Effective clinical decision procedures must balance multiple competing objectives such as time-to-decision, acquisition costs, and accuracy. We describe and evaluate POSEIDON, a data-driven method for PrOspective SEquentIal DiagnOsis with Neutral zones to individualize clinical classifications. We evaluated the framework with an application in which the algorithm sequentially proposes to include cognitive, imaging, or molecular markers if a sufficiently more accurate prognosis of clinical decline to manifest Alzheimer's disease is expected. Over a wide range of cost parameter data-driven tuning lead to quantitatively lower total cost compared to ad hoc fixed sets of measurements. The classification accuracy based on all longitudinal data from participants that was acquired over 4.8 years on average was 0.89. The sequential algorithm selected 14 percent of available measurements and concluded after an average follow-up time of 0.74 years at the expense of 0.05 lower accuracy. Sequential classifiers were competitive from a multi-objective perspective since they could dominate fixed sets of measurements by making fewer errors using less resources. Nevertheless, the trade-off of competing objectives depends on inherently subjective prescribed cost parameters. Thus, despite the effectiveness of the method, the implementation into consequential clinical applications will remain controversial and evolve around the choice of cost parameters.