Information on coverage was available from 131 countries: 16 countries have no services (zero coverage), 85/131 (64.9%) countries have poor (≤10%) coverage, 30/131 (22.9%) countries have better (>10%) coverage.
2
Thirty-six service-related (
Table 1) and 17 socioeconomic and demographic critical factors were considered (
Table 2). At first, all 53 critical factors were included in the CART. However, conflicting information was found in the following service-related critical factors:
national referral guidelines for low vision services and
standards of practice guidelines for low vision service. These two variables were found to have a negative impact on coverage of low vision services, where the authors had expected the reverse to be true. There may be other factors affecting these two variables and coverage that were not measured. It was determined that these two factors may not be directly linked to coverage and were thus removed from the CART analysis, leaving 51 critical factors to be included in the CART model. These two variables are an example of data dredging.
The critical success factors (adjusted for all service-related, socioeconomic, and demographic variables) are exemplified in the form of a decision tree by the CART (
Fig. 1): the first box at the very top of the CART tree displays the outcome—coverage. To avoid repetition, the results of one side of the outcome are shown; that is, no or poor (≤ 10%) coverage. The boxes in gray are the important predictors to the outcome. Level 1 is the most important predictor followed by levels 2 and 3. The first predictor at level 1 splits the tree roots (parent node) into three branches (child nodes) and so on. Each of these branches then becomes a parent node and splits into further branches until the CART tree stops growing and the node terminates (e.g., node 13). Each node displays: the node number, the total number of countries, and the percentage of countries with poor (≤10%) coverage.
Six critical success factors were found by the CART to be significant predictors of coverage. The most important factor identified was the proportion of children obtaining devices when prescribed (χ2 = 44.0; P < 0.0001), followed by level 2 predicators, namely percentage of population urbanized (χ2 = 14.5; P = 0.002), monodisciplinary versus multidisciplinary care (χ2 = 4.7; P = 0.03), and the number of rehabilitation workers per 10 million of population (χ2 = 4.5; P = 0.034). The third level predictors included private expenditure on health as percentage of total expenditure on health (χ2 = 14.6; P = 0.015) and fully funded by government (χ2 = 6.0; P = 0.014).
In the first branch, where there are a higher percentage of children obtaining devices but less urbanization (most people in many countries live in rural areas), the proportion of countries with poor coverage is 78.9%. Furthermore, if countries have either lower (≤35.5%) or higher (>43.6%) private expenditure on health, then the proportion of countries with poor coverage is both 100%. This denotes that countries with the above characteristics will have poor coverage of low vision services. Examples of countries in these nodes included Guyana, the Gambia, Croatia, India, Guatemala, and the Dominican Republic. On the other hand, in more urbanized countries, if services were fully funded by government, the likelihood of that country having poor coverage is reduced to 0%. Countries classified under this node were UK (Wales), The Netherlands, Taiwan, Sweden, and Norway.
Where there are a lower proportion of children with access to low vision devices and only monodisciplinary care, the proportion of countries with poor coverage is 68.8%. Sri Lanka, Laos, South Africa, Bahrain, and Argentina are examples of countries in this category.
Nodes 7, 3, and 9 have been displayed by the CART as missing nodes. Unlike logistic regression, where variables with missing data are excluded from the analysis, the CART model groups missing data with the predictor or category it is most similar or highly related to and displays them as surrogate nodes. Therefore, in this instance, the CART tree indicates that countries in node 7 all have poor coverage and these countries are related to the proportion of children obtaining devices when prescribed and the predictor monodisciplinary versus multidisciplinary care. Examples of countries under node 7 are Tunisia, Namibia, Liberia, Gabon, and East Timor.
Node 8 shows that the proportion of countries with poor coverage is related to countries having ≤3 rehabilitation workers per 10 million and the proportion of children obtaining devices when prescribed. Benin, Armenia, Cambodia, Ghana, and Cameroon were some of the countries here, while the Czech Republic, Germany, Cook Islands, and Haiti were a few examples of countries under node 9 where the proportion of countries with poor coverage is related to an unknown number of rehabilitation workers.
Finally, cross validation analysis indicated that the predictive performance of this CART model was 90.1% with a sensitivity of 93.1% and specificity of 80.0%. This implies that very few countries have been incorrectly classified in their respective categories of coverage.