Estimation and inference for exposure effects with latency in the Cox proportional hazards model in the presence of exposure measurement error

Abstract

Researchers are often interested in estimating the effects of time-varying exposures on health outcomes. The latency period, defined as the critical period of susceptibility, can be an important component of exposure effect assessment. Although it is widely known that many environmental, nutritional, and other exposure measurements are prone to error and are also likely to act only during a critical time window of susceptibility, no one has yet considered the impact of this on the estimation of latency parameters in survival models. In this paper we derived methods for point and interval estimation for the latency parameter and the regression coefficients in rare disease situations. Under a linear measurement model, although the estimated hazard ratios are biased, as has been previously demonstrated, we show that the latency parameter is approximately unbiased. Simulations and an illustrative example investigating the prospective association between PM${}_{2.5}$ and lung cancer incidence in the Nurses’ Health Study are included to evaluate the performance of our method.