Sequential probability ratio tests for generalized linear mixed models

The sequential probability ratio test (SPRT) is a hypothesis testing procedure, which evaluates data as it is collected. The original SPRT was developed by Wald for one-parameter families of distributions and later extended by Bartlett to account for nuisance parameters. We adapt Bartlett's SPRT to Generalized Linear Mixed Models (GLMM), in which the observations are non-identically and non-independently distributed and illustrate the approach taken with two applications. In the first application, we incorporate a Poisson GLMM into sequential procedure to design a multicenter randomized clinical trial that compares two preventive treatments for surgical site infections. In the second application, we incorporate a Negative Binomial spatial GLMM into sequential procedure to design a pest assessment protocol. We also consider a generative spatial model in the context of sequential procedures as an alternative to spatial GLMMs.