based criterion was used to select x % credible interval for shrinkage Bayesian MI-LASSO and evaluated performances. We took advantages of the modified version of Bayesian Information Criterion (BIC, referring to formula (10) and ( 11)) to assess different selection of credible interval. Also, this modified BIC was used to evaluate the five Bayesian MI-LASSO models on data.…”

“…However, this may have inadequate performance, because different sets of significant variables can be possibly selected for each imputed set, which leads to inconsistency of variable selection across all imputed datasets. In literature, various solutions [10][11][12][13][14][15][16][17] have been proposed to solve this problem. MI-LASSO, proposed by Chen and Wang [17] and acknowledged successful in application [18][19][20][21], provides a flexible method to select the same important variables jointly among all imputed datasets.…”