It is a great pleasure to provide a discussion of Adam Szpiro’s and Chris Paciorek’s (SP) comprehensive and clarifying paper on measurement error in air pollution epidemiology. I see this paper as a culmination of much methodological work, some conducted by Szpiro and Paciorek themselves, that has been conducted over the past decade regarding the estimation of associations between air pollution concentrations and health outcomes. Not only do SP provide insight into how measurement error arises in cohort studies of air pollution and health, they clearly specify its impacts on the estimation of the health effects parameters and propose a novel solution for accouting for the various types of measurement error. For those unfamiliar with the general area of air pollution epidemiology, it may be worthwhile to review briefly the context in which this paper sits in order to clarify its significance. A key point to note is that a fundamental problem of essentially all studies of the health effects of air pollution is that the relevant exposure is not directly measured. With the exception of experimental studies, where exposures are controlled, and smaller-scale observational studies where direct monitoring of personal or ambient air pollution concentrations can be accomplished, studies requiring air pollution exposure estimates require some kind of surrogate. One advantage of conducting air pollution epidemiological studies is that there are extensive monitoring networks sited in major metropolitan areas that provide publicly accessible data. However, measurement error is the price one must pay when it comes to linking that data with health outcomes in a human population. Broadly speaking, there are at least two targets of exposure estimation one can usefully imagine. The first is a peron’s personal exposure to air pollution, which is a combination of outdoor pollution levels and indoor pollution levels, say in their home or work place. The second is simply a person’s exposure to outdoor concentrations, which is commonly the true target of estimation, even if it is not explicitly stated. While a person’s personal exposure might appear to be the best exposure measure, health effects estimated using this measure may be challenging to interpret because modifying a person’s personal exposure may involve multiple types of interventions. On the other hand, outdoor exposure, which represents a part of a person’s overall exposure, has a more clear tool for intervention in the formulation of outdoor air quality standards by regulatory agencies such as the Environmental Protection Agency. This paper by SP focuses on the estimation of outdoor concentrations, for example outside a person’s home, estimated from outdoor monitoring networks. This focus raises some unique measurement error problems and SP do a nice job of extending the traditional measurement error framework into this setting. In the development of our understanding of measurement error in air pollution studies, a key recent contribution came from Gryparis et al. (2009). They showed that prediction of exposures can introduce a Berkson-like error component which is not like typical Berkson error because of the spatial correlation between study subjects. However, that paper did not directly address the issue of possible error introduced by the estimation of the prediction model itself. Later, Szpiro et al. (2011) noted that estimation of the prediction model introduces a classical-like error component. Paciorek (2010) laid some of the groundwork for proper estimation of health effects in cross-sectional studies while adjusting for potential unmeasured confounding. This work combines the previous work into a single overarching framework and proposes a method