Mallick R, Fung K, Krewski D
School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada K1S 5B6.
J Cancer Epidemiol Prev. 2002;7(4):155-64.
The Harvard Six Cities Study (Dockery et al.) was the first large-scale cohort study to demonstrate an association between long-term exposure to fine particulate matter less than 2.5 microns in aerodynamic diameter (PM2.5) and mortality in urban centres in the United States. Because of the pivotal role of this study in the establishment of the first U.S. national ambient air quality objective for PM2.5 in 1997 (Greenbaum et al.), the results of this study were subjected to an independent detailed re-analysis to test the robustness of the findings to alternative analytic methods (Krewski et al.), including an assessment of the effect of exposure measurement error on estimates of risk based on the Cox proportional hazards model. It is well-known that random measurement error leads to downward bias in estimates of risk, and overstatement of the precision of such estimates.
Data from the Harvard Six Cities Study were used to evaluate the potential impact of measurement error on estimates of risk. After introducing a known amount of measurement error into the original data, estimates of risk were calculated using two methods for adjusting for measurement error: regression calibration (RCAL) and simulation extrapolation (SIMEX). With RCAL, the observed value of PM2.5 is replaced by its expected value with respect to the measurement error distribution. SIMEX adjusts for measurement error by adding progressively larger errors to the data and then extrapolating back to the case of no measurement error. Computer simulation was used to evaluate the accuracy and precision of both RCAL and SIMEX, and to assess the robustness of RCAL to mis-specification of the measurement error distribution.
When the measurement error distribution was correctly specified, RCAL greatly reduced the downward bias in risk estimates induced by random measurement error, even when the degree of measurement error was relatively large. SIMEX, on the other hand, failed to adequately adjust for the effects of random measurement error in the Cox model, even in the presence of a moderate degree of measurement error. Although RCAL is thus preferable to SIMEX, RCAL was not robust against mis-specification of the measurement error distribution, seriously overestimating (underestimating) risk when the measurement error was overstated (understated).
哈佛六城市研究（多克里等人）是首个大规模队列研究，证实了长期暴露于空气动力学直径小于2.5微米的细颗粒物（PM2.5）与美国城市中心地区死亡率之间的关联。由于该研究在1997年美国首个PM2.5国家环境空气质量目标的制定中发挥了关键作用（格林鲍姆等人），该研究结果接受了独立的详细重新分析，以检验研究结果对替代分析方法的稳健性（克列夫斯基等人），包括基于Cox比例风险模型评估暴露测量误差对风险估计的影响。众所周知，随机测量误差会导致风险估计出现向下偏差，并夸大此类估计的精度。
利用哈佛六城市研究的数据评估测量误差对风险估计的潜在影响。在原始数据中引入已知量的测量误差后，使用两种测量误差调整方法计算风险估计值：回归校准（RCAL）和模拟外推（SIMEX）。采用RCAL时，PM2.5的观测值被其相对于测量误差分布的期望值所取代。SIMEX通过向数据中逐步添加更大的误差，然后外推到无测量误差的情况来调整测量误差。使用计算机模拟评估RCAL和SIMEX的准确性和精度，并评估RCAL对测量误差分布错误设定的稳健性。
当正确设定测量误差分布时，即使测量误差程度相对较大，RCAL也能大幅减少随机测量误差导致的风险估计向下偏差。另一方面，即使存在中等程度的测量误差，SIMEX也未能充分调整Cox模型中随机测量误差的影响。因此，尽管RCAL比SIMEX更可取，但RCAL对测量误差分布的错误设定不稳健，当测量误差被高估（低估）时，会严重高估（低估）风险。
