Adjusting for measurement error in the Cox proportional hazards regression model.
Bibliographic record
Abstract
BACKGROUND: 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. METHODS: 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. RESULTS AND CONCLUSIONS: 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).
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.075 | 0.180 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.004 | 0.002 |
| Research integrity | 0.001 | 0.004 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".