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In this article, we study nonparametric inference for a covariate-adjusted regression function. This parameter captures the average association between a continuous exposure and an outcome after adjusting for other covariates. Under certain causal conditions, it also corresponds to the average outcome had all units been assigned to a specific exposure level, known as the causal dose–response curve. We propose a debiased local linear estimator of the covariate-adjusted regression function and demonstrate that our estimator converges pointwise to a mean-zero normal limit distribution. We use this result to construct asymptotically valid confidence intervals for function values and differences thereof. In addition, we use approximation results for the distribution of the supremum of an empirical process to construct asymptotically valid uniform confidence bands. Our methods do not require undersmoothing, permit the use of data-adaptive estimators of nuisance functions, and our estimator attains the optimal rate of convergence for a twice differentiable regression function. We illustrate the practical performance of our estimator using numerical studies and an analysis of the effect of air pollution exposure on cardiovascular mortality.
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Semiparametric regression calibration for general hazard models in survival analysis with covariate measurement error; surprising performance under linear hazard
Abstract Observational epidemiological studies often confront the problem of estimating exposure‐disease relationships when the exposure is not measured exactly. Regression calibration (RC) is a common approach to correct for bias in regression analysis with covariate measurement error. In survival analysis with covariate measurement error, it is well known that the RC estimator may be biased when the hazard is an exponential function of the covariates. In the paper, we investigate the RC estimator with general hazard functions, including exponential and linear functions of the covariates. When the hazard is a linear function of the covariates, we show that a risk set regression calibration (RRC) is consistent and robust to a working model for the calibration function. Under exponential hazard models, there is a trade‐off between bias and efficiency when comparing RC and RRC. However, one surprising finding is that the trade‐off between bias and efficiency in measurement error research is not seen under linear hazard when the unobserved covariate is from a uniform or normal distribution. Under this situation, the RRC estimator is in general slightly better than the RC estimator in terms of both bias and efficiency. The methods are applied to the Nutritional Biomarkers Study of the Women's Health Initiative.
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- Award ID(s):
- 1916411
- PAR ID:
- 10451013
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Biometrics
- Volume:
- 77
- Issue:
- 2
- ISSN:
- 0006-341X
- Format(s):
- Medium: X Size: p. 561-572
- Size(s):
- p. 561-572
- Sponsoring Org:
- National Science Foundation
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