LA EVALUACIÓN INSTITUCIONAL EN LA ENSEÑANZA OBLIGATORIA EN PARAGUAY
9.3. Organización de la evaluación
In this section, and the following two sections, we give a more detailed analysis of the strength of some of the relation the MDT BN model. The main challenge of applying the technique described above is to present the information in a manner that can be understood by a domain expert.
In the MDT BN model, the variable Age connects Organ and Type with two links; we start, in this section, by investigating the impact of Age. In relation to Age →Organ, the question that clinicians in HPB Centre are interested in is whether changes have occurred in the cancerous organs according to the age of cancer patients (see Table 5.8), and in relation to Age →Type, the question of their interest is whether changes have
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occurred in the types (Benign, Malignant and Unknown) according the age of cancer patients.
Figure 7-6 shows a simple plot of the number of patients per cancerous organ for each of the seven age groups. Using the classical statistical approach, the clinicians mainly focus on these numbers to answer to a clinical question. However, the numbers of patients for two different age groups in any of the organs are not sufficient to estimate a difference in the particular organ between the two age groups; for a reliable estimate, both the values and the uncertainty must be considered, as our method does.
Figure 7-6 Number of patients per cancerous organ for each of the seven age groups
After calculating BFs (see Table 7-9) for the link Age →Organ, we analyse these values to assess: (1) changes that occur in each organ compared with other age groups in relation to a particular age group and (2) change that occurs in each organ for an older age group compared with younger age groups. Figure 7-7 (a) and (b) represent comparisons (1) and (2), respectively. In Figure 7-7 (a), we take the geometric mean of the BFs that result from the hypothesis tests, which each corresponds to one of the followings: 74 92 85 87 84 73 81 107 91 82 98 93 102 85 21 21 24 34 35 40 35 9 2 11 14 15 16 15 0 50 100 150 200 250 Under 46 46-54 >54-60 >60-66 >66-71 >71-77 77+ N u mb er of p ati en ts Age group Gallbladder Bile duct Liver Pancreas
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• The probability estimated for the corresponding organ is higher for each successive older age group compared with the particular age group;
• The probability estimated for the corresponding organ is higher for the age group than each younger age group;
To calculate the BF of interest, each hypothesis test for the youngest ‘under 46’ age group checks (a), whereas each hypothesis test for any other age group checks either (a) or (b). For example, if our interest is in combining the BFs for the 46-54 age group in the pancreas then the hypothesis tests we carry out are: ‘46-54’ > ‘under 46’ , ‘>54-60’
> ‘46-54’ , ‘>60-66’ > ‘46-54’ , ‘>66-71’ > ’46-54’ , ‘>71-77’ > ‘46-54’ and ‘77+’ > ‘46-54’.
Figure 7-7 (b) includes the followings features:
• A BF value of 1 for the ‘under 46’ age group. This is because the youngest age group is the starting point for comparison situation (2) change that occurs in each organ for an older age group compared with younger age groups.
• The calculated BF of the test (i.e. ‘46-54’ > ‘under 46’) for 46-54 age group.
The geometric mean of the BFs from 2 or more hypothesis tests for the remaining age groups. Each of these tests checks if the probability estimated for the corresponding organ is higher for the age group than for each younger age group. Thus, for the >54-60 age group we calculate the geometric mean of the BFs from the hypothesis tests: ‘>54-
60’ > ‘under 46’, ‘>54-60’ > ‘46-54’ and ‘46-54’ > ‘under 46’.
Both of the graphs (a) and (b) in Figure 7-7 represent the geometric mean of BFs in a log scale. A value greater than ‘1’ indicates evidence about an increase whereas a value which is lower than ‘1’ indicates evidence about a decrease. In particular, Figure 7-7 (a) demonstrates that gallbladder and bile duct cancers for older age groups are higher than younger age groups. In particular, considering the calculated means, we get the highest evidence (mean of BFs is 19.08) for concluding that gallbladder cancer for the older age groups is a significantly higher proportion than for the 46to54 age group. Also we get
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an almost equal strength of evidence regarding a change when bile duct cancer for each age group is compared with others. Figure 7-7 (b) further demonstrates that the bile duct cancer is consistently higher for the older age groups than younger age groups.
Figure 7-7 Geometric mean of BFs to assess a) changes that occur in each organ for other age groups in relation to a particular age group and b) a change that occurs in each organ for an older
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In comparison, Figure 7-6 makes it difficult to assess the strength of influence Age has on Organs, and consequently, to find if changes have occurred in the cancerous organs according to the age of cancer patients. But our analyses show that the link captures the impact between the variables properly. The liver and pancreas cancers decrease for older age groups (i.e. negatively influenced by the older age groups) whereas the bile duct and gallbladder cancers increase for older age groups (i.e. positively influenced by the older age groups).
Similar to the Age → Organ, we follow the same procedure to assess two comparisons for Age → Type link: (1) changes that occur in each type of cancer for other age groups in relation to a particular age group and (2) a change that occurs in each type of cancer for an older age group when compared with all younger age groups. Figure 7-9 (a) and (b) represent comparisons (1) and (2), respectively. The BFs used for the analyses are presented in Appendix B.1.
Figure 7-9 (a) demonstrates that the proportion of malignant cancer is higher in older age groups than younger age groups. In particular, we obtain the highest evidence (a geometric mean of 736.4) to conclude that the proportion of malignant cancer for the older age groups is significantly higher than under 46 age group. Also, the malignant cancer for the older age groups is higher than for the 46to54 age group (a geometric mean of 313.4). Evidence in relation to the proportion of benign cancer shows that this is lower for the older age groups than younger age groups.
Figure 7-9 (b) demonstrates that apart from the age groups 46-54 and 77+ malignant cancer is significantly higher (a geometric mean of >100) for each of the five other age groups compared to the corresponding younger age groups. In both graphs, we obtain only weak evidence for a change in an unknown cancer for older age groups compared to younger age groups.
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Figure 7-8 Number of patients per cancer type for each of the seven age groups
Figure 7-9 Geometric mean of BFs to assess a) changes that occur in each type of cancer for other age groups in relation to a particular age group and b) a change that occurs in each type of cancer
for an older age group when compared with younger age groups
137 105 72 71 64 54 64 72 96 122 156 158 170 142 2 5 8 6 5 7 10 0 50 100 150 200 250 Under 46 46-54 >54-60 >60-66 >66-71 >71-77 77+ N u mb er of p ati en ts Age group Unknown Malignant Benign
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