The identification of factors underlying complex trait variation is a major goal in the field of genetics. For normally distributed, fully observed trait data there are many well established statistical methods for partitioning phenotypic variation and for mapping quantitative trait loci (QTL). Survival or time-to-event traits often follow non-normal distributions and frequently contain partially-known (or censored) trait data. If standard statistical methods are used to analyse age at onset data a bias can be introduced through a failure to account for the non-normal distribution of the data and the presence of censoring. Complex statistical methods have been developed to partition trait variation and map QTL for age at onset or survival traits. In this thesis, the use of these survival analysis methods is compared to more established statistical methods for the analysis of age-at-onset data. A brief introduction to the analysis of human variation and the issues associated with the analysis of age at onset data is given. The methods currently used to partition trait variation and map QTL for survival traits are discussed (Chapter 1). Age-specific penetrances can be used to model the age-at-onset of disease in unaffected individuals. This parametric method is used to identify loci underlying susceptibility to a novel co-morbid psychiatric phenotype (depression and unexplained swelling). The method is compared to a non-parametric variance component (VC) QTL mapping method that does not account for the age at onset of the disease. Parametric linkage analysis identified two suggestive loci, neither of which were supported by the standard variance component analysis. VC analysis identified a suggestive linkage region on chromosome 14 which decreased upon fine mapping (Chapter 2). Many of the current methods used to analyse survival data in human genetics are based on methods originally derived by animal geneticists. The analysis of survival traits in some experimental populations is simplified by the presence of fully inbred lines. However, for complex traits the methods are both computationally intensive and not widely available. A grouped linear regression method is proposed for the analysis of continuous survival data in fully inbred lines. Using simulation the method is compared to both the Cox and Weibull proportional hazards models and a standard linear regression method that ignores censoring. The grouped linear regression method is of equivalent power to both the Cox and Weibull proportional hazards methods, is significantly better than the standard linear regression method when censored observations are present and is computationally simple (Chapter 3). A sample of 446 monozygotic (MZ) twins, 633 dizygotic (DZ) twins and 223 siblings was used to partition the inter-individual variance in age at menarche. The analysis was carried out using both a standard method which failed to account for the censored nature of the data and a mixed effects Cox model which fits a frailty model to the random effects. The standard methodology suggested that an additive genetic model best described the data. The most parsimonious model when using the frailty method included additive genetic and common environmental effects (ACE). The difference between the two models was caused by the different ascertainment of the siblings. The frailty model estimated the heritability of age at menarche to be 0.57 (Chapter 4). In Chapter 5, a sample of 2,685 pseudo-independent sib-pairs is used in a genomewide linkage scan for QTL underlying variation in age-at-menarche. The sample comprises of the adolescent sample discussed in chapter 4, and three adult cohorts. The proportion of censoring in the sample is 1.20% so a standard QTL mapping method is used. Two QTL of suggestive significance are identified on chromosomes 11p and 3p. The candidate genes WT1 and FSHB are located within the linkage peak on 11p. After the removal of bivariate outliers a locus on chromosome 12q was identified. No significant QTL were detected which suggests age-at-menarche is influenced by multiple genes of small effect. The thesis concludes with a general discussion (Chapter 6).