Theory and applications of delayed censoring models in survival analysis
The objective of this thesis is to develop new statistical models for the analysis of censored survival data, particularly for the study of recidivism data, such as the reoffence data used in the analysis here. This has been an area of great interest in criminology in recent years. There is a growing literature on survival analysis in criminology, where interest centres on the time from an offender's conviction, or release from prison, to the first reconviction or reimprisonment. In deciding whether to release a prisoner on parole, the Parole Board is provided with a statistical score which estimates the chance that the prisoner will reoffend within the period of time that he or she would otherwise be in prison. This score is based on a survival analysis of data on a sample of releases from long-term prison sentences. To capture most reoffences which occur within 2 years of release, follow-up must continue for at least 3 years to allow for the delay between offence and conviction. We reanalyse the data by using a model which explicitly allows for this delay. We refer to this as 'delayed censoring model'. The new analysis can be applied to data with a substantially shorter length of follow-up. This means that risk scores can be constructed from more up-to-date data and at less cost. It is models of this kind that we shall be concerned with in this thesis, and this is the principal motivation of the work done. The statistical models that this thesis provides bring in a number of new ideas which are undoubtedly useful both at a theoretical level and in applications. Other major divisions of the work include: (i) Assessing the possibility of an association between the delay and reoffence times by studying truncated distributions fitted to these data, by parametric, semi-parametric and nonparametric models. With the nonparametric approach we have developed a 'backward regression model' which is similar to the Cox model. (ii) We have also discussed delayed censoring modification to the Cox model, and developed a more general semi-parametric model for all the data including both observed and censored cases. In this model the delay and reoffence times are allowed to be correlated. We refer to this as the 'generalized weighted hazards model'. (iii) Finally, we have compared the results by applying all these models to the data. Although the parametric models give a good fit to the data, the semi-parametric and nonparametric models give a slightly better fit, as expected.