We would like to thank Dr. Freundlich and colleagues for their informed comments regarding our study. The concerns regarding the lack of adjusting the analysis to reflect serum pH, serum lactate, and the cationic difference between calcium gluconate and calcium chloride are points well taken. Serum pH does impact free calcium levels through ionic coupling with bicarbonate. In vivo this equilibration occurs very quickly. Thus measured iCa 2+ levels reliably reflect available calcium stores unless the pH is changing very rapidly. Error can be introduced into iCa 2+ measurements if samples are stored for a long period of time before being analyzed. In refrigerated samples, the pH generally drops and the measured iCa 2+ will be falsely elevated whereas the opposite occurs in frozen samples. All of the labs we report were from fresh samples. Lactate is known to bind calcium similar to

Objective This study aimed to develop and validate a claims-based, machine learning algorithm to predict clinical outcomes across both medical and surgical patient populations. Methods This retrospective, observational cohort study, used a random 5% sample of 770,777 fee-for-service Medicare beneficiaries with an inpatient hospitalization between 2009–2011. The machine learning algorithms tested included: support vector machine, random forest, multilayer perceptron, extreme gradient boosted tree, and logistic regression. The extreme gradient boosted tree algorithm outperformed the alternatives and was the machine learning method used for the final risk model. Primary outcome was 30-day mortality. Secondary outcomes were: rehospitalization, and any of 23 adverse clinical events occurring within 30 days of the index admission date. Results The machine learning algorithm performance was evaluated by both the area under the receiver operating curve (AUROC) and Brier Score. The risk model demonstrated high performance for prediction of: 30-day mortality (AUROC = 0.88; Brier Score = 0.06), and 17 of the 23 adverse events (AUROC range: 0.80–0.86; Brier Score range: 0.01–0.05). The risk model demonstrated moderate performance for prediction of: rehospitalization within 30 days (AUROC = 0.73; Brier Score: = 0.07) and six of the 23 adverse events (AUROC range: 0.74–0.79; Brier Score range: 0.01–0.02). The machine learning risk model performed comparably on a second, independent validation dataset, confirming that the risk model was not overfit. Conclusions and relevance We have developed and validated a robust, claims-based, machine learning risk model that is applicable to both medical and surgical patient populations and demonstrates comparable predictive accuracy to existing risk models.

The recently proposed Highly Optimized Tolerance (H.O.T.) model [Carlson & Doyle, 1999, 2000], which aims to describe the statistics of robust complex systems in uncertain environments, is compared with data from the Western United States (W.S.C.C.) power distribution system. We use for comparison a 15-year record of all power outages occurring on the grid, measured in the size of megawatts lost and the number of customers without service. In applying the model to the power grid data, we find that the problem of determining how the resources in the system scale with event size is nontrivial given the assumptions of the model and the information about how the power grid actually operates. Further, we observe that the model agrees closely with the W.S.C.C. data for the megawatts but not the customers, and consequently propose that the assumption in the model of optimal resource distribution is not valid in general when more than one measure of event size is used. A modified H.O.T. model which allows for resource misallocation is introduced and we find that this model can be made to fit both data sets reasonably well.

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