A joint model of survival outcome and covariates subject to measurement errors and detection limits

Music City Center 

Biomarkers are measured longitudinally with measurement errors and detection limits, associating these variables with a survival outcome needs to take both into account. We propose a joint model using linear mixed effects models and Cox proportional hazard model. Parameters are found with Monte-Carlo Expectation Maximization method with Newton-Raphson steps. The model is compared with the ideal model of assuming measurement errors are known, the naïve model of ignoring the measurement errors and the two-step approach. Simulations show that the proposed model has the lowest bias in estimating the coefficient on the left-censored biomarkers comparing to the last two methods when the censoring proportion is high on the markers, and it has lower standard errors than the two-step approach on the parameter across the censoring proportions. These three methods were applied to a real-world data from longitudinal study of oncogenic HPV infections among HIV positive women to find the associations with the plasma HIV viral load and CD4+ cell count. The topic will be of interest to researchers working at the intersection of statistics and biomedical sciences.

longitudinal data

measurement error

detection limit

Cox proportional hazard model

joint model

Monte Carlo Expectation-Maximization 

Biometrics Section