Inference on Survival Data with Covariate Measurement Error - An Imputation-based Approach

We propose a new method for fitting proportional hazards models with error-prone covariates. Regression coefficients are estimated by solving an estimating equation that is the average of the partial likelihood scores based on imputed true covariates. For the purpose of imputation, a linear spline model is assumed on the baseline hazard. We discuss consistency and asymptotic normality of the resulting estimators, and propose a stochastic approximation scheme to obtain the estimates. The algorithm is easy to implement, and reduces to the ordinary Cox partial likelihood approach when the measurement error has a degenerative distribution. Simulations indicate high efficiency and robustness. We consider the special case where error-prone replicates are available on the unobserved true covariates. As expected, increasing the number of replicate for the unobserved covariates increases efficiency and reduces bias. We illustrate the practical utility of the proposed method with an Eastern Cooperative Oncology Group clinical trial where a genetic marker, c-myc expression level, is subject to measurement error.

ON THE MERITS OF VOXEL-BASED MORPHOMETRIC PATH-ANALYSIS FOR INVESTIGATING VOLUMETRIC MEDIATION OF A TOXICANT'S INFLUENCE ON COGNITIVE FUNCTION

We previously showed that lifetime cumulative lead dose, measured as lead concentration in the tibia bone by X-ray fluorescence, was associated with persistent and progressive declines in cognitive function and with decreases in MRI-based brain volumes in former lead workers. Moreover, larger region-specific brain volumes were associated with better cognitive function. These findings motivated us to explore a novel application of path analysis to evaluate effect mediation. Voxel-wise path analysis, at face value, represents the natural evolution of voxel-based morphometry methods to answer questions of mediation. Application of these methods to the former lead worker data demonstrated potential limitations in this approach where there was a tendency for results to be strongly biased towards the null hypothesis (lack of mediation). Moreover, a complimentary analysis using anatomically-derived regions of interest volumes yielded opposing results, suggesting evidence of mediation. Specifically, in the ROI-based approach, there was evidence that the association of tibia lead with function in three cognitive domains was mediated through the volumes of total brain, frontal gray matter, and/or possibly cingulate. A simulation study was conducted to investigate whether the voxel-wise results arose from an absence of localized mediation, or more subtle defects in the methodology. The simulation results showed the same null bias evidenced as seen in the lead workers data. Both the lead worker data results and the simulation study suggest that a null-bias in voxel-wise path analysis limits its inferential utility for producing confirmatory results.