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Copy number variation (CNV) has been acknowledged as an important contributor to variation in the human genome, and copy-variable regions harbouring genes are interesting subjects of research for their potential phenotypic effects. However, despite the extensive and continuing discovery of CNVs, multiallelic loci remain technically challenging to measure and study. In this thesis, a PCR-based measurement system for the tandemly repeated CNV that harbours the DEFA1A3 locus has been developed. This locus can either have the DEFA1 or the DEFA3 gene in any given copy of the repeat; the two genes differ by a single nucleotide difference in the coding sequence. This CNV has previously been shown to vary from 4 to 11 copies in a sample of the UK population. The use of this measuring system has allowed a usefully accurate measure and some characterization of this CNV in Europeans, Asians (Chinese and Japanese) and African (Ibadan, Nigeria) samples from the HapMap project, agreeing with the previously found copy number range in Europeans and showing more variability in non-Europeans. Typing of three-generation CEPH families has allowed the inference of haplotype copy numbers from segregation analysis. Combining haplotype data for some CEPH HapMap samples that were part of these families with their SNP genotypes in the same LD block has shown copy number lineages that are surprisingly well-tagged by SNPs. SNP rs4300027 allows the division of copy number haplotypes into low (2 and 3-copy) and high (4 and 5-copy) groups in European HapMap samples, a result that has been corroborated in an independent set of European samples. The Asian and African HapMap samples have failed to show this particular association. However, Japanese samples show copy number lineages tagged by other SNPs, an association not observed in other populations. In the second part of the study, an attempt has been made to explore the phenotypic effects of this variable locus. Copy number-tagging SNPs have been used to investigate published GWAS for indirect signals of association with DEFA1A3 copy number. Preliminary experiments for studying protein expression levels of DEFA1 and DEFA3 have been carried out and the possible role of this CNV as a modifier locus in Cystic Fibrosis disease severity has been investigated through direct typing of CF samples with clinical data, and indirectly through interrogating a CF GWAS.

Finally, two main extensions of this approach were considered - linkage approaches to examine more than two loci, and extending the method in this study to include a test of association.

The study of social network dynamics has become an increasingly important component of many disciplines in the social sciences. In the past decade, statistical models and methods have been proposed which permit researchers to draw statistical inference on these dynamics. This thesis builds on one such family of models, the stochastic actor oriented model (SAOM) proposed by Snijders [2001]. Goodness of fit for SAOMs is an area that is only just beginning to be filled in with appropriate methods. This thesis proposes a Mahalanobis distance based, Monte Carlo goodness of fit test that can depend on arbitrary features of the observed network data and covariates. As remediating poor fit can be a difficult process, a modified model distance (MMD) estimator is devised that can help researchers to choose among a set of model elaborations. In practice, panel data is typically used to draw SAOM-based inference. This thesis also proposes a score-type test for time heterogeneity between the waves in the panel that is computationally cheap and fits into a convenient, forward model selecting workflow. Next, this thesis proposes a rigorous method for aggregating so-called relational event data (e.g. emails and phone calls) by extending the SAOM family to a family of hidden Markov models that suppose a latent social network is driving the observed relational events. Finally, this thesis proposes a measurement model for SAOMs inspired by error-in-variables (EiV) models employed in an array of disciplines. Like the relational event aggregation model, the measurement model is a hidden Markov model extension to the SAOM family. These models allow the researcher to specify the form of the mesurement error and buffer against potential attenuating biases and other problems that can arise if the errors are ignored.