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Harmonic Mean Point Processes: Proportional Rate Error Minimization for Obtundation Prediction

In healthcare, the highest risk individuals for morbidity and mortality are rarely those with the greatest modifiable risk. By contrast, many machine learning formulations implicitly attend to the highest risk individuals. We focus on this problem in point processes, a popular modeling technique for the analysis of the temporal event sequences in electronic health records (EHR) data with applications in risk stratification and risk score systems. We show that optimization of the log-likelihood function also gives disproportionate attention to high risk individuals and leads to poor prediction results for low risk individuals compared to ones at high risk. We characterize the problem and propose an adjusted log-likelihood formulation as a new objective for point processes. We demonstrate the benefits of our method in simulations and in EHR data of patients admitted to the critical care unit for intracerebral hemorrhage.