Multiple imputation in the presence of high-dimensional data

Abstract

Missing data are frequently encountered in biomedical, epidemiologic and social research. It is well known that a naive analysis without adequate handling of missing data may lead to bias and/or loss of efficiency. Partly due to its ease of use, multiple imputation has become increasingly popular in practice for handling missing data. However, it is unclear what is the best strategy to conduct multiple imputation in the presence of high-dimensional data. To answer this question, we investigate several approaches of using regularized regression and Bayesian lasso regression to impute missing values in the presence of high-dimensional data. We compare the performance of these methods through numerical studies, in which we also evaluate the impact of the dimension of the data, the size of the true active set for imputation, and the strength of correlation. Our numerical studies show that in the presence of high-dimensional data the standard multiple imputation approach performs poorly and the imputation approach using Bayesian lasso regression achieves, in most cases, better performance than the other imputation methods including the standard imputation approach using the correctly specified imputation model. Our results suggest that Bayesian lasso regression and its extensions are better suited for multiple imputation in the presence of high-dimensional data than the other regression methods.

Multiple Imputation for General Missing Data Patterns in the Presence of High-dimensional Data

“…Different penalty specifications give rise to various regularized regression methods. Zhao and Long (2013) 20 investigated the use of regularized regression for MI including lasso 21 , elastic net 22 (EN), and adaptive lasso 23 (Alasso). They also developed MI using a Bayesian lasso approach.…”

Variable selection in the presence of missing data: imputation‐based methods

“…Some recent work by Zhao and Long 49 and Deng et al 50 has investigated imputation methods in the presence of high-dimensional data, but methods in this area are largely under-developed and additional research is urgently needed.…”

Vitamin D and clinical symptoms in First Episode Psychosis (FEP): A prospective cohort study

“…Serum 25(OH)D level (ng/ml), ethnicity and gender were the only variables in the dataset that did not have any missing information. It has now been recognised that complete case analysis without adequate handling of missing data may lead to biased results, or reduced power and precision of estimates (Zhao and Long, 2016). We assumed that the missing variables were missing at random (MAR).…”

“…We imputed the missing values using multiple imputation by chained equations (MICE) (Deng et al, 2016). MICE has been shown to be a robust method for dealing with missing data across empirical and longitudinal studies (He et al, 2011;Zhao and Long, 2016). In the MICE procedure a series of regression models are run whereby each variable with missing data is modelled according to its distribution (Azur et al, 2011); for continuous variables, this would be a multivariable linear regression; and for binary variables, a logistic regression.…”