Multiple imputation of covariates by fully conditional specification: accommodating the substantive model

TL;DR

This paper improves multiple imputation methods for missing covariate data, ensuring compatibility with complex substantive models like non-linear or interaction models, leading to more accurate statistical estimates.

Contribution

It introduces a modified fully conditional specification approach for MI that maintains compatibility with complex substantive models, including non-linear and interaction effects.

Findings

Simulation shows consistent estimates with the proposed method

Method performs well with non-linear and interaction models

Requires correctly specified and mutually compatible imputation models

Abstract

Missing covariate data commonly occur in epidemiological and clinical research, and are often dealt with using multiple imputation (MI). Imputation of partially observed covariates is complicated if the substantive model is non-linear (e.g. Cox proportional hazards model), or contains non-linear (e.g. squared) or interaction terms, and standard software implementations of MI may impute covariates from models that are incompatible with such substantive models. We show how imputation by fully conditional specification, a popular approach for performing MI, can be modified so that covariates are imputed from models which are compatible with the substantive model. We investigate through simulation the performance of this proposal, and compare it to existing approaches. Simulation results suggest our proposal gives consistent estimates for a range of common substantive models, including models which contain non-linear covariate effects or interactions, provided data are missing at random and the assumed imputation models are correctly specified and mutually compatible.