Ensemble Kalman methods constitute an increasingly important tool in both state and parameter estimation problems. Their popularity stems from the derivative-free nature of the methodology which may be readily applied when computer code is available for the underlying state-space dynamics (for state estimation) or for the parameter-to-observable map (for parameter estimation). There are many applications in which it is desirable to enforce prior information in the form of equality or inequality constraints on the state or parameter. This paper establishes a general framework for doing so, describing a widely applicable methodology, a theory which justifies the methodology, and a set of numerical experiments exemplifying it.

Type 2 diabetes leads to premature death and reduced quality of life for 8% of Americans. Nutrition management is critical to maintaining glycemic control, yet it is difficult to achieve due to the high individual differences in glycemic response to nutrition. Anticipating glycemic impact of different meals can be challenging not only for individuals with diabetes, but also for expert diabetes educators. Personalized computational models that can accurately forecast an impact of a given meal on an individual’s blood glucose levels can serve as the engine for a new generation of decision support tools for individuals with diabetes. However, to be useful in practice, these computational engines need to generate accurate forecasts based on limited datasets consistent with typical self-monitoring practices of individuals with type 2 diabetes. This paper uses three forecasting machines: (i) data assimilation, a technique borrowed from atmospheric physics and engineering that uses Bayesian modeling to infuse data with human knowledge represented in a mechanistic model, to generate real-time, personalized, adaptable glucose forecasts; (ii) model averaging of data assimilation output; and (iii) dynamical Gaussian process model regression. The proposed data assimilation machine, the primary focus of the paper, uses a modified dual unscented Kalman filter to estimate states and parameters, personalizing the mechanistic models. Model selection is used to make a personalized model selection for the individual and their measurement characteristics. The data assimilation forecasts are empirically evaluated against actual postprandial glucose measurements captured by individuals with type 2 diabetes, and against predictions generated by experienced diabetes educators after reviewing a set of historical nutritional records and glucose measurements for the same individual. The evaluation suggests that the data assimilation forecasts compare well with specific glucose measurements and match or exceed in accuracy expert forecasts. We conclude by examining ways to present predictions as forecast-derived range quantities and evaluate the comparative advantages of these ranges.

ObjectiveTo study the effect on patient cohorts of mapping condition (diagnosis) codes from source billing vocabularies to a clinical vocabulary.Materials and MethodsNine International Classification of Diseases, Ninth Revision, Clinical Modification (ICD9-CM) concept sets were extracted from eMERGE network phenotypes, translated to Systematized Nomenclature of Medicine - Clinical Terms concept sets, and applied to patient data that were mapped from source ICD9-CM and ICD10-CM codes to Systematized Nomenclature of Medicine - Clinical Terms codes using Observational Health Data Sciences and Informatics (OHDSI) Observational Medical Outcomes Partnership (OMOP) vocabulary mappings. The original ICD9-CM concept set and a concept set extended to ICD10-CM were used to create patient cohorts that served as gold standards.ResultsFour phenotype concept sets were able to be translated to Systematized Nomenclature of Medicine - Clinical Terms without ambiguities and were able to perform perfectly with respect to the gold standards. The other 5 lost performance when 2 or more ICD9-CM or ICD10-CM codes mapped to the same Systematized Nomenclature of Medicine - Clinical Terms code. The patient cohorts had a total error (false positive and false negative) of up to 0.15% compared to querying ICD9-CM source data and up to 0.26% compared to querying ICD9-CM and ICD10-CM data. Knowledge engineering was required to produce that performance; simple automated methods to generate concept sets had errors up to 10% (one outlier at 250%).DiscussionThe translation of data from source vocabularies to Systematized Nomenclature of Medicine - Clinical Terms (SNOMED CT) resulted in very small error rates that were an order of magnitude smaller than other error sources.ConclusionIt appears possible to map diagnoses from disparate vocabularies to a single clinical vocabulary and carry out research using a single set of definitions, thus improving efficiency and transportability of research.

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