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This was observed in the case study, and may affect the reliability and/or validity of results and predictions. To explore how missingness may affect the CART and BRT models, a simulation study was conducted, such that CART and BRT models were applied to smaller data sets with missing data inserted artificially. These are described following the results of the case study analysis. As noted earlier, the case study contained a very large amount of missing data. The overall proportion missing was 0.63. The missingness map (from the R package ��Amelia��,19 shown in figure 1, displays whether data is missing (grey) or present (black), for each case. Figure?1 Missingness map showing the amount of missing data in the case study. The horizontal axis indicates the learn more variables in the data set, and each individual in the study is a row in the y axis. Black indicates present data, grey indicates absent data. Results As an exploratory assessment to determine whether there was sufficient missingness to warrant an investigation, t tests and ��2 tests were used to assess whether the presence or absence of BMI, FEV1, FVC, FEV1/FVC, and concentration, influenced either the mean values of other variables (via a t test), or the expected count of a particular factor (via a ��2 test). Results indicated that consistent sets of variables were affected, suggesting a potential pattern or structure of missingness. Those variables affected are listed in table 1. These variables, and their mean values or expected counts, were reported to the industry collaborator to help explore the causes of missing data and consider down-weighting them in other analyses. Table?1 Variables affected by presence/absence of BMI, FEV1, FVC, FEV1/FVC and concentration The CART and BRT models were run as described in the Materials and methods section. The CART model obtained from the analysis of the case study data is represented in figure 2. The tree indicates that the type of data best predicts the proportion of missing data in an individual's record. There are three main classes of data type: medical (Type 1), follow-up medical (Type 2), and hygiene or environmental exposure (Types 3�C6). The missingness proportion for each type can be seen in the violin plot in online supplementary figure S1. The prediction from the CART model is such that when Type is 1 (medical data), there is a lower proportion of missing data (30%), compared with the right split, when data are of Type=2�C6, (repeated medical and environmental exposure; 74% missing data). Another split occurs within Type 1, where data from site 3 has less missing data (22%) compared to sites 1 and 2 (34%). Another split occurs based on Type 2 (repeated medical data) compared to Types 3�C6 (environmental exposure), where data of Type 2 has 64% missing data, and data of Types 3�C6 has 76% missing data.