Predictive inference for clinical trials with the parametric bootstrap

尖端医学治疗的发展需要有针对性的统计方法来分析临床试验数据。在这个舞台上，许多感兴趣的问题都具有独特的因果关系。随着时间的推移，新药或疫苗对患者预后的预期影响是什么？这种影响在不同的人群中有何不同？这些结论是否可以通过纳入观察或历史数据来加强？很明显，21世纪的生物医学研究需要在因果推理领域取得深思熟虑的、原创性的进步。该项目的总体目标是在贝叶斯框架内发展预测推理的理论和实践，作为解决这些问题的新颖而独特的方法。给定来自未知参数抽样分布的观测数据，标准贝叶斯方法是推导出先验密度和似然函数，然后推导出后验密度。然而，预测方法指出，这种后验的统计不确定性完全来自于我们只能观察到有限的数据样本，因此缺少观察值的事实。如果我们能观察到无限的数据，那么任何感兴趣的参数都将被完全定义。因此，另一种方法是直接对预测密度建模，然后通过自举重采样过程推算进一步的观测结果，有效地将统计推断问题转化为缺失数据问题。这种预测性重采样的观点为观察临床试验的分析提供了一个有趣的视角。特别是，临床试验的重点通常是治疗将如何影响患者的结果。因此，预测方法通过将实际的未来数据点作为推理对象来更直接地解决这个问题，而不是通过可能是人工模型构造的参数来工作。贝叶斯预测推理也为不确定性量化和假设检验等问题提供了新的视角。标准的频率假设检验可能会尝试为某些估计量导出密度函数，然后使用它来计算置信区间和p值。相反，我们的方法再次考虑了重复采样缺失或未观察到的数据的概念，以生成几个完整的数据集。然后，任何假设都可以根据这些数据集产生的“真实参数”的多元宇宙进行评估。最终的结果是一个无先验的贝叶斯替代传统的假设检验方法。通过与诺和诺德的合作，我们将把这些方法应用于现实世界的临床试验数据，包括心脏病和糖尿病的治疗。该项目属于EPSRC的“统计与应用概率”研究领域，涉及“受应用启发的统计方法和新概率技术的开发”。它由诺和诺德共同资助，由Chris Holmes教授监督，Stephen Walker教授也参与了合作。

The development of cutting-edge medical treatments requires targeted statistical methods for the analysis of clinical trial data. In this arena, many questions of interest have a distinctively causal flavor. What is the expected effect of a new drug or vaccine on patient outcomes over time? How does that effect vary across different subgroups of the population? Can these conclusions be strengthened by incorporating observational or historical data? It is clear that 21st-century biomedical research necessitates thoughtful and original advancements in the area of causal inference.The general aim of this project is to develop the theory and practice of predictive inference within a Bayesian framework as a novel and unique approach to these questions. Given observed data from an unknown parametric sampling distribution, the standard Bayesian approach would be to elicit a prior density and likelihood function, then derive the posterior density. The predictive approach, however, notes that the statistical uncertainty in this posterior arises entirely from the fact that we can only observe a limited sample of data and are therefore missing observations. If we could observe infinite data, then any parameter of interest would be fully defined. An alternative method is therefore to directly model the predictive density and then impute further observations through a bootstrap resampling procedure, effectively transforming the statistical inference problem into a missing data problem. This predictive resampling viewpoint provides an interesting lens through which to view the analysis of clinical trials. In particular, the focus of a clinical trial is generally on how the treatment will affect patient outcomes. The predictive approach therefore addresses this question more directly by taking the actual future data points as the objects of inference, rather than working through a parameter which may be an artifical model construct.Bayesian predictive inference also provides a novel perspective on questions related to uncertainty quantification and hypothesis testing. A standard frequentist hypothesis test would likely attempt to derive a density function for some estimator, then use it to calculate confidence intervals and p-values. Instead, our approach again considers the concept of sampling the missing or unobserved data repeatedly in order to generate several complete datasets. Any hypothesis can then be evaluated with respect to the multiverse of "true parameters" arising from these datasets. The final result is a prior-free Bayesian alternative to traditional methods of hypothesis testing. Through our collaboration with Novo Nordisk, we will apply these methods to real-world clinical trial data, including treatments for heart disease and diabetes.This project falls under the "Statistics and applied probability" EPSRC research area, which involves "statistical methodology and development of new probabilistic techniques inspired by applications". It is co-funded by Novo Nordisk and supervised by Professor Chris Holmes, with additional collaboration from Professor Stephen Walker.