Likelihood testing populations modeled by autoregressive process subject to the limit of detection in applications to longitudinal biomedical data

Dependent and often incomplete outcomes are commonly found in longitudinal biomedical studies. We develop a likelihood function, which implements the autoregressive process of outcomes, incorporating the limit of detection problem and the probability of drop-out. The proposed approach incorporates the characteristics of the longitudinal data in biomedical research allowing us to carry out powerful tests to detect a difference between study populations in terms of the growth rate and drop-out rate. The formal notation of the likelihood function is developed, making it possible to adapt the proposed method easily for various different scenarios in terms of the number of groups to compare and a variety of growth trend patterns. Useful inferential properties for the proposed method are established, which take advantage of many well-developed theorems regarding the likelihood approach. A broad Monte-Carlo study confirms both the asymptotic results and illustrates good power properties of the proposed method. We apply the proposed method to three data sets obtained from mouse tumor experiments.