A probabilistic model to investigate the properties of prognostic tools for falls

Background: Falls are a prevalent and burdensome problem in the elderly. Tools for the assessment of fall risk are fundamental for fall prevention. Clinical studies for the development and evaluation of prognostic tools for falls show high heterogeneity in the settings and in the reported results. Newly developed tools are susceptible to over-optimism. Objectives: This study proposes a probabilistic model to address critical issues about fall prediction through the analysis of the properties of an ideal prognostic tool for falls. Methods: The model assumes that falls occur within a population according to the Greenwood and Yule scheme for accident proneness. Parameters for the fall rate distribution are estimated from counts of falls of four different epidemiological studies. Results: We obtained analytic formulas and quantitative estimates for the predictive and discriminative properties of the ideal prognostic tool. The area under the receiver operating characteristic curve (AUC) ranges between about 0.80 and 0.89 when prediction on any fall is made within a follow-up of one year. Predicting on multiple falls results in higher AUC. Conclusions: The discriminative ability of current validated prognostic tools for falls is sensibly lower than what the proposed ideal perfect tool achieves. A sensitivity analysis of the predictive and discriminative properties of the tool with respect to study settings and fall rate distribution identifies major factors that can account for the high heterogeneity of results observed in the literature.