Statistical inference in variance components models for biomedical applications

Confidence intervals are an essential research topic in statistics. Based on confidence intervals we can draw conclusions about the uncertainty of the estimates. Confidence intervals are not simple to construct for complex functions, such as functions of variance components. Functions of variance components, like intraclass correlation coefficients (ICCs), are used in the biomedical area as measures of agreement, heritability, and heterogeneity. Agreement assesses the closeness in judgements among physicians on measurements. Heritability measures the variance contribution due to genetics in phenotype variance. Heterogeneity is mostly used in the context of meta-analysis, when variation between studies is of interest. These three measures played a dominant role in our research. Methods for the construction of confidence intervals for these complex functions of variance components and their performance on coverage probabilities were studied in non-trivial epidemiological applications. These applications consist of (1) an agreement study of radiologists measuring the volume of glands in the neck and head, (2) a meta-analysis of nonlinear dose-response models for the effect of antipsychotic medications on the occupancy of the dopamine in the brain, (3) a meta-analysis of test-negative case-control studies to estimate the influenza vaccine effectiveness, and (4) a three-generation family study (LifeLines) to investigate the effect of body mass index on mental and physical component scores, and determine the variance contributions due to heredity and shared environment. The latter study contributes to research in healthy ageing. This thesis also explores the causal inference for plant genetics. For all applications improved or new statistical methodology were developed