# MGHT: Statistical Methodology for Missing-Data Imputation in Food Composition Databases
## 2 Materials and Methods
### Food Composition Data  
There are several international bodies, organizations and projects working on food composition. One of them is EuroFIR (European Food Information Resource Network) AISBL, which is an international, non-profit association under the Belgian law [20]. Its purpose is to develop, publish and exploit food composition information and promote international cooperation and harmonization of standards to improve data quality, storage and access. One of the aims of the EuroFIR Network of Excellence [20] was to develop the standard \"Food data structure and format standard\" BS EN 16104:2012 [21], which can be used as a framework for compiling and disseminating FCD that is comparable and unambiguous with respect to the identity and description of foods, components and compositional values [20; 22]. Each EuroFIR member country has compiled one or more national FCDBs that are published online and are accessible by the public through the FoodEXplorer tool [23]. For the purpose of this study, we chose to collect data from the national FCDBs of 10 countries: Italy (IT), United Kingdom (UK), Switzerland (CH), Sweden (SE), Slovenia (SI), Belgium (BE), Denmark (DK), Netherlands (NL), United States of America (USA), and Canada (CA). In the process of collecting, we also considered the following key points:  
1. Choosing method type: As mentioned, there are several types of FCD with differing quality. Terms for documenting the method used to obtain a compositional value, including analysis, calculation and imputation, are presented in the EuroFIR Method Type Thesaurus [24]. In the thesaurus, the terms are organized in a hierarchy and for each method a short abbreviation with a full description used for classification is given. Since we are proposing a method for borrowing data for imputation of missing FCD between countries, it is also important that the data are relevant and genuine, therefore, we only included data whose method type is listed as:  
* \"A\" (Analytical result/s): The value is based on an analytical result or a statistic of multiple measurements of the same food sample (replicates). * \"AG\" (Analytical, generic): The value is known to be analytical, but no further information on the nature of analysis is available, whether the value derives from the same or different statistical distributions. 2. Choosing food groups: For this study, we decided to include the food groups: \"Fruits\", \"Vegetables\" and \"Meats\". 3. Choosing foods that belong to the selected food groups: In this stage of the study, we decided to include only simple, raw foods for the convenience of easily selecting the same foods from different countries, and because, generally, there more available data worldwide for simple, raw foods. Choosing nutrients: This step is highly dependent on the available data. Given the selections from the previous steps, we chose nutrients with the most data available. For the evaluation of the proposed methodology, for the food group \"Fruits\", the nutrients chosen are Sodium (Na) and Potassium (K); for the food group \"Vegetables\", Sodium (Na); and for the food group \"Meats', Protein (PROT). 5. Choosing countries: The last step is to manually choose specific countries for each of the selected food groups. For this purpose, we constructed a binary matrix for each nutrient in each food group. The matrix rows correspond to the selected foods belonging to one food group, the columns are the identification numbers of the national FCDBs in EuroFIR FCDB, \"\(1\)\" represents the presence and \"\(0\)\" the absence of the required nutrient value. Using this matrix, we can find the countries, i.e., the national FCDBs for which the methodology can be evaluated. After the data collection process, before assembling it all in one table, the last step is to ensure that all the values are in the same measure unit; if not, the needed unit conversions are made. Table 1 presents a binary matrix for the nutrient Potassium (K) in the food group \"Fruits\".