A latent variable model approach for assembling and scoring screening tests for dementia

In dementia studies, the diagnosis of dementia often relies on results of screening tests aimed at measuring various dimensions of cognitive functions. The current practice of scoring a screening test involves simply summing the correct responses from each item. However, this method may be imprecise and inefficient in the predictive power of the score for dementia. We propose a latent variable model approach for the scoring and item selection of such tests. We model the item responses to be random variables based on latent variables. We also model the disease outcomes to be a function of the latent variables. Maximum likelihood estimates are obtained by maximizing the joint likelihood functions of disease and the item responses over a specified distribution function for the latent variables. Variances of model parameters are estimated using a nonparametric bootstrap method. We illustrate the approach using a screening test for dementia from a community-based study.