ABSTRACT
Longitudinal study designs have been widely used in clinical trials. The defining feature of a longitudinal study design is that the measurements of the response are recorded repeatedly over time for every subject in the study. In practice, the measurements are often recorded at the onset of a treatment and then at some key time points. In a longitudinal study design, the effectiveness of the treatment can be better evaluated by comparing change over time in responses. Moreover, each subject serves as its own control and the variability between subjects can be isolated, thus statistical analysis can focus more precisely on the treatment effect. In addition, along with the treatment as-
signment and the primary outcome response, many associated covariates that may have strong effect on the patient’s clinical response to the treatment are also measured repeatedly over time. Adjusting for these covariates properly in a randomization procedure can not only improve the efficiency of inference on the treatment effect, but also increase the probability of success without undermining the validity and integrity of the intended trial. There is a limited number of research papers on adaptive randomization procedures for longitudinal data. For example, Biswas and Dewanji [1] and Sutradhar, Biswas and Bari [29] extended the randomized play-the-winner (RPW) rule of Wei and Durham [36] to longitudinal binary data with and without covariates, respectively, and Sutradhar and Jowaheer [30] extended the RPW to longitudinal count data. These works are confined to the urn model and only to discrete longitudinal data. Huang, Liu, and Hu [15] proposed a general framework for longitudinal covariate-adjusted response-adaptive (LCARA) randomization procedures, which utilize all available information and dynamically update the allocation probability on the basis of all previous patients’ treatment assignments, longitudinal covariates and responses, and the current patient’s baseline covariate vector. In particular, the randomization probabilities for the next patient are specified as a function of the fitted conditional expectations of the outcomes given the covariates and the treatments. This type of adaptive design is closely related to the so-called multi-armed bandit problem and the optimal dynamic treatment regime [4, 18] in computer science and medical research, where one aims to carry out the optimal dynamic treatment by learning from past data.
