Optimal design of experiments for MNAR data

Abstract

The presence of missing data leads to biases in data analyses. To overcome these biases, it is crucial to understand the type of missing data that is present in the data. Amongst the three types of missing data (known as missing data mechanisms) that will be formally introduced in this thesis, the Missing Not At Random (MNAR) mechanism is the most complex. MNAR poses the most difficulties as it is an untestable assumption based on the current incomplete data. A recovery of some of the missing data is required to test its presence. In this research, we developed two statistical tests for testing the presence of MNAR in datasets and provide the theoretical framework of the tests. In the first test, the recovery design consists of a random sampling of the responses whose covariates lie within a particular region while the second test is based on an assignment of probabilities. We introduced techniques from Design of Experiments to improve the properties of these tests. The developed tests are compared with a random follow-up of missing responses, which will act as our benchmark design throughout. We formulate an easy and simple conjecture that uses the empirical density of the covariates to obtain the recovery region. Through simulations, the performance of the
tests is evaluated.

Keywords: Missing data; Missing not at random; Selection model; Recovery region;
Conjecture.

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Identifiers

ORCID for Antony Overstall: orcid.org/0000-0003-0638-8635

ORCID for Dankmar Böhning: orcid.org/0000-0003-0638-7106

ORCID for Stefanie Biedermann: orcid.org/0000-0001-8900-8268

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