Comparison of Methods for Parameter Estimation in a Circular Linear Mixed Effect Model Incorporating the Diurnal Variation for Evaluating the Treatment Effects of Glaucoma Therapy

Glaucoma is the primary cause of vision loss in Japan. The most important glaucoma therapy is to decrease intraocular pressure (IOP) for preventing visual field defects in the pre-stage of vision loss. Considering a systematic diurnal variation of IOP, Kuwayama et al. (2006) proposed to use a circular linear mixed effect (CLME) model for evaluating the efficacy of therapy on IOP decrease for patients with normal tension glaucoma (NTG) and applied it to the data analysis in a clinical trial (Nipradilol trial) with 28 NTG patients. In this application, there occurred an issue that the parameter estimates were different depending on the method of estimation and the best method was not identified. We, therefore, compared six methods for parameter estimation (standard two-stage (STS) method, global two-stage (GTS) method, first order approximation (FOA) method, Laplacian approximation (LAP) method, Monte Carlo integration (MCI) method and Gaussian quadrature (GAUS) method) through a simulation experiment with the bias and square root of mean squared error as the criteria for evaluation. The GAUS method proved to be superior to others in realizing least bias and mean squared error under various simulation conditions, although it was most time consuming.