Development and application of methods in parametric survival models: interval censoring, inverse probability weighting and multistate survival models

Although semi- and non-parametric approaches are frequently used to analyse survival data, there are advantages to using parametric survival models. This thesis develops and applies methods in parametric models to address, or investigate the impact of, issues that arise in survival data. Specifically, the thesis focuses on three key topics: interval censoring, inverse probability (IP) weighting and multistate models. Data are interval-censored if the event is only known to occur within an interval. Often a single time (beginning, midpoint or end of the interval) is imputed and standard methods for right-censored data are employed. The impact of this naive imputation on interval-censored data is explored in a literature review and simulation study. As with all projects, the methods are demonstrated on an example dataset. IP weighting can be used to estimate causal effects in the presence of confounding. Two types of weights, stabilised and unstabilised, can be employed and can result in different estimates when used in an IP weighted analysis on survival data. A simulation study was performed to confirm that both weighs result in an unbiased estimator. A novel, closed-form variance estimator was then proposed for IP weighted parametric models, using M-estimation to account for the uncertainty in the weight estimation. The novel estimator was validated in a simulation study and can be used an alternative to bootstrapping in large samples, especially when reproducibility or computational time are key concerns. User-friendly software was developed and made freely available. Disease pathways may consistent of multiple stages and warrant the use of multistate models. While modelling the transitions is straightforward, obtaining the predictions can be complex. Predictions were obtained for hospital acquired infection data from a flexible multistate model using a recently proposed, general simulation algorithm. Non-parametric estimates can serve as a reference and software was developed to facilitate this.