Confidence Interval for the Risk-Score Index

Risk-score indices are a simple, applicable, and easy-to-calculate tool for regression models, which can be used when computers are not available. The risk-score index is a partial summation of the rounded model coefficients that maintains essential properties of the model coefficients, such as their weight in the model and the correlation matrix. In a certain sense, the risk score can be viewed as a transformation into a pre-selected scale. The risk score is generally represented as a point estimate. Thus, the risk-score index is a categorical variable that relates each and every category uniquely to risk. The main argument of this paper is that the risk score, which is calculated as a partial summation of rounded beta coefficients, is a statistic, and, therefore, it has its own variance. This variance is divided into three factors—the original β-coefficients variances, the rounding-error variance, and the variance from the relations between these two factors. Since the variance of the score is typically not negligible, it is preferable to consider the confidence interval centered at the point estimate and not just the point estimate itself. By using the confidence interval for the risk score, one can quantify the accuracy of the score and also compare different scores, which otherwise is not always possible.