The Regression Discontinuity Design: a novel approach to evaluating the effect of drugs and treatments in primary care

临床实践中的一项基本任务是确定特定药物是否以最有效的方式处方，以增加从其使用中获得的临床益处。虽然随机临床试验（RCT）被正确地认为是评价药物疗效的最佳科学方法，但由于患者选择，特别是避免合并症，这些研究通常具有较差的外部效度。处方指南并不总是以证据为基础的，通常是由临床专家福尔斯来制定的。回归不连续设计（RDD）是一种计量经济学准实验设计，旨在通过利用自然发生的处理规则来估计处理的因果效应。它最早出现在20世纪60年代的教育经济学文献中，但直到最近才在该领域之外得到广泛应用。RDD利用了这样一个事实，即许多治疗是根据预先决定的规则分配的，例如英国NICE制定的规则。RDD背后的想法是，如果我们可以假设个人只是在预先选择的阈值的任何一侧，（例如血压140/90 mmHg）属于一个共同的人群，其特征是分配规则和决定结果，那么阈值可以被看作是一种随机干预，它将治疗分配给那些刚好落在上面的人，而不治疗那些落在上面的人。由于RDD的准随机性质，消除或至少减轻了混杂。因此，我们可以使用RDD来估计治疗的效果或阈值附近人群中的相关暴露。然而，尽管RDD模拟了随机化，但在我们的特定病例中，为了减少估计值的偏倚，仍有必要在分析中进一步考虑可能影响处方决定的其他因素，包括患者虚弱或合并症的标志物。在完全遵守该设置的情况下（即当所有高于（低于）阈值的个体都（不）接受治疗时），RDD被称为“尖锐”。相反，如果存在明确的指南，但由于某些原因（可能是完全合法的，从临床角度来看）没有完全遵循，RDD被称为“模糊”。RDD估计与统计研究中的其他因果推断估计有着密切的联系。然而，在我们的病例中，我们面临着流行病学和临床研究中经常出现的并发症，感兴趣的结果由二元变量表示（例如临床事件的发生或死亡率）。针对这种情况的具体方法尚未得到广泛的发展，尽管工具变量（IV）理论可以发挥作用。具体来说，主要的困难在于，在这种情况下，人们感兴趣的是因果比率，而不是因果差异（这与连续结果的情况有关）。可用于导出此类估计量的方法是基于除了标准IV设置之外的其他假设。假设A1）涉及结局函数与治疗和未观察到的混杂因素之间的近似线性; A2）假设治疗和未观察到的混杂因素之间没有相互作用（称为"乘法量表上的无效应修正"）。这些无法直接测试（因为它们涉及不可观察的变量），但我们将使用模拟来研究它们的合理性。电子医疗记录，如"健康改善网络"（THIN）初级保健数据库提供了一个很好的机会，调查这些问题，如上述。通过THIN，我们可以获得有关初级保健处方和处方开始前后测量以及不良事件的详细信息。

A fundamental task in clinical practice is to determine whether a particular drug is being prescribed in the most effective way, in order to increase the clinical benefit derived from its use. While Randomised Clinical Trials (RCTs) are correctly considered to be the best scientific method for evaluation of drug efficacy, these studies often have poor external validity, because of patient selection, in particular the avoidance of comorbidities. Prescription guidelines are not always evidence based and it typically falls to clinical experts to set them. The regression discontinuity design (RDD) is an econometric quasi-experimental design aimed at estimating the causal effects of a treatment by exploiting naturally occurring treatment rules. It was first introduced in the educational economics literature in the 1960s but it has not been widely used outside of this field until recently. The RDD exploits the fact that many treatments are assigned according to pre-decided rules, eg those set by NICE in the UK. The idea behind the RDD is that if we can assume that individuals just on either side of a pre-selected threshold (eg blood pressure of 140/90mmHg) belong to a common population with respect to the characteristics that inform the assignment rule and determine the outcome, then the threshold can be seen as a random intervention which assigns the treatment to those that fall just above and no treatment to those that fall just below it. Due to the quasi-randomised nature of the RDD, confounding is eliminated or at least mitigated. We can thus use the RDD to estimate the effect of the treatment or a related exposure within the population around the threshold. However, although the RDD mimics randomisation, in our particular case, in order to reduce bias of the estimates it will still be necessary to further account in the analyses for other factors which may impact the decision to prescribe, including markers of patients frailty or comorbidities. In situations where the set up is fully adhered to (ie when all individuals above (below) the threshold are (not) given the treatment, the RDD is termed "sharp". Conversely, in cases where well-defined guidelines exist, but for some (possibly completely legit, under a clinical perspective) reason they are not fully followed, the RDD is termed "fuzzy". RDD estimators have strong connections with other causal inference estimators in statistical research. However, in our case, we are faced with the complication that often in epidemiology and clinical research the outcome of interest is represented by a binary variable (eg the occurrence of a clinical event, or mortality). Specific methods for such a case have not been extensively developed, although Instrumental Variable (IV) theory can be brought to bear. Specifically, the main difficulty lies in the fact that in this case the interest is in causal ratios, rather than causal differences (which are relevant in the case of continuous outcomes). Methods that can be used to derive such estimators are based on making additional assumptions in addition to the standard IV setting. Assumption A1) involves approximate linearity between a function of the outcome and the treatment and unobserved confounders; and A2) assumes no interaction between the treatment and the unobserved confounders (termed "no-effect modification on the multiplicative scale"). These cannot be directly tested (because they involve unobservable variables), but we will investigate their plausibility using simulations. Electronic healthcare records such as "The Health Improvement Network" (THIN) primary care database provide an excellent opportunity to investigate questions like those mentioned above. From THIN we can obtain detailed information on prescriptions made in primary care and measurements both before and after initiation of prescription, as well as adverse events.