Mr Joseph Descallar

The estimation of cause-specific hazards with partly-interval censored data

Cause-specific hazards are widely used when analysing time-to-event competing risks outcomes. Partial likelihood methods such as Cox regression is a standard approach when data contain right censoring only. When interval censored data arise, such as in events that occur between follow up appointments (e.g. cancer recurrence or progression), these methods are not directly applicable. In practice, time to a single point (medical appointment date) is analysed with the partial likelihood method applied. These can result in bias coefficient estimates and under-estimation of variance. Additionally, since the baseline hazard is not estimated with Cox regression, prediction is not optimal. Estimation of CSH for interval-censored competing risks and with full likelihood estimation require extended computation times, have limited functionality, or rely on optimisers that often result in convergence issues.

Maximum penalized likelihood (MPL) algorithms have been applied to Cox regression for single event outcomes. This involves the estimation of risk coefficients, baseline hazard, and variance. Implementation of the MPL in a competing risk with interval-censored outcomes requires numerical integration which are computationally demanding. This project aims to develop fast computational methods for parameter estimation of CSH with partly-interval censoring using the MPL algorithm. Extensions to accommodate cure fractions and time-varying covariates will also be implemented.