A comparative investigation of methods for longitudinal data with limits of detection through a case study

The statistical analysis of continuous longitudinal data may be complicated since quantitative levels of bioassay cannot always be determined. Values beyond the limits of detection (LOD) in the assays may not be observed and thus censored, rendering complexity to the analysis of such data. This article examines how both left-censoring and right censoring of HIV-1 plasma RNA measurements, collected for the study on AIDS-related Non-Hodgkin’s lymphoma (AR-NHL) in East Africa, affects the quantification of viral load and explores the natural history of viral load measurements over time in AR-NHL patients receiving anticancer chemotherapy. Data analyses using Monte Carlo EM algorithm (MCEM) are compared to analyses where the LOD or LOD/2 (left censoring) value is substituted for the censored observations, and also to other methods such as multiple imputation, and maximum likelihood estimation for censored data (generalized Tobit regression). Simulations are used to explore the sensitivity of the results to changes in the model parameters. In conclusion, the antiretroviral treatment was associated with a significant decrease in viral load after controlling the effects of other covariates. A simulation study with finite sample size shows MCEM is the least biased method and the estimates are least sensitive to the censoring mechanism.