Sickness-absence (SA) is a serious financial burden to UK industry totalling £10-12 billion in 1999 the equivalent of £434 and 7.8 days lost per worker. A major change in the reporting of SA occurred on 14 June 1982 with the introduction of self certification. Up to then all episodes had to be certified by a general practitioner. Since then, events that lasted for seven calendar or less have not required a GP's certificate and are 'self-certified'. A SA episode consists of the date the individual went off sick, the duration of the episode and a medical diagnosis given by either a GP or self diagnosis. A common approach to the analysis of SA data is to model the number of times an individual went off sick during a period of follow up via Poisson regression. Some studies on SA have examined the duration of SA, though most concentrated on the probability of going off sick. This thesis uses an intensity based approach to model the joint probability that a person goes off sick with a specific disease and has a specific duration of absence (the 'joint analysis'). A Bayesian hierarchical model, based on the conditional proportional hazards model, is formulated for the joint analysis and sampled using Markov chain Monte Carlo methods. Posterior expectations and 90% credible intervals are presented as summaries of the marginal posterior distributions of the parameters of the joint analysis. Trace plots of the log-joint posterior distribution are given to assess convergence of the MCMC sampler.