A Non-Parametric Approach to Scale Reduction for Uni-Dimensional Screening Scales

To select items from a uni-dimensional scale to create a reduced scale for disease screening, Liu and Jin (2007) developed a non-parametric method based on binary risk classification. When the measure for the risk of a disease is ordinal or quantitative, and possibly subject to random censoring, this method is inefficient because it requires dichotomizing the risk measure, which may cause information loss and sample size reduction. In this paper, we modify Harrell's C-index (1984) such that the concordance probability, used as a measure of the discrimination accuracy of a scale with integer valued scores, can be estimated consistently when data are subject to random censoring. By evaluating changes in discrimination accuracy with the addition or deletion of items, we can select risk-related items without specifying parametric models. The procedure first removes the least useful items from the full scale, then, applies forward stepwise selection to the remaining items to obtain a reduced scale whose discrimination accuracy matches or exceeds that of the full scale. A simulation study shows the procedure to have good finite sample performance. We illustrate the method using a data set of patients at risk of developing Alzheimer's disease, who were administered a 40-item test of olfactory function before their semi-annual follow-up assessment.