Center for Health Sciences, Exponent, Inc., Menlo Park, CA, USA.
Stanford Cancer Institute, Stanford, CA, USA.
Crit Rev Toxicol. 2020 Mar;50(3):189-200. doi: 10.1080/10408444.2020.1727410. Epub 2020 Mar 12.
The proportional hazards (PH) model is commonly used in epidemiology despite the stringent assumption of proportionality of hazards over time. We previously showed, using detailed simulation data, that the impact of a modest risk factor cannot be estimated reliably using the PH model in the presence of confounding by a strong, time-dependent risk factor. Here, we examine the same and related issues using a real dataset. Among 97,303 women in the prospective Nurses' Health Study cohort from 1994 through 2010, we used PH regression to investigate how effect estimates for cigarette smoking are affected by increasingly detailed specification of time-dependent exposure characteristics. We also examined how effect estimates for fine particulate matter (PM), a modest risk factor, are affected by finer control for time-dependent confounding by smoking. The objective of this analysis is not to present a credible estimate of the impact of PM on lung cancer risk, but to show that estimates based on the PH model are inherently unreliable. The best-fitting model for cigarette smoking and lung cancer included pack-years, duration, time since cessation, and an age-by-pack-years interaction, indicating that the hazard ratio (HR) for pack-years was significantly modified by age. In the fully adjusted best-fitting model for smoking including pack-years, the HR per 10-µg/m increase in PM was 1.06 (95% confidence interval (CI) = 0.90, 1.25); the HR for PM in the full cohort ranged between 1.02 and 1.10 in models with other smoking adjustments, indicating a residual confounding effect of smoking. The HR for PM was statistically significant only among former smokers when adjusting for smoking pack-years (HR = 1.35, 95% CI = 1.00, 1.82 in the best-fitting smoking model), but not in models adjusting for smoking duration and average packs (pack-years divided by duration). The association between cumulative smoking and lung cancer is modified by age, and improved model fit is obtained by including multiple time-varying components of smoking history. The association with PM is residually confounded by smoking and modified by smoking status. These findings underscore limitations of the PH model and emphasize the advantages of directly estimating hazard functions to characterize time-varying exposure and risk. The hazard function, not the relative hazard, is the fundamental measure of risk in a population. As a consequence, the use of time-dependent PH models does not address crucial issues introduced by temporal factors in epidemiological data.
比例风险 (PH) 模型在流行病学中被广泛应用，尽管它对风险随时间的比例性有严格的假设。我们之前使用详细的模拟数据表明，在存在强的、随时间变化的风险因素混杂时，使用 PH 模型无法可靠地估计适度风险因素的影响。在这里，我们使用真实数据集来研究相同和相关的问题。在 1994 年至 2010 年期间的前瞻性护士健康研究队列中，我们使用 PH 回归来研究吸烟的时间依赖性暴露特征的日益详细的规范如何影响对吸烟的影响估计。我们还研究了细颗粒物 (PM) 的影响估计值，PM 是适度的风险因素，受吸烟的时间依赖性混杂的更精细控制的影响。这项分析的目的不是提供 PM 对肺癌风险影响的可信估计，而是表明基于 PH 模型的估计值本质上是不可靠的。吸烟与肺癌的最佳拟合模型包括包年、持续时间、戒烟时间和年龄与包年的交互作用，这表明包年的危害比 (HR) 明显受到年龄的影响。在包括包年的吸烟的最佳拟合模型中，PM 每增加 10μg/m 的 HR 为 1.06（95%置信区间 [CI] = 0.90，1.25）；在包括其他吸烟调整的全队列模型中，PM 的 HR 在 1.02 到 1.10 之间，表明吸烟存在残余混杂效应。仅在调整吸烟包年数时，PM 的 HR 才有统计学意义（在最佳拟合吸烟模型中为 1.35，95%CI=1.00，1.82），而在调整吸烟持续时间和平均包数（包年数除以持续时间）的模型中则没有。吸烟与肺癌之间的关联受年龄影响，通过包括吸烟史的多个随时间变化的成分，可以获得更好的模型拟合。与 PM 的关联受吸烟的残余混杂影响，并受吸烟状况的影响。这些发现强调了 PH 模型的局限性，并强调了直接估计危险函数来描述随时间变化的暴露和风险的优势。在人群中，危险函数而不是相对危险函数是风险的基本度量。因此，使用随时间变化的 PH 模型并不能解决流行病学数据中时间因素带来的关键问题。
