Resampling-based inference methods for repeated measures data with missing values
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2022
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Abstract
The primary objective of this dissertation was to (i) develop novel resampling approaches
for handling repeated measures data with missing values, (ii) compare their
empirical power against other existing approaches using a Monte Carlo simulation
study, and (iii) pinpoint the limitations of some common approaches, particularly for
small sample sizes. This dissertation investigates four different statistical problems.
The first is semiparametric inference for comparing means of matched pairs with
missing data in both arms. Therein, we propose two novel randomization techniques;
a weighted combination test and a multiplication combination test. They are based
upon combining separate results of the permutation versions of the paired t-test and
Welch test for the completely observed pairs and the incompletely observed components,
respectively. As second problem, we consider the same setting but missingness
in one arm only. There, we investigate a Wald-type statistic (WTS), an ANOVA-type
statistic (ATS), and a modified ANOVA-type statistic (MATS). However, ATS and
MATS are not distribution free under the null hypothesis, and WTS suffers from
the slow convergence to its limiting 2 distribution. Thus, we develop asymptotic
model-based bootstrap versions of these tests. The third problem is on nonparametric
rank-based inference for matched pairs with incompleteness in both arms. In this
more general setup, the only requirement is that the marginal distributions are
not one point distributions. Therein, we propose novel multiplication combination
tests that can handle three different testing problems, including the nonparametric
Behrens-Fisher problem (Hp
0 : {p = 1/2}). Finally, the fourth problem is nonparametric
rank-based inference for incompletely observed factorial designs with repeated
measures. Therein, we develop a wild bootstrap approach combined with quadratic
form-type test statistics (WTS, ATS, and MATS). These rank-based methods can be
applied to both continuous and ordinal or ordered categorical data and (some) allow
for singular covariance matrices. In addition to theoretically proving the asymptotic
correctness of all the proposed procedures, extensive simulation studies demonstrate
their favorable small samples properties in comparison to classical parametric tests.
We also motivate and validate our approaches using real-life data examples from a
variety of fields.