Chapter 6 CONSTRUCTING MODELS FOR PREDICTING ADHERENCE RISK
6.3 Construction of a Bayesian Network with the Ontology
Prior Probability Class
hasProbValue data Double
hasVariable instance of Variable
hasState instance of State
hasCondition instance of Condition Condition Probability Class
hasProbValue data Double
hasVariable instance (Variable)
hasState instance of State
hasCondition instance of Condition Table 6.1: Prior Probability class description
6.2.2.5 The Condition Class
The Condition class was introduced in the SWAP-Uncertainty ontology [49] [115]. This class is very useful for the extension of the TB adherence ontology as it allows for multiple states of influencing variables to be added to ConditionProbability. This made it easier to explicitly declare all possible condition probabilities that are associated with a variable represented in the BN. The condition class has two object properties: hasVariable and hasState. The hasVariable property links the condition to the influencing variable and the hasState links it to the corresponding state that the condition is defining.
6.3 CONSTRUCTION OF A BAYESIAN NETWORK
appropriate belief network structure. The ontology will be queried to select the list of influencing factors that are required to compose the list of the root nodes and their states. The query below is used to select the factors required for the network construction, based on the narratives given in the above paragraph.
Decision Network Query:
Personal_Attitude and (isAssertedNegInfFactorBy some (ClinicalStudyEvidence and ((isCarriedOutAt value SouthAfrica) and (isDocumentedAs value Naidoo2013))))
For a set of factors selected through querying, the combined process of translating the result into nodes and states, and the identification of the parent node of each factor will produce the primitives required for constructing a BN model. Another query will be used to generate the sets of parent nodes for these factors. The queries below are used to generate the parent node for the Gender Class. The result of the query shows that Gender class is dependent on WorkingCondition class. The query returns UnfavourableWorkingCondition, an independent variable for Male instance of Gender class.
Interdependency Query:
TABInfluencingFactor AND inverse hasIndependentFactor (Interdependency AND hasDependentFactor value “Male”) OR TABInfluencingFactor AND inverse hasIndependentFactor (Interdependency AND hasDependentFactor value “Female”)
Table 6.2 (below) shows the combined results for the example case, using the combination of queries presented above. The table consists of the selected nodes/variables, states and parent node that will be used for the construction of the BN network structure. The classes of the selected factors become the node and the selected instances become the states. The class of the independent
factor generated from the Interdependency Query becomes the parent node, while its instances become the state of that node.
Node/Variable State Parent Node
Comment
Gender Male
Female
-
Depression Depression-True Depression-False
-
Emotion NegativeEmotion PositiveEmotion
-
TobaccoUse TobaccoAbuse NonTobaccoUse
-
AlcoholConsumption AlcoholAbuse NonAlcoholUse
-
WorkingCondition FavourableWorkingCondition
UnfavourableWorkingCondition Parent node of Gender node Table 6.2: Selected influencing factors for the BN model
Figure 6.4 shows how the example network will be represented in the extended ontology. The BayesianNetwork instance, created for the example case, is the South_Africa_TAB_BDN. This instance has hasVariable relationship with six Variable instances namely Gender, Depression, Emotion, AlcoholConsumption, TobaccoUse and WorkingCondition. Each of the Variable instances has a “hasState” relationship with its sets of states. For example, the Gender node has two discrete states, namely “Male” and “Female”.
Figure 6.4: BN model representation using the extended ontology
A hypothesis “TAB” variable is also created to represent the state associated with the behaviour of a patient that determines his/her decision to take drugs. The TAB node represents the mental state of a patient that determines his/her decision to take drugs. To form a BN structure as shown in Figure 6.5, the Variables instances become parent nodes of the TAB node, except the Working Condition which is the parent node to Gender node.
Figure 6.5: Example decision network model
It is important to note the causal relationship between Working Condition node and the Gender node. According to Daniel et al, 2005 [41], unfavourable working conditions, such as long working hours and manual labour, have a negative influence on adherence behaviour of male TB patients. Poor adherence behaviour of male TB patients is due to their unfavourable working conditions.
The ProbabilityObject class defines the interdependency between the variables as well as the probability of each of the variable states. This will form the structure of the BN for the example case. Firstly the PriorProbability for the parent nodes is defined with their properties. Table 6.3 below shows the instances of PriorProbability that are defined with the values, and linked with the corresponding variables and states. The values in the tables are manually inserted in the ontology as an example implementation of South Africa.