to address both the Berkson-like and classical-like problems at once. One tension that arises in many areas of biomedical science is between the need to have a single estimate of whatever parameter is of interest and the recognition that there is no perfect model that accounts for all sources of uncertainty and bias. Air pollution epidemiology is certainly not immune to this problem. Almost all would agree that there is no perfect model and in fact there are likely many unmeasured (or unmeasurable) factors that could confound the association between pollution exposure and a health outcome. However, most might also agree that there is often a need to come up with a single “best" estimate that can be used as a summary while accounting for known sources of uncertainty and bias. This debate played out previously in the literature on time series analyses of air pollution and health data which primarily are used to estimate short-term or acute health effects (Dominici et al., 2004; Peng et al., 2006). The time series literature roughly complements the work that is covered here by SP. In time series studies, the advent of multi-site studies and the use of hierarchical models allowed for the estimation of a robust summary estimate (averaged across communities) while also allowing for reasonable sensitivity analysis with respect to the site-specific models. SP have produced in this paper an analogous development, essentially a method that accounts for known sources of uncertainty and bias, providing a “best" estimate, while also allowing for reasonable sensitivity analysis. In Table 2 of SP’s analysis of the MESA Air cohort data, it is interesting to note that the range of variation found across the different approaches in estimating the health effect parameter β is relatively small. The most naive model produces an estimate of 0.66 (SE: 0.62) while perhaps the best model (5 degrees of freedom with bias correction + bootstrap) produces an estimate of 0.69 (SE: 0.67). Across the 9 different models, if one were to convert the estimates and standard errors into approximate p-values, they would range from 0.11 to 0.16. Even the most optimistic investigator would struggle to claim that any of those estimates were significantly different from zero. Therefore, if one’s primary question is to the effect of “Is there an assocation between NOx and LVMI", it seems clear that the answer is no. SP’s analysis gives us comfort that our qualitative conclusion is not seriously biased and that we would not draw an incorrect conclusion from the analysis. For the purpose of producing a single best estimate, I am struck by the similarity between the result from the optimal model and the result of the naive estimate. Although the simulations indicate that there is a potential for serious bias and undercoverage, in the analysis of the real data, the range of outcomes does not seem to match as closely that which was found in the simulation. Ultimately, it is useful to separate SP’s work into two parts. There is the framework which decomposes the various sources of error that are induced in the common practice of estimating health effects in cross-sectional studies. The delineation of this framework is critical and provides new insights into model development for such studies. The practical advantages of SP’s methodological development (bias correction with nonparametric bootstrap) will likely depend on how estimates of health effects are interpreted and for what they will subsequently be used. If the estimates are used to answer the basic question of “Is there an effect?" then I would argue one is more interested in conducting a thorough sensitivity analysis that presents a range of estimates based on assumptions about unmeasured