Maximum likelihood inference for left-censored HIV RNA data

Left-censored data are characteristic of many bioassays due to inherent limit of detection and limit of quantitation (LOQ) in the assays. This paper examines how the left-censoring of plasma HIV RNA measurements, collected for the Hemophilia Growth and Development Study, affects the quantification of viral load and the assessment of its association with a continuous or dichotomous outcome. Data analyses using maximum likelihood estimation are compared to analyses where the LOQ or LOQ/2 value is substituted for the left-censored observations, and also to other methods like multiple imputation. A Gaussian distribution is assumed for the log-transformed plasma HIV RNA data, and simulations are used to explore the sensitivity of the results to changes in the model parameters. The robustness of the estimators is also investigated when the data are generated from a mixture of two Gaussian distributions. Maximum likelihood is in general the least biased method. However, multiple imputation assuming a censored Gaussian imputation model and substituting the censored values with the expectation of its conditional predictive distribution are also competitive to maximum likelihood, and may be appealing because of their simpler computational algorithms.