Prior Probability Table
Instance hasVariable hasState hasProValue
WoC_FA WorkingCondition FavourableWC 0.20 WoC_UF WorkingCondition UnfavourableWC 0.80
Dep_DE Depression Depression-True 0.10
Dep_ND Depression Depression-False 0.90
Emo_PO Emotion PositiveEmotion 0.85
Emo_NE Emotion NegativeEmotion 0.15
AlC_AA AlcoholConsumption AlcoholAbuse 0.60 AlC_NA AlcoholConsumption NonAlcoholUse 0.40
ToU_TA TobaccoUse TobaccoAbuse 0.55
ToU_TN TobaccoUse TobaccoNonAbuse 0.45
Table 6.1: Table showing the instances of PriorProbability for the example case
Secondly, the conditions that determine the relationship of the factors nodes to the TAB and Gender nodes are defined in the Condition class, see Table 6.4 below. Instances are defined under the Condition class and linked to their variables and states
Condition Table
Instance hasVariable hasState
GEN_WoC_FA WorkingCondition FavourableWC
GEN_WoC_UF WorkingCondition UnfavourableWC
TAB_Gen_MA Gender Male
TAB_Gen_FE Gender Female
TAB_Dep_DE Depression Depression-True
TAB_Dep_ND Depression Depression-False
TAB_Emo_PO Emotion PositiveEmotion
TAB_Emo_NE Emotion NegativeEmotion
TAB_AlC_AA AlcoholConsumption AlcoholAbuse TAB_AlC_NA AlcoholConsumption NonAlcoholUse
TAB_ToU_TA TobaccoUse TobaccoAbuse
TAB_ToU_TN TobaccoUse TobaccoNonAbuse
Table 6.2: Table showing the instances of Condition for the example case
Thirdly and lastly, the instances of ConditionProbability class are defined for all the variables that influence the TAB variable. See Table 6.5 below. The OWL representation of the example case is included in the ontology presented in OWL format (see Appendix 1).
Condition Probability Table
Instance hasVariable hasState hasProbValue hasCondition GEN_CM_1 WorkingCondition FavourableWC 0.30 GEN_WoC_FA GEN_CF_1 WorkingCondition FavourableWC 0.99 GEN_WoC_FA GEN_CM_2 WorkingCondition UnfavourableWC 0.70 GEN_WoC_UF GEN_CF_2 WorkingCondition UnfavourableWC 0.01 GEN_WoC_UF
TAB_CP_1 Gender Male 0.70 TAB_Gen_MA
TAB_CG_1 Gender Male 0.30 TAB_Gen_MA
TAB_CP_2 Gender Female 0.15 TAB_Gen_FE
TAB_CG_2 Gender Female 0.85 TAB_Gen_FE
TAB_CP_3 Depression Depressed 0.80 TAB_Dep_DE
TAB_CG_3 Depression Depressed 0.20 TAB_Dep_DE
TAB_CP_4 Depression NotDepressed 0.01 TAB_Dep_ND TAB_CG_4 Depression NotDepressed 0.99 TAB_Dep_ND TAB_CP_5 Emotion PositiveEmotion 0.05 TAB_Emo_PO TAB_CG_5 Emotion PositiveEmotion 0.95 TAB_Emo_PO
TAB_CP_6 Emotion NegativeEmotion 0.99 TAB_Emo_NE TAB_CG_6 Emotion NegativeEmotion 0.01 TAB_Emo_NE TAB_CP_7 AlcoholConsumption AlcoholAbuse 0.99 TAB_AlC_AA TAB_CG_7 AlcoholConsumption AlcoholAbuse 0.01 TAB_AlC_AA TAB_CP_8 AlcoholConsumption NonAlcoholUse 0.01 TAB_AlC_NA TAB_CG_8 AlcoholConsumption NonAlcoholUse 0.99 TAB_AlC_NA TAB_CP_9 TobaccoUse TobaccoAbuse 0.90 TAB_ToU_TA TAB_CG_9 TobaccoUse TobaccoAbuse 0.10 TAB_ToU_TA TAB_CP_10 TobaccoUse TobaccoNonAbuse 0.01 TAB_ToU_TN TAB_CG_10 TobaccoUse TobaccoNonAbuse 0.99 TAB_ToU_TN
Table 6.3: Table showing the instances of ConditionProbability for the example case.
The BN model generated using the ontology can be further customise for the given community.
For instance, the prior and condition probabilities are default values from the ontology, the modeller can manually refine these values for the network to be representative of the target community.
Other nodes that could be generated with the ontology by the modeller, aside from the TAB node which is the hypothesis node, include the “Take Drugs” and “Adherence Utility” nodes. The take drug node is a decision node that is influenced by the mental state of the patient. The adherence utility node predicts the adherence risk of a TB patient in a given community.
The model presented in this section shows how the ontology can be used to generate a BN model for a specific community. A BN model was generated by following the approach and consists of sets of variable and states.
The implementation of the use case example was done using the Java Jena API to automate the construction of the BN model. The queries above, to extract classes and instances from the ontology, were written in SPARQL. The Jena API provided a platform for automating the transformation of the classes into node lists, states and the dependency information required to construct the network structure. The nodes, states and dependency information are then captured back into the TB adherence ontology as a BN model.