Estimation Methods for Data Subject to Detection Limits

Abstract

Data subject to detection limits appear in a wide variety of studies. Data subject to detection limits are usually left-censored at the detection limit, often due to limitations in the measurement procedure being used. This thesis addresses three issues common to the analysis of data subject to detection limits. The first of these is the estimation of the limit of detection using repeated measurements from known analyte concentrations. An innovative change-point model is proposed to more accurately model the standard deviation of measured analyte concentrations, resulting in improved estimation of the limit of detection. The proposed methodology is applied to copy number data from an HIV pilot study. The second topic concerns estimation using generalized linear models when multiple covariates are subject to a limit of detection. We propose a Monte Carlo version of the EM algorithm similar to that in Ibrahim, Lipsitz, and Chen to handle a large number of covariates subject to detection limits in generalized linear models. Censored covariate values are sampled using the Adaptive Rejection Metropolis Algorithm of Gilks, Best, and Tan. This procedure is applied to data from the National Health and Nutrition Examination Survey (NHANES), in which values of urinary heavy metals are subject to a limit of detection. Through simulation studies, we show that the proposed approach can lead to a significant reduction in variance for parameter estimates in these models, improving the power of such studies. The third and final topic addresses the joint modeling of longitudinal and survival data using time-varying covariates that are both intermittently missing and subject to a limit of detection. The model is motivated by data from the Multicenter AIDS Cohort Study (MACS), in which HIV+ subjects have viral load and CD4 cell counts measured at repeated visits along with survival data. The viral load data is subject to both left-censoring due to detection limits (17%) and intermittent missingness (27%). A Bayesian analysis is conducted on the MACS data using the proposed joint model. The proposed method is shown to improve the precision of estimates when compared to alternative methods.