Project overview
In survival studies, usually some of the observations are censored. That means the event of interest, e.g. the death of a patient, is not observed. There can be many different reasons for censoring. For example, the study may end before all patients have died. In some situations, the fact an observation was censored may in itself provide further information about the potential survival times. Consider for example the waiting list for an organ transplant. If a donor organ becomes available, usually the sickest eligible patient on the list will be prioritised for transplantation. Hence knowing an observation was censored due to transplantation tells us that this patient - if he had remained on the waiting list - would have been more likely to die within a short period of time than the average patient on the list. Ignoring this extra information when analysing the data may lead to incorrect conclusions. For example, survival probabilities for patients on the waiting list may be seriously overestimated since the sickest patients have been removed from the waiting list for transplantation. Similarly, since many of the patients receiving a transplant are already very ill, they are still at a high risk of dying shortly after the operation. This may lead to the incorrect conclusion that patients on the waiting list survive longer, on average, than patients receiving a transplant. It is therefore vital to take informative censoring into account accordingly when analysing the data. There is no statistical test, which could detect informative censoring in a data set. However, there is a statistical tool called sensitivity analysis, which gives an idea of the effects of informative censoring on the data analysis. If the sensitivity analysis shows these effects to be negligible, a standard analysis can be done with no detriment. If, however, the sensitivity analysis flags up a problem, then several different, sophisticated methods need to be applied to the data, in order to draw valid conclusions. The existing sensitivity analyses have several drawbacks. They are either reasonably easy to apply and to interpret, but may not always flag up problems with informative censoring, since they are based on models that are too simple to be realistic. On the other hand, more sophisticated sensitivity analyses are difficult to apply, and thus practitioners do not use them on a large scale. Moreover, there is no clear guidance as to which sensitivity analysis should be used in a specific situation, and how it can be done, so often informative censoring is ignored in practice. This is where our research comes in. Our aim is to provide a sensitivity analysis, which is as realistic as necessary to assess the impact of informative censoring, while still retaining computational simplicity. This includes a general investigation into how complex a model needs to be in order to result in a powerful sensitivity analysis for a broad range of realistic scenarios. This in itself contains many interesting and challenging statistical problems, but our main motivation to pursue this research stems from the potential impact it can have on medical research. We want to encourage practitioners to use sensitivity analyses, and thus prevent them from drawing the wrong conclusions from their data due to informative censoring. In particular, we will: (a) Assess our modelling approach, and compare different models within and outside this class, using real data from NHS Blood and Transplant (NHSBT) and the Renal Registry, and extensive simulations in order to investigate the necessary complexity of the models; (b) Provide a computer package incorporating our results, which is easy and convenient to use by practitioners. Informative censoring on waiting lists is a special case of problems known as competing risks. After developing our methods to address this issue, we will extend them to tackle this more general problem.