confounding, model misspecification, and many other factors. Here, I do not think modest differences in the standard errors such as those shown in Table 2 would dramatically alter any conclusions drawn regarding this qualitative question. However, in a scenario where one might be feeding a health effects estimate into a subsequent analysis, such as a risk analysis where health impacts might be calculated, then it seems far more important to have a set procedure that obtains the “best” estimate on which to make inference. It is here that I think SP’s approach will be quite applicable and should draw attention. Given that SP’s method does not appear to be unreasonable in terms of computational demands, there is not a substantial tradeoff to consider when applying it and it should be feasible to use if appropriate software were available. Overall, I have found SP’s analysis framework enlightening and it has helped me understand the impact of various modeling decisions in the estimation of health effects in a cross-sectional setting. I think this is a key contribution to the field and will result in a number of readily implementable and practical methodological recommendations.

中文翻译：

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空气污染流行病学测量误差：不确定时期指南

很高兴提供对 Adam Szpiro 和 Chris Paciorek (SP) 关于空气污染流行病学测量误差的全面和澄清的论文的讨论。我认为这篇论文是许多方法论工作的高潮，其中一些工作是由 Szpiro 和 Paciorek 自己进行的，这些工作在过去十年中就空气污染浓度与健康结果之间的关联进行了评估。SP 不仅可以深入了解空气污染和健康队列研究中测量误差是如何产生的，而且它们清楚地说明了其对健康影响参数估计的影响，并提出了一种新的解决方案来计算各种类型的测量误差。对于那些不熟悉空气污染流行病学一般领域的人，或许值得简要回顾一下本文所处的背景，以阐明其重要性。需要注意的一个关键点是，基本上所有关于空气污染对健康影响的研究都存在一个基本问题，即相关暴露并未直接测量。除了控制暴露的实验研究和可以直接监测个人或环境空气污染浓度的小规模观察研究外，需要估计空气污染暴露的研究需要某种替代方法。进行空气污染流行病学研究的优势之一是主要大都市区设有广泛的监测网络，可提供可公开访问的数据。然而，测量误差是人们在将数据与人群健康结果联系起来时必须付出的代价。从广义上讲，至少有两个暴露估计目标可以很好地想象。首先是一个人对空气污染的个人暴露，这是室外污染水平和室内污染水平的组合，比如在他们的家中或工作场所。第二个只是一个人暴露于室外浓度，这通常是估计的真正目标，即使没有明确说明。虽然一个人的个人暴露可能看起来是最好的暴露措施，但使用这种措施估计的健康影响可能难以解释，因为修改一个人的个人暴露可能涉及多种类型的干预。另一方面，户外曝晒，它代表了一个人整体暴露的一部分，在环境保护局等监管机构制定室外空气质量标准时有更明确的干预手段。SP 的这篇论文侧重于室外浓度的估计，例如从室外监测网络估计的一个人的家外。这种关注引发了一些独特的测量误差问题，SP 在将传统测量误差框架扩展到此设置方面做得很好。在我们对空气污染研究中测量误差的理解的发展过程中，最近的一项重要贡献来自 Gryparis 等人。(2009)。他们表明，由于研究对象之间的空间相关性，暴露的预测会引入类似伯克森的误差成分，这与典型的伯克森误差不同。然而，那篇论文并没有直接解决由预测模型本身的估计引入的可能错误的问题。后来，Szpiro 等人。(2011) 指出，预测模型的估计引入了类似经典的误差分量。Paciorek (2010) 为在横断面研究中正确估计健康影响奠定了一些基础，同时调整了潜在的未测量混杂因素。这项工作将之前的工作结合到一个单一的总体框架中，并提出了一种同时解决类伯克森和类经典问题的方法。在生物医学科学的许多领域中出现的一种紧张关系是需要对感兴趣的任何参数进行单一估计，以及认识到没有完美的模型可以解释所有不确定性和偏差的来源。空气污染流行病学当然不能幸免于这个问题。几乎所有人都会同意没有完美的模型，事实上，可能存在许多无法测量（或无法测量）的因素，可能会混淆污染暴露与健康结果之间的关联。然而，大多数人可能也同意，通常需要提出一个单一的“最佳”估计，该估计可以用作总结，同时考虑到已知的不确定性和偏差来源。这个争论以前在关于时间序列的文献中进行过空气污染和健康数据的分析，主要用于估计短期或急性健康影响（Dominici 等人，2004 年；Peng 等人，2006 年）。时间序列文献大致补充了 SP 在此处涵盖的工作. 在时间序列研究中，多站点研究的出现和分层模型的使用允许进行可靠的汇总估计（跨社区平均），同时还允许对特定站点模型进行合理的敏感性分析。SP 在本文中产生了类似的发展，本质上是一种考虑已知不确定性和偏差来源的方法，提供“最佳”估计，同时还允许进行合理的敏感性分析。SP 对 MESA Air 队列数据的分析表 2 ，有趣的是，在估计健康影响参数 β 时，不同方法发现的变化范围相对较小。最朴素的模型产生的估计值为 0.66（SE: 0. 62）而也许最好的模型（带有偏差校正的 5 个自由度 + 引导）产生 0.69 的估计值（SE：0.67）。在 9 个不同的模型中，如果将估计值和标准误差转换为近似的 p 值，它们的范围将从 0.11 到 0.16。即使是最乐观的调查员也很难声称这些估计中的任何一个都与零显着不同。因此，如果一个人的主要问题是“NOx 和 LVMI 之间是否存在关联”的影响，答案似乎很明显是否定的。SP 的分析让我们感到欣慰的是，我们的定性结论没有严重偏差，我们不会得出分析得出的错误结论。为了产生单一的最佳估计，我对最佳模型的结果与朴素估计的结果之间的相似性感到震惊。尽管模拟表明存在严重偏差和覆盖不足的可能性，但在对真实数据的分析中，结果的范围似乎与模拟中发现的不匹配。最终，将 SP 的工作分成两部分是有用的。有一个框架可以分解在横断面研究中估计健康影响的常见做法中引起的各种误差来源。该框架的描述至关重要，并为此类研究的模型开发提供了新的见解。SP 方法论开发（使用非参数引导程序进行偏差校正）的实际优势可能取决于如何解释健康影响的估计值以及随后将使用的内容。如果估计值用于回答“有影响吗？”的基本问题，那么我认为人们更感兴趣的是进行彻底的敏感性分析，该分析基于关于未测量混杂、模型错误指定和许多假设的假设提供一系列估计值。其他因素。在这里，我认为标准误差的微小差异（例如表 2 中所示的那些）不会显着改变关于这个定性问题得出的任何结论。但是，在一个可能将健康影响估计值输入到后续分析，例如可能计算健康影响的风险分析，那么拥有一套程序来获得“最佳”估计值以进行推断似乎更为重要。正是在这里，我认为 SP 的方法将非常适用并且应该引起注意。鉴于 SP 的方法在计算需求方面似乎并非不合理，因此在应用它时没有实质性的权衡考虑，如果有合适的软件可用，使用它应该是可行的。总的来说，我发现 SP 的分析框架很有启发性，它帮助我理解了各种建模决策对横断面环境中健康影响估计的影响。我认为这是对该领域的关键贡献，并将产生许多易于实施和实用的方法论建议。