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.

Effects of Atmospheric Nitrogen Deposition on the Herbaceous Layer of a Central Appalachian Hardwood Forest

Additions of nitrogen (N) have been shown to alter species diversity of plant communities, with most experimental studies having been carried out in communities dominated by herbaceous species. We examined seasonal and inter-annual patterns of change in the herbaceous layer of two watersheds of a central Appalachian hardwood forest that differed in experimental treatment. This study was carried out at the Fernow Experimental Forest, West Virginia, using two adjacent watersheds: WS4 (mature, second-growth hardwood stand, untreated reference), and WS3. Seven circular 0.04-ha sample plots were established in eachwatershed to represent its full range of elevation and slope aspect. The herbaceous layer was sampled by identifying and visually estimating cover (%) of all vascular plants. Sampling was carried out in mid-July of 1991 and repeated at approximately the same time in 1992. In 1994, these same plots were sampled each month fromMay to October. Seasonal patterns of herb layer dynamics were assessed for the complete 1994 data set, whereasinter-annual variability was based on plot data from 1991, 1992, and the July sample of 1994. There were nosignificant differences between watersheds for any sample year for any of the other herb layer characteristics measured, including herb layer cover, species richness, evenness, and diversity. Cover on WS4 decreased significantly from 1991 to 1992, followed by no change to 1994. By contrast, herb layer cover did not varysignificantly across years on WS3. Cover of the herbaceous layer of both watersheds increased from early in the growing season to the middle of the growing season, decreasing thereafter, with no significant differencesbetween WS3 and WS4 for any of the monthly cover means in 1994. Similar seasonal patterns found for herblayer cover—and lack of significant differences between watersheds—were also evident for species diversityand richness. By contrast, there was little seasonal change in herb layer species evenness, which was nearlyidentical between watersheds for all months except October. Seasonal patterns for individual species/speciesgroups were closely similar between watersheds, especially for Viola rotundifolia and Viola spp. Species richnessand species diversity were linearly related to herb layer cover for both WS3 and WS4, suggesting that spatialand temporal increases in cover were more related to recruitment of herb layer species than to growth of existingspecies. Results of this study indicate that there have been negligible responses of the herb layer to 6 yr of additions to WS3.