A patient’s health information is generally fragmented across silos. Though it is technically feasible to unite data for analysis in a manner that underpins a rapid learning healthcare system, privacy concerns and regulatory barriers limit data centralization. Machine learning can be conducted in a federated manner on patient datasets with the same set of variables, but separated across sites of care. But federated learning cannot handle the situation where different data types for a given
 patient are separated vertically across different organizations. We call methods that enable machine learning model training on data separated by two or more degrees “confederated machine learning.” We built and evaluated a confederated machine
learning model to stratify the risk of accidental falls among the elderly. Significance. Access to a large amount of high quality data is possibly the most important factor for success in advancing medicine with machine learning and data science. However, valuable healthcare data are usually distributed across isolated silos, and there are complex operational and regulatory concerns. Data on patient populations are often horizontally separated,each other across different practices and health systems. In addition, individual patient data are often vertically separated, by data type, across her sites of care, service, and testing. We train a confederated learning model in a manner to stratify elderly patients by their risk of a fall in the next two years, using diagnoses, medication claims data and clinical lab test records of patients. Traditionally, federated machine learning refers to distributed learning on horizontally separated data (Yue Zhao, Meng Li, Liangzhen Lai, Naveen Suda, Damon Civin, Vikas Chandra 2018; Cano, Ignacio, Markus Weimer, Dhruv Mahajan, Carlo Curino, and Giovanni Matteo Fumarola 2016; H. Brendan McMahan, Eider Moore, Daniel Ramage, Seth Hampson, Blaise Agüera y Arcas 2016; Anon n.d.) . Algorithms are sent to different data silos (sometimes called data nodes) for training. Models obtained are aggregated for inference. Federated learning can reduce data duplication and costs associated with data transfer, while increasing security and shoring up institutional autonomy. (Geyer, R. C., Klein, T., Nabi, M. 2017; , (Yue Zhao, Meng Li, Liangzhen Lai, Naveen Suda, Damon Civin, Vikas Chandra 2018; al. 2015) (Geyer, R. C., Klein, T., Nabi, M. 2017; ). Notably, a patient's vertically separated data may span data types-for example, diagnostic, pharmacy, laboratory, and social services. Machine learning on vertically separated data has used a split neuron network (Praneeth et al. 2018 ) and homomorphic encryption (Praneeth et al. 2018; Stephen et al. 2017) . However, these new methods require either information communication at each computational cycle or state-of-art computational resource organization, which are usually impractical in many healthcare systems where support for data analysis is not the first priority, high speed synchronized computation resources are often not available, and data availability is inconsistent. To accelerate a scalable and collaborative rapid learning health system (Friedman et al. 2010; Mandl et al. 2014 ), we propose a confederated machine learning method that trains machine learning models on data both horizontally and vertically separated by jointly learning a high level representation from data distributed across silios (Qi et al. 2017; Zhang Xiao 2015; Zhai et al. 2014 ). This method does not require frequent information exchange at each training epoch nor state-of-the-art distributed computing infrastructures. As such, it should be readily implementable, using existing health information infrastructure. We demonstrate this approach by developing a model of accidental falls among people at least 65 years, a problem which causes approximately 50.7 deaths per 100,000 in the US annually (Anon 2019) . Women and men from 65 to 74 years old had a 12-month fall incident rate of 42.6 and 41.3 per 100, respectively; once over 74 years old, the incident rate climbed to 50.6 and 62.0 per 100 respectively, according to the 2008 National Health Interview Survey in 2008 (Verma et al. 2016 . Nationally, the direct medical costs attributable to falls is 34 billion dollars (Kramarow et al. 2015; Verma et al. 2016; Heinrich et al. 2010; Haasum Johnell 2017; Yang et al. 2016; Dollard et al. 2012; Overstall 1985; Lord et al. 2007 ). There are highly effective approaches to mitigating the risk of falls that could be selectively applied to individuals identified as being at high risk. These include medication adjustments, exercises, and home interventions (McMurdo et al. 2000; Kosse et al. 2013) . Multifactorial clinical assessment and management can reduce falls by more than 20 We train a confederated learning model to stratify elderly patients by their risk of a fall in the next two years, using horizontally and vertically separated diagnosis data, medication claims data and clinical lab test records of patients. The goal is to compare confederated learning with both centralized learning and traditional federated learning, and specifically test whether a confederated learning approach can simultaneously address horizontal and vertical separation. Currently, the clinical screening process generally involves asking patients 65 years old and above questions about their previous falls and walking balance. People who give positive answers to the question can be further assessed for their balance and gait (Panel on Prevention of Falls in Older Persons, American Geriatrics Society and British Geriatrics Society 2011). Though the guidelinesbased clinical assessment reduces falls, it is costly and time consuming to conduct large scale screening. A machine learning approach can stratify individuals by risk of fall, using their electronic health record data. We demonstrate that health data distributed across silos can be used to train machine learning models without moving or aggregating data, even when data types vary across more than one degree of separation. Compared with other methods for model training on horizontally and vertically separate data, this confederated learning algorithm does not require sophisticated computational infrastructure , such homomorphic encryption, nor frequent gradient exchange. We anticipate that this confederated approach can be extended to more degrees of separation. Other type of separation, such as separation by temporality , separation by insurance plan, separation by healthcare provider can all be potentially be explored using confederated learning strategy. One such example of additional degree of separation is a patient's diagnosis might be distributed with different healthcare providers or his/her medication information is with more than one pharmacy
a confederated learning method that train model from horizontally and vertically separated medical data  A "confederated" machine learning method that learns across divides in medical data separated both horizontally and vertically.