Statistical Sciences Research institute

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.

Our main objectives are to:
(I) Provide researchers in Medicine with new tools to get an intuition about the bias introduced in the estimates by ignoring the presence of informative censoring in survival data sets. This will prevent situations where informative censoring is ignored, which would lead to unreliable conclusions from the data.
(II) Develop the area of medical statistics further through new theory and applications.
To address these problems, we will develop a new class of sensitivity analyses, which is as realistic as necessary to assess the impact of informative censoring, while still retaining the advantages of a parametric model. This includes an investigation into how complex a model needs to be in order to yield a powerful and robust sensitivity analysis for a range of realistic scenarios.
(III) Complete the bigger picture within the competing risks framework.

Work Packages:
1) Derive the theoretical framework to approximate the sensitivity equations analytically, for different modelling approaches: model the baseline hazard as a polynomial spline; model the log-cumulative hazard as a polynomial spline; further parametric lifetime distributions, within and outside the class of proportional hazards models

2) Check the quality of these approximations through simulations, and if necessary improve their accuracy

3) Apply our sensitivity analyses to data provided by NHSBT. Use these results for assessment, and for dissemination into the user community

4) Conduct an extensive simulation study to assess the benefits of our approach and its robustness to model assumptions, and to compare our method with existing sensitivity analyses and inverse probability weighting methods, in order to give guidance to practitioners

5) Extend our methodology to the general competing risks framework

6) Provide a software package incorporating all results, which is easy and convenient to use, to encourage practitioners to use our methodology

If a good sensitivity analysis is available, and in particular comes implemented in an easy-to-use software package, practitioners will use it more readily to assess the potential effect of informative censoring. This will lead to more reliable data analyses, and thus to more reliable identification of superior treatments. Two particularly important examples for impact are outlined in what follows:

1) Patients on the waiting list for an elective organ transplant: Death on the waiting list will only be observed for a small subset of patients, as the majority will be removed for transplantation (usually the sickest patients on the list). Furthermore, those with a deteriorating condition are likely to be removed from the list before death. The patients removed for these reasons, had they stayed on the list, would have a lower expected survival time than those who remain on the waiting list. This means that if informative censoring is ignored the estimated survival function for patients on the waiting list may lie considerably above the true survival function. In this case, there may be less effort by the authorities to encourage organ donation, potentially worsening the lack of organs available for transplantation.
Our research will contribute to avoiding situations as described above.

2) Oncology trial for a new treatment, where patients are withdrawn for ethical reasons, when their condition becomes too serious: Those patients have a high risk to die soon after leaving the trial, but only their time of withdrawal will be recorded, thus leading to potential bias in estimating the expected survival time under the new treatment and the comparator (standard treatment), respectively. In this situation, it is possible that - due to ignoring informative censoring - the new treatment appears to be beneficial compared with the standard treatment, when in reality the standard treatment is better. The new treatment would then be taken forward to the next phase trial, exposing many more patients to an inferior treatment (ethical issues), and wasting a large amount of money, which otherwise could have either been used for further important (cancer) research (beneficiaries: (cancer) patients), or could have been passed on to consumers through lower prices (pharmaceutical industry). Similarly, the new treatment may be superior to the standard treatment, but a data analysis ignoring informative censoring may not identify the difference in treatment effects, and therefore the development of the new treatment may not be pursued further, although it could have improved the quality of life for many patients.

Clearly our research will have impact in the area of organ transplantation and related application areas, as in example (1) above. The Project Partner (NHSBT) and Professor Roderick will play a crucial role in helping us to maximise the impact here, and the Renal Registry are also keen on implementing our results.
The structure of the data in example (2) is the same as in example (1); there are possibly informatively censored survival times along with a range of potentially relevant covariates and prognostic factors. Thus, our methodology and corresponding software package will clearly be transferable to survival trials in other medical areas. Here Professor Roderick and colleagues in the Faculty of Medicine at the University of Southampton will facilitate potential impact in clinical trials units. Contacts of the PI, CoI and colleagues in the Southampton Statistical Sciences Research Institute with the pharmaceutical industry (in particular GlaxoSmith Kline where the PI and CoI have established research links) and discussions at the PSI conference will increase the impact in this area.

In a geriatric population with considerable co-morbidities, the competing risk of death is especially high. Input from the Ageing and Lifelong Health University Strategic Research Group will ensure maximum impact of our research in this area.