New statistics for the self-controlled case series method: weakening the assumptions

在许多领域中，一个重要的统计问题是确定一个变量，称为暴露，是否影响感兴趣的事件的发生。例如，给药是否会导致不良反应;某些生产模式是否会增加制造过程中出现故障的可能性;一个生活事件的发生是否会影响另一个事件的可能性。已经开发了各种统计方法来识别诸如此类的关联，并估计其强度。该项目涉及一种特殊的方法，即最近出现的病例系列方法，这种方法与其他方法的不同之处在于，只需要对经历过感兴趣事件的个体（或项目）进行抽样。因此，不需要没有经历过该事件的个人。当感兴趣的事件很少时，这是有利的。比较是在每个人的观察期内进行的，还有一个额外的好处是，许多可能扭曲暴露与事件之间关联的因素，即所谓的混杂因素，被自动考虑在内。这种双重好处-减少研究规模和良好的控制混杂因素-是有代价的，即需要比其他方法所需的更强的假设。本项目的目的是研究这些假设，以便更好地了解它们的作用，如果可能的话，削弱它们，从而扩大该方法的应用范围，该项目很重要，因为病例系列方法越来越多地用于一系列领域，特别是流行病学。这是因为它相对便宜，并使研究成为可能，否则将是不切实际的或有偏见的（例如，在流行病学中，如果最有可能遭受事件的患者也往往是那些经历过暴露的人）。然而，随着该方法越来越受欢迎，在不适当考虑假设的情况下应用该方法的诱惑也在增加。相对而言，很少有人去检查这些假设是否真的有必要，以及它们是否可以以各种方式被削弱。我们来看看四个关键假设。第一个，也可能是最严格的要求，是风险暴露不受先前事件的影响。例如，如果感兴趣的事件是死亡，则该假设失败。我们在这个标题下的主要目标将是开发一种适用于死亡等事件的病例系列方法。第二个关键假设与点暴露有关，即在特定时间点发生的暴露，如疫苗接种或电源浪涌。对于这样的风险，定义了一个风险函数，它描述了在点风险之后结果事件发生的机会如何变化。目前，需要对风险函数的形状，特别是风险增加期的持续时间作出一些假设。我们将研究更灵活的风险函数，它不需要这样的假设，我们将研究的第三个假设是，如果一个人经历了几个事件，那么这些事件的发生是相互独立的。在实践中，这往往不是真的：例如，一台机器出现一次故障可能会增加后续故障的机会。我们将发展一个检验复发事件的独立性的方法，该方法适用于病例系列分析。最后，我们将研究的第四个假设是，观察期不依赖于事件发生的时间。例如，当事件增加死亡的可能性时，情况就不是这样了，就像心脏病发作一样。我们将研究这个假设的失败对结果的影响程度。这个项目将为病例系列方法提供新的统计理论，从而更好地理解和更广泛地使用这种方法。研究结果将发表在同行评审期刊和案例系列网站http://statistics.open.ac.uk/sccs上。

An important statistical problem in many fields is to determine whether one variable, called the exposure, affects the occurrence of an event of interest. For example, does administering a drug cause adverse reactions; do certain production modes increase the chance of faults in a manufacturing process; does the occurrence of one life event affect the likelihood of another. Various statistical methods have been developed to identify associations such as these, and to estimate their strength. This project is concerned with one particular method, the case series method, which has emerged relatively recently.This method differs from others in that only individuals (or items) that have experienced the event of interest need to be sampled. Thus, individuals who have not experienced the event are not needed. This is advantageous when the event of interest is rare. Comparisons are made within each individual's period of observation, with the additional benefit that many of the factors that might distort the association between the exposure and the event, known as confounding factors, are automatically allowed for. This double benefit - reduced study size and good control of confounding factors - comes at a price, namely the need for stronger assumptions than are required by other methods. The purpose of the present project is to study these assumptions, in order better to understand their role, if possible weaken them, and hence widen the range of application of the method.The project is important because the case series method is increasingly being used in a range of fields, particularly in epidemiology. This is because it is relatively cheap, and makes possible studies which otherwise would be impractical or biased (for example, in epidemiology, if the patients most likely to suffer the event also tend to be those that experience the exposure). However, as the method grows in popularity, the temptation to apply it without due regard to the assumptions increases. Relatively little work has been done to check whether the assumptions are really needed, and whether they may be weakened in various ways. We will look at four key assumptions. The first, and probably most restrictive requirement, is that exposures are unaffected by previous events. This assumption fails if, for example, the event of interest is death. Our main objective under this heading will be to develop a case series method that works for events such as deaths.The second key assumption relates to point exposures, that is, exposures that occur at a particular point in time, like a vaccination, or a power surge. For such exposures, a risk function is defined which describes how the chance of occurrence of the outcome event varies after the point exposure. At present, some assumptions are required about the shape of the risk function, and in particular the duration of the increased risk period. We will study more flexible risk functions, which do not require such assumptions.The third assumption we will investigate is that, if an individual experiences several events, then these occur independently of each other. This is often not true in practice: for example, occurrence of one failure in a piece of machinery might increase the chance of subsequent failures. We will develop a test of independence of recurrent events, valid for case series analyses.Finally, the fourth assumption we will study is that the period of observation does not depend on the timing of events. This is not the case when, for example, the event increases the chance of death, as with heart attacks. We will study the extent to which failure of this assumption affects the results.This project will produce new statistical theory for the case series method, leading to better understanding and hence wider use of the method. The findings will be published in peer-reviewed journals and on the case series website at http://statistics.open.ac.uk/sccs.