Framework for constructing an optimal weighted score based on agreement

In many medical studies, questionnaires or instruments with item ratings are often used to measure the health outcomes reflecting the disease status. Therefore, combining these item ratings to derive a score that reflects the disease status is an important issue. This paper proposes a new weighted method with the weights determined by maximizing the broad sense agreement Peng et al. [L. Peng, R. Li, Y. Guo, and A. Manatunga, A framework for assessing broad sense agreement between ordinal and continuous measurements, J. Am. Stat. Assoc. 106 (2011), pp. 1592-1601.] between the new score and the disease status measured by an ordinal scale. Theoretical and simulation results demonstrate the validity of our proposed optimal weights. We illustrate our method via an application to a post-traumatic stress disorder (PTSD) study.