Multiple Imputation of Missing Data in Multilevel Models

Abstract

Missing data and its occurrence in statistical analysis has plagued medical and public health researchers for decades. The last few years has seen statisticians and methodologists across the world unite and come together to develop and improve the tools and approaches used in this fight against missing data. This has been made possible due to the increase in implementation of multiple imputation in statistical software, and a stronger push against rudimentary approaches like complete case analysis and single imputation methods. Multiple Imputation (MI) has been in the literature since the 1980s. Despite this, we still observe a huge disparity between awareness and implementation of MI in research. Scientists are aware about the existence of MI, but are hesitant to employ it in practice.

MI has been long recognized as an attractive approach to handle missing values. Despite its early conception and its numerous advantages over the traditional ad hoc methods, there is still limited application of MI in public health research. Multiple imputation methods can be broadly categorized into two: Joint modelling (JoMo) and Multiple Imputation using Chained Equations (MICE). MICE imputes missing data sequentially from a series of univariate distributions while JoMo draws imputations for missing data simultaneously from a multivariate distribution. While these methods have been extensively studied in single level (and some two level contexts), there is limited knowledge about the performance of these methods to handle missing values in more than two levels.

The theory of multiple imputation requires the sampling design be incorporated in the imputation process. Not accounting for complex sample design features, such as stratification and clustering, during imputations can yield biased estimates from a design-based perspective. Most datasets in public health research show some form of natural clustering (individuals within households, households within the same district, patients within wards, etc.). Cluster effects are often of interest in health research. These data structures are commonly observed in medical and health settings where individuals are clustered within households, health care providers and so on. Missing values can occur at any level in multilevel data, but guidance on multiple imputation in data with more than two levels is currently an open research question.

This thesis implements and extends the Gelman and Hill approach for imputation of missing data at higher levels by including aggregate forms of individual-level measurements to impute for missing values at higher levels. We demonstrate how we can implement this extension in MICE and JoMo to impute for missing values in the three level data structures and produce better estimates than ad hoc approaches, when varying proportions of missing values occur together across all levels in the dataset. In this thesis, we also demonstrate how the performance of extensions of MI to handle missingness in three level datasets, varies with the number of clusters at each level in the dataset. This is verified by using simulation studies as a proof of concept. The analytic work and simulations in this thesis results in several practical recommendations to medical and health researchers.

Finally, my thesis highlights the strengths and limitations of multiple imputation for variables in datasets with more than two levels. The results from the simulation study led to real world clinical and health examples to further illustrate its application. The illustrative examples demonstrate the impact of accounting for data structure in analysis, constructing rich imputation models for clinical laboratory data, and the effect of MI in developing health profiles using national surveys. Show more