Statistical Sciences Research institute

在生存研究中，通常有些观察结果会被删减。这意味着没有观察到感兴趣的事件，例如病人死亡。审查可能有很多不同的原因。例如，研究可能在所有患者死亡之前结束。在某些情况下，观察结果被审查的事实本身可能提供有关潜在生存时间的进一步信息。以器官移植的等待名单为例。如果供体器官可用，通常名单上病情最严重的符合条件的患者将优先进行移植。因此，得知一项观察结果因移植手术而遭到审查，我们就知道，如果这个病人一直在等待名单上，他比名单上的普通病人更有可能在短时间内死亡。在分析数据时忽略这些额外信息可能会导致不正确的结论。例如，由于病情最严重的患者已被从移植等待名单中除名，等待名单上患者的生存概率可能被严重高估。同样，由于许多接受移植的病人已经病得很重，他们在手术后不久仍然有很高的死亡风险。这可能会导致一个错误的结论，即等待名单上的病人平均比接受移植的病人活得更长。因此，在分析数据时相应地考虑“信息审查”是至关重要的。没有统计检验可以检测数据集中信息的删减。然而，有一种称为敏感性分析的统计工具，它可以让我们了解信息审查对数据分析的影响。如果敏感性分析表明这些影响可以忽略不计，则可以进行标准分析而不会造成损害。但是，如果敏感性分析指出了一个问题，那么需要对数据应用几种不同的复杂方法，以便得出有效的结论。现有的敏感性分析存在一些缺陷。它们要么相当容易应用和解释，但可能并不总是标记出信息审查的问题，因为它们基于过于简单而不现实的模型。另一方面，更复杂的敏感性分析很难应用，因此从业者不会大规模使用它们。此外，对于在特定情况下应该使用哪种敏感性分析以及如何进行敏感性分析，没有明确的指导，因此在实践中经常忽略信息审查。这就是我们研究的切入点。我们的目标是提供一种敏感性分析，它在评估信息审查的影响时尽可能现实，同时仍然保持计算的简单性。这包括对模型需要有多复杂的一般调查，以便对广泛的现实场景进行强大的敏感性分析。这本身包含许多有趣和具有挑战性的统计问题，但我们进行这项研究的主要动机源于它可能对医学研究产生的潜在影响。我们希望鼓励从业者使用敏感性分析，从而防止他们由于信息审查而从数据中得出错误的结论。特别是，我们将：(a)评估我们的建模方法，并比较本课程内外的不同模型，使用来自NHS血液和移植（NHSBT）和肾脏登记处的真实数据，以及广泛的模拟，以调查模型的必要复杂性；(b)提供一个载有我们的研究结果的电脑包，方便从业员使用。等候名单上的信息审查是一种被称为“竞争风险”的特殊情况。在开发了解决这个问题的方法之后，我们将扩展它们来解决这个更普遍的问题。

